Using the growth model N = N_{o}(2^{0.2t}), with t in hours, what is the doubling time for this growth?

A) 2 hours

B) 10 hours

C) 4 hours

D) 5 hours

(D) For N_{o} to double, 2^{0.2t} must equal 2, or 0.2t must equal 1, requiring that t = 5

The graph above depicts current vs voltage for a filament lightbulb. The resistance of the filament:

A) increases with increasing voltage

B) decreases with increasing voltage

C) at first increases at a constant rate with voltage, but then the rate of increase declines.

D) at first decreases at a constant rate with voltage, but then the rate of decrease declines.

(A) According to Ohm's Law, V=IR. Thus, the inverse of the slope of the graph is resistance.

A force varying from 0 to 60 N is applied to a sled, pushing it a distance, x, as shown in the above graph. What is the amount of work done on the sled?

A) 54 J

B) 60 J

C) 72 J

D) 80 J

(A) To find the work done, calculate the area under the curve. This is a triangle plus a rectangle. This is equal to 54 J.

What is the relation between the energy imparted to the ions by the accelerating electric field and their velocity?

A) Bqv = mv^{2}/R

B) qV = mv^{2}/2

C) Bqv = mv^{2}/2

D) qV = mv^{2}/R

(B) The energy given to the ion is the ionic charge times the accelerating voltage. This equals the kinetic energy of the ion.

What is the magnetic force on an ion with velocity 1.0 x 10^{6} m/s in a 0.25 T magnetic field? (The charge is equal to 1.6 x 10^{-19})

A) 4.0 x 10^{-14} N

B) 2.5 x 10^{5} N

C) 1.4 x 10^{-8} N

D) 6.0 x 10^{-7 }N

(A) The force on the orbiting ion is qvB, so that multiplying these three quantities gives the answer.

Which expression is the correct one for the orbit radius in the mass spectrometer?

A) R = mv^{2}/2F

B) R = mv/qB

C) R = mv^{2}/2

D) R = qvB

(B) The answer is calculated from the force balance between magnetic force, qBv, and center directed force, mv^{2}/R.

What is the potential energy at point C?

A) mgh

B) mgh-mgR

C) 2mgR

D) mgR

(C) The total potential energy is relative to level B. The height off of the ground is twice the radius of the circle.

Compared to a light with a wavelength of 400 nm, light of wavelength 600 nm would have:

A lower frequency and a lower energy

The gravitational force on Mars is a little more than 1/3 of that on Earth. If a basketball player were to jump vertically with the same initial velocity on Mars as she does on Earth, then the amount of time taken to reach the maximum height would be:

A) 3 times less

B) 3 times more

C) 9 times less

D) 9 times more

(B). V_{final} = V_{initial} + acceleration*time

If the velocities are the same, then with a 1/3 of the acceleration decreased, we need 3 times as much time to keep the same conditions.

The gravitational force for an object at 9 km from the surface of Earth versus 1 km from the surface of Earth is:

a) about 1/3 in accordance with the inverse square law

b) about 3 times as much with the inverse square law

c) about the same because the distance from the center of the Earth has not changed significantly

d) about the same because gravity does not follow the inverse square law

(C) Gravity follows the inverse square law, but it is from the center of the Earth.

Human perception of loudness is that a 10-fold increase in intensity is perceived as a doubling of loudness. What approximate decrease in distance from the source produces this 10-fold increase in intensity?

A) ~10

B) ~14

C) ~6.4

D) ~3.2

(D) Because of the inverse square relationship, decreasing the distance by a third results in a 10-fold increase in intensity (example: going from 12 to 9 would result in a 10-fold increase).

Protons in an atomic nucleus are bound together by the strong nuclear force. The strong force must:

a) also follow the inverse square law because all fundamental forces of nature do

b) decrease more rapidly with distance than an inverse square in order to overwhelm the electromagnetic repulsion only at very short distances

c) decrease less rapidly with distance than an inverse square in order to overwhelm the combindation of electromagnetic forces and gravitational attraction only at larger distances

d) decrease less rapidly with distance than an inverse square in order to prevent nuclear collapse from the gravitational attraction of neutrons

(b) the strong nuclear force is stronger than the electromagnetic force at short distances which is why protons do not repel each other. At larger distances, protons do repel, so the strong nuclear force must be decreasing more rapidly with distance.

A radio station broadcasts at a frequency of 90.5 MHz. Given that the speed of the radio waves is 3 x 10^{8} m/s, what is the distance between adjacent crests of the radio waves?

Speed = wavelength x frequency.

(300,000,000 m/s) = (wavelength) x (90,500,000 1/s)

3.3 m = wavelength

If a conducting ball hanging by an insulated string is attracted by a positively charged rod, which of the following statements can be true?

I. The conducting ball was originally negatively charged

II. The conducting ball was originally positively charged

III. The conducting ball was originally neutral.

I and III. Unlike charges attract. Electrostatic induction could also cause an attraction by pushing electrons to the opposite side of the hanging sphere and attracting the resulting positive side.

For an automobile tire in contact with the surface of the road, when the car is moving at constant velocity, the force of friction between the tire and the road acts in what direction as the velocity of the car?

Acts in the same direction as the velocity of the car. The tire pushes down on the road and the friction force is in the same direction as the car.

In the diagram, a pulling force of 30 N is applied causing the blocks to accelerate the same rate. Assuming no friction, what is the tension, T, in the cord between the two blocks?

The 30 N force causes the total mass (15 kg) to have an acceleration of 2 m/s^{2}. Now, T = 5 kg * 2 m/s^{2} = 10 N.

When real gas deviations due to intermolecular forces and particle volume are accounted for, the following formula, attributed to the work of JD van der Waal, is the result: (P+a(n/v) ^{2} )*(V-nb)=nRT *a is an empirical value accounting for the strength of intermolecular forces. b is an empirical value accounting for the volume occupied by gas particles.

The a-value for a halocarbon increases proportionally with which characteristic?

Increased polarity means the molecules would experience more intermolecular forces related to dipole-dipole interactions. Thus, the empirical a-value would need to be larger to account for increased deviation from ideal gas behavior.

When real gas deviations due to intermolecular forces and particle volume are accounted for, the following formula, attributed to the work of JD van der Waal, is the result: (P+a(n/v) ^{2} )*(V-nb)=nRT *a is an empirical value accounting for the strength of intermolecular forces. b is an empirical value accounting for the volume occupied by gas particles

Relative to the b-value for 1,1-difluoropropane, what is the b-value for 1,1-dichloropropane?

Relative to the b-value for 1,1-difluoropropane, the b-value for 1,1-dichloropropane is slightly greater, because the particles of 1,1-dichloropropane occupy slightly more real space.

How does the experimentally derived volume for a real gas compare to that of a true ideal gas?

ideal volume is greater than observed volume, because real gas particles occupy space. If real gas particles occupy space, then ideal volume is an over approximation of the real (observed) volume.

What is the power delivered to the anode of the tube when the voltage is 40 MV and the current is 0.005 A?

Power is voltage times current: (40 x 10^{6} V)(0.005 A) = 200 x 10^{3} W

How could the number of electrons in the X-ray tube be increased?

A) Increase the accelerating voltage

B) Change targets

C) Make the filament hotter

D) Increase the cathode to anode distance

(C) To increase the number of X-rays, increase the number of electrons striking the target. This is accomplished by increasing the temperature of the filament supplying those electrons.

Static electricity can cause charge to build up on an object only if:

The object cannot be grounded. Both insulators and conductors can have static electriciy on them, but they cannot be grounded or the charge dissipitates.

Which of the following would most likely have the highest boiling point?

A) NaCl

B) CaO

C) NH_{3}

D) OF_{2}

(B) The highest boiling point would belong to one of the ionic compounds, either NaCl or CaO. But since calcium oxide has +2 and -2 charges, the electrical attraction between ions is greater in calcium oxide.

Using energy analysis find the maximum velocity of a 24 amu atom if the energy of the particle was 10^{-23} cal/atom/ºC and that 4 J = 1 cal and that 1 amu is 2 x 10^{-27} kg.

Energy = 4 x 10^{-23} J

E = mv^{2}/2

(8 x 10^{-23} J) / (24 x 2 x 10^{-27} kg) = v^{2}

v = 40 m/s

Given that atomic spacing in metals is around 2 x 10^{-10} m, what is the approximate side of a cube of one mole of a metal?

If there are 6.0 x 10^{23} atoms in the mole, then a cube would have the cube root of the number of atoms along each edge. Estimate the cube root of 6.0 x 10^{23} atoms to be about 8.0 x 10^{7} atoms. With atomic spacing roughly 2.0 x 10^{-10} m, the cube must have a side of roughly 1.6 cm.

In general, the output of lasers is coherent because:

A) the excited electrons are in a metastable state

B) stimulated emission causes the emitted photons to be in the same phase as the incident photon

C) photons of the same energy are emitted when spontaneous emission occurs

D) the system has a population inversion

(B) Coherent radiation has the same phase.

If the wavelength of a CO_{2} laser is 10.6 um, what is the amount of energy in a photon?

Use speed = wavelength x frequency to find the frequency: 3 x 10^{8} m/s = 10.6 um x frequency = 2.8 x 10^{13} Hz. Then, E = hf, so multiplying that by Planck's constant (6.63 x 10^{-34}) = 1.8 x 10^{-20} J.

Given that the mode spacing is given by c/2L, where c is the speed of light and L is the length of the cavity, at a given pressure, five modes can be simultaneously supported in a cavity that is 2 meters long. What is the total frequency ranges allowed in the cavity?

The mode spacing is c/2L = 75 MHz. With 5 modes, this is 75 MHz x 5 = 300 MHz.

A flash of lightning is seen and the sound is heard about 6 seconds later. The distance to the lightning is approximately:

Speed of sound: 330 m/s.

330 m/s * 6 s = 1980 m = 2 km.

Which of the following will be most effective at increasing the voltage from an electrochemical cell from the reduction of zinc ions to metallic zinc?

A) increasing the surface area of the anode

B) increasing the molar concentration of the zinc ion solution

C) increasing the volume of the solution of zinc ions

D) increasing the surface area of both the anode and the cathode

(B) surface area of either the anode or cathode has no effect on cell voltage. Cell voltage is affected by ion concentration and the identity of the anode and cathode.

When transmitting electrical power over long distances, it is best to use:

A) high current and lower voltage

B) high voltage and lower current

C) high voltage and high current

D) power transmission is independent of both voltage and current

B. P = I^{2}R is relevant for power transmission. High current results in more power loss than high voltage.

If you were to remove the built in dielectric (with dielectric constant 6) from one of the 12F capacitors, which would occur?

A. The capacitance would decrease to 0F, since capacitors can’t function without a dielectric

B. The capacitance would remain the same, 12F

C. The capacitance would decrease to 2F

D. The capacitance would increase to 24F

(C) Since adding a dielectric always increases the capacitance, and we removed a dielectric from a capacitor, the capacitance must go down.

Of the available capacitors, which could you connect in series to replace one of the burned out capacitors to achieve an equivalent capacitance of 12 F?

A. 1F, 2F, 4F, 6F

B. 20F, 30F

C. 4F, 6F, 20F

D. 2F, 4F, 6F

(B) Since the inverse of 1/20F + 1/30F gives 12F, they could be connected in series to form a capacitor equivalent to the 12F capacitor.

Of the available capacitors, which could you connect in parallel to replace one of the burned out capacitors to achieve an equivalent capacitance of 12 F?

A. 1F, 2F, 4F, 6F

B. 20F, 30F

C. 4F, 6F, 20F

D. 2F, 4F, 6F

(D) Since 2F + 4F + 6F adds up to 12F, they could be connected in parallel to form a capacitor equivalent to the 12F capacitor

In the properly functioning monitoring equipment, what is the charge stored by the 12F capacitor with a 3 V voltage?

36 C. Plug in the capacitance of 12F for C, and the voltage of 3V for V. Then solve for Q = CV.

In the properly functioning monitoring equipment, what is the energy stored by the 12F capacitor with a 3 V voltage?

54 J. Plug in the capacitance of 12F for C, and the voltage of 3V for V. Then solve for E. The energy stored in a capacitor is E=1/2 CV^{2}

The hospital you work for uses a defibrillator that has a single capacitor with a capacitance of 5 x 10^{−6} F. When it is about to be used, the defibrillator is charged to a voltage of 4000 V. How much charge is stored on the defibrillator ‘s capacitor when it has been fully charged?

0.02 C. The definition of capacitance is C = Q/V. Plug in the capacitance of 5 x 10^{−6} F for C, and the voltage of 4000V for V. Then solve for Q.

Increasing the separation between the capacitor plates while hooked up to the voltage source will decrease the charge stored for the following reason:

A. it decreases the capacitance of the capacitor.

B. it increases the voltage across the capacitor plates.

C. it increases the capacitance of the capacitor.

D. it decreases the voltage across the capacitor plates.

(A) The separation between plates is the variable d, and in the formula C=eoA/d, as d increases the capacitance decreases.

Total internal reflection can occur inside a glass fiber surrounded by another material because:

a) the index of refraction inside the fiber is lower than the surrounding material

b) the index of refraction inside the fiber is higher than the surrounding material

c) the frequency of light is lower than the glass fiber

d) the frequency of light is higher than the glass fiber

(A) This is a requirement of total internal reflection.

A short sound blast is emitted somewhere between two reflecting cliffs. Two echoes are heard, one at 0.6 seconds and one at 0.9 seconds. Given a speed of sound of 330 m/s, how far apart are the reflecting cliffs?

x = 330 m/s * (0.6/2) seconds = 99 m

y = 330 m/s * (0.9/2) seconds = 148.5 m

x + y = 247.5 = 250 m.

Light travels into the eye through a converging lens and is focused on the retina. The image on the retina is:

a) virtual, not inverted, and the same size.

b) real, not inverted, and diminished

c) real, inverted, and diminished

d) virtual, inverted, and the same size.

(C) A real image can be focused on a screen. Converging lenses invert images. The images must be diminished.

Why is it important to place the light bulb at the focal point?

A) So that the reflected light from the mirror gets focused into a single point on the principal axis

B) So that the curved parabolic mirror does not allow any light to reach point A

C) So that the reflected light from the mirror will be composed of light rays traveling parallel to the principal axis

D) So that the curved parabolic mirror reflects all the light and doesn’t absorb any

(C) So that the reflected light from the mirror will be composed of light rays traveling parallel to the principal axis. The light bulb should be at the focal point so that light rays emanating from it will be reflected parallel to the principal axis similar to a car headlight

Which of the following candle locations would create the smallest possible real image?

Being further from the mirror will create a smaller image, so point 1 will cerate the smallest real image

If you moved the candle location from point 8 to point 6 what would be seen to happen to the size of the image?

The image would be seen to get consistently larger. Getting closer and closer to a convex mirror will cause the image to consistently get larger

Which of the following candle locations would create the largest virtual image?

Since point 5 is a virtual image created by a concave mirror it will be larger than the images created by the convex side of the mirror

A man entered a cave and walked 100 m north. He then made a sharp turn 150 degrees to the west and walked 87 m straight ahead. How far is the man from where he entered the cave?

When the man turns, he is making a 30 degree angle in the triangle. So the distance back to the entrance is half the hypotenuse (100sin30).

The earth moves around the sun at approximately 30 m/s. Is the earth accelerating?

Acceleration is the rate of change of velocity. Since velocity is a vector, it specifies direction. The direction of the earth's motion is constantly changing. So yes, the earth is accelerating.

All of the following describe the magnitude and direction of a vector EXCEPT:

a) 10 m/s West

b) 10 m/s in a circle

c) 20 m to the left

d) 20 m straight up

B. The direction for a vector must specify a straight line at a specific point.

A car accelerates at a constant rate from 0 to 25 m/s over a distance of 25 m. Approximately, how long does it take the car to reach the velocity of 25 m/s?

The average velocity is 12.5 m/s. To reach 25 m/s, it will take two seconds.

A driver moving at a constant speed of 20 m/s sees an accident up ahead and hits the brakes. If the car decelerates at a constant rate of ~5 m/s^{2}, how far does the car go beore it comes to a stop?

Velocity is reduced by 5 m/s each second. Starting from 2 m/s requires 4 seconds. Average velocity between 20 and 0 is 10 m/s. 10 m/s for 4 seconds is 40 meters.

If an apple that is dropped from an altitude of 100 m reaches an altitude of 80 m after falling for t = 2 seconds, what altitude will it be at in t = 4 seconds?

The distance traveled by the apple is 80 m so it reaches 20 m in altitude. x = (1/2)at^{2} so x = (1/2)(10)(16) and so x = 80 m.

If an antelope is running at a speed of 10 m/s, and can maintain that horizontal velocity when it jumps, how high must it jump in order to clear a horizontal distance of 20 m?

To clear a horizontal distance of 20 m, it must be in the air for 2 seconds. The upward trip equals the downward trip, so the upward trip is equal to 1 second. At the end of 1 second, the body is traveling at 10 m/s. The average velocity is thus 5 m/s and so 5 m.

A projectile is launched at an angle of 30 degrees to the horizontal and with a velocity of 100 m/s. How high will the projectile be at its maximum height?

125 m. The peak height can be found by this equation: v_{o}sinθ = sqrt(2gh)

100sin(30) = sqrt(2*10)h

50^{2} = 20h

2500/20 = 125 m.

A hiker throws a rock horizontally off a cliff that is 40 m above the water below. If the speed of the rock is 30 m/s, how long does it take for the rock to hit the water, ignoring air resistance?

The horizontal speed has no effect on the length of time that a projectile is in the air. Because the initial vertical speed is zero, you can use the equation below:

x = (1/2)gt^{2}

40 m = (1/2)(10 m/s^{2})(t^{2})

t^{2} = 8 = 2.8 seconds

A bottle rocket is launched into the air. The black powder, which propels it, burns leaving an exhaust trail mainly consisting of CO2 gas. If the force propelling the rocket is constant, the rate of change in its velocity, ignoring air resistance:

Since the mass of the rocket is decreasing, and the force remains constant, the rate of change in velocity must be increasing.

A 10 kg mass is in free fall with no air resistance. In order to slow the mass at a rate equal to the magnitude of g, and upward force must be applied with magnitude: _ N?

The downward force is mg = 100 N. The first 100 N upward counters this to give a net force of zero and thus a constant velocity. We want a net force of mg = 100 N upwards. This requires adding 100 more N for a total of 200 N.

A system has three spheres of equal mass *m* on a number line from 1 to 9. M_{1} is on 2, M_{2} is on 3, and M_{3} is on 7. The center of mass of the system is located at what point?

Because the masses are all on a line, you can just average the distance of the masses from the origin to get the cenral point. The average distance is: 2 + 3 + 7 = 12 / 3 = 4.

An automobile with a mass of 3000 kg is traveling down a straight flat road at a constant speed of 20 m/s. If the coefficient of friction between the tires and the road is 0.5, the net force acting on the autmobile is:

If the car is moving in a straight line at a constant speed, then it is not accelerating. From Newton's second law, if there is no acceleration, then there is no net force

If M is the mass of the earth, m is the mass of the moon, and d is the distance between their centers, what gives the instantaneous velocity of the moon as it orbits the earth with a univeral gravitational constant given by G?

Set the gravitational force between the earth and the moon equal to the centripetal force:

F = GMm/r^{2} = mv^{2}/r

This gives: sqrt(GM/d).

The owner of a warehouse asks an engineer to design a ramp which will reduce the force necessary to lift boxes to the top of a 1/2 m step. If there is only room enough for a 4 m ramp, what is the maximum factor by which the lifting force could be reduced?

The work done will remain the same (W = Fd). The distance increased from 1/2 to 4. This is an increase by a factor of 8. Since work remains constant, force must decrease by a factor of 8.

As a ball rolls down a slope, what happens to the magnitude of velocity and acceleration?

The acceleration is gsinθ. Since θ is constantly decreasing, and with it, the sine of it too. The acceleration is decreasing. Since there is some acceleration throughout the drop, the velocity is increasing.

A box starts from rest and slides 40 m down a frictionless inclined plane. The total vertical displacement of the box is 20 m. How long does it take for the block to reach the end of the plane?

The force down on an incline is mgsinθ. The acceleraton down an incline is gsinθ. The sine is equal to (20/40) making our acceleration: 1/2g or 5 m/s^{2}. Using x = 1/2at^{2}, where x is the length of the incline, we find: 40 = 2.5t^{2} where t is 4 seconds.

A box rests on an incline. Describe the forces on the box as the angle of the incline is increased (namely the parallel and perpendicular force).

The force parallel to the ramp is the same as the net force: mgsinθ. As θ increases, sinθ increases and so does the net force. The force perpendicular to the ramp is the same as the normal force, mgcosθ. As θ increases, cosθ decreases and so does the normal force.

If the rear wheels of a truck drive the truck forward, then the frictional force on the rear tires due to the road is:

static or kinetic?

forward direction or backward direction?

Static and forward.

If we look at the point on the tire that makes contact with the road, that point does not move relative to the road or else the tires would spin in place. Since there is no relative movement, the friction must be static. The force of friction is in the direction opposite to the way that the tires are trying to slide against the road, which is the force that accelerates the vehicle. So the only way that the truck can move forward is if the force on the tires is in this direction.

If a rope capable of withstanding 900 N of tension is attached to a wall as shown, what is the maximum force that can be applied in pulling the rope before the rope will break?

Tension in a static system is defined by the force in one direction. The rope will also experience a force from the right, but that does not double the tension. That force necessary to make the tension equal to 900 N.

In many harbors, old autmobile tires are hung along the sides of wooden docks to cushion them from the impact of docking boats. The tires deform in accordance with Hooke's Law. As a boat is brought to a stop by gently colliding with the tires, the rate of deceleration of the boat:

The rate of deceleration increases until the boat stops. The force changes with the displacement of the tires. The greater the displacement, the greater the force, the greater the magnitude of acceleration. F = kx = ma.

On a particular stretch of wet pavement, the kinetic coefficient of friction μ for a particular car with mass *m* is 0.08. If the car is moving at a velocity *v *and suddenly locks its wheels and slides to a stop. What expression gives the distance that it will slide?

Since the frictional force is constant, this is a linear motion problem with constant acceleration. The normal force is mg, so the frictional force is mgμ. The acceleration is just gμ. Using v^{2} = v_{o}^{2} + 2ax, and plugging this acceleration in, we get the answer: v^{2} / 2gμ.

A diagram shows two different masses hung from identical Hooke's law springs. The Hooke's law constant *k* from the springs is equal to:

The difference in mass between the two situations is 0.5 kg. The difference in force is 5 N. The difference in displacement is 1 cm. k = F / x = 5 N/cm.

In a very tall building, an elevator with weight *W* is moving quickly upward at a constant speed. The entire weight of the elevator is supported by a single cable. The tension of the cable is:

a) greater than W

b) less than W

c) equal to W

d) dependent on the speed of the elevator

C.

If the elevator is moving at constant speed, then there is no acceleration and no net force, so the tension must exactly balance the weight of the elevator.

A circus tightrope walker wishes to make his rope as straight as possible when he walks across it. If the tightrope walker has a mass of 75 kg, and the rope is 150 m long, how much tension must be in the rope in order to make it perfectly straight?

When the tightrope walker stands in the middle of the rope, he is in static equilibrium. The vertical and horizontal net force must equal zerio. The force downward is the weight of the tightrope walker (750 N). The force upward is equal to 750 N. The upward force must come from the vertical component of the tension of the rope. If the rope if perfectly straight, there is no vertical component, however. So no amount of tension in the rope could make it perfectly straight.

A rescue helicopter lifts a 50kg rock climber by a rope from a cliff face. The rock climber is accelerated vertically at 5 m/s^{2}. What is the tension in the rope?

The tension in the rope with no acceleration is 500 N. If we want to pull the climber upward, we must increase the tension by ma, which is 250 N. The tension of the rope will be 750 N.

A pulley is old and rusted. When the 50 kg mass is allowed to drop, the friction in the pulley creates a constant 200 N force upward. What is the tension of the rope?

The force upwards is defined to be 200 N. The force on either end of a massless rope must be the same. The tension of the rope should be 200 N.

A telephone pole stands immobile. Line A is 4 m off the ground and line B is 3 m off the ground. The tensions in line A and line B are 200 N and 400 N, respectively. What is the net torque of the pole?

The pole is not rotating, so the net torque must be zero.

A sign hands by a rope attached at 30º to the middle of its upper edge. It rests against a frictionless wall. If the weight of the sign were double, what would happen to the tension in the string?

The sign is in static equilibrium. Since the wall is frictionless, there is no torque in this problem. The vertical component of the force must be equal to the weight of the sign. The vertical component is equal to the tension times sin(30º). mg = Tsin30º, so by doubling the mg, we double the tension.

If all the forces in the diagram have equal magnitude, which one creates the most torque?

The longest lever arm is on A. The entire wrench is the lever arm on A.

A one meter board with uniform density hangs in static equilibrium from a rope with tension T. A weight hands from the left end of the board. What is the mass of the board?

The point of rotation to be the point on the board where the string attaches to the board, the weight of the board acts at the center of gravity which is the center of the board. The counter-clockwise torque is 3 kg x 0.2 m. The clockwise torque is the weight of the board times 0.3 m. The mass becomes 2 kg.

A carpenter who is having a difficult time loosening a screw puts away his screwdriver and chooses another with a handle with a larger diameter. He does this because:

Increasing the diameter of the screwdriver handle increases the lever arm for the force applied by his grip. Increased lever arm gives him more torque to turn the screw.

A meteor with a mass of 1 kg moving at 20 km/s collides with Jupiter's atmosphere. The meteor penetrates 100 km into the atmosphere and disintegrates. What is the average force on the meteor once it enters Jupiter's atmosphere, ignoring gravity.

The frictional force applied by Jupiter's atmosphere times the distance along which it is applied equals the change in mechanical energy of the meteor. If we ignore the gravitational force of Jupiter, the change in the mechanical energy is a loss of all kinetic energy. So (1/2)mv^{2} = Fd to solve for force.

20000 = F*100

F = 2000 N

Objects A and B are placed on a spring. Object A has twice as much mass as object B. If the spring is depressed and released, propelling the objects into the air, object A will rise how high in comparison to object B?

When do the masses become projectiles? They must become projectiles the moment the spring stops pushing. From F = ma, this is when the spring stops accelerating. That means the masses become projectiles at the same moment and with the same velocity. Mass is irrelevant to projectile motion. They rise to the same height.

Ball A is moving at 12 m/s and collides elastically with ball B. If both balls have the same mass, what is the final velocity of ball A?

The initial and final momentums must be equal. The initial vertical momentum is mvcos60. Since ball B has no vertical momentum, all the vertical momentum remains in ball A. Ball A has no vertical momentum after the collision, so all of its momentum is represented by mvcos60.

The chemical potential energy in gasoline is converted to kinetic energy in cars. If a car accelerates from zero to 60 km/h, compared to the energy necessary to increase the velocity of the car from zero to 30 km/h, the energy necessary to increase the velocity of the car from 30 to 60 km/h is: ?

All of the energy is kinetic energy. If we double the velocity, we increase energy by four times. The question asks for the difference in the energies: 4 - 1 - 0 = 3.

A 3 kg cat sitting on a 1.5 piece of cardboard on a frozen on a frozen lake wants to jump to shore without touching the ice. If there is no friction between the cardboard and ice, when the cat jumps, the cardboard will move in a opposition direction with a velocity:

a) half as great as the cat's velocity

b) equal to the cat's velocity

c) twice as great as the cat's velocity

d) four times as great as the cat's velocity

(C) The initial momentum of the cat-cardboard system is zero, so the final momentum must be zero. Since the cat has twice the mass as the cardboard, the cardboard will have twice the velocity.

A block of mass m_{1} slides across a frictionless surface with speed v_{1} and collides with a stationary block of ice m_{2}. The blocks stick together after the collision and move away with a speed of v_{2}. Which of the following statement is (are) true about the blocks?

I. m_{1}v_{1} = (m_{1} + m_{2})v_{2}

II. (1/2)m_{1}v^{2}_{1} = (1/2)(m_{1} + m_{2})v^{2}_{2}

III. v_{1} = v_{2}

Choice I represents conservation of momentum, which is always true. Choice II is conservation of kinetic energy. In an inelastic collision, kinetic energy is not conseerved. As for Choice II, if the masses are different before and after the collision and momentum is conserved, then the velocities before and after must be different.

Two 1 kg cars with spring bumpers undergo a collision on a frictionless track as shown in the before and after pictures. The total momentum of the system is equal to:

__ kg-m/s before the collision

__ kg-m/s after the collision

Momentum is a vector quantitiy, so that two vectors with the same magnitude and opposite directions will add up to zero both before and after the collision.

A trapeze artist who accidentally falls builds up a great deal of momentum before he is brought safely up to rest by a safety net. The safety net serves to:

From the Ft = mv impulse equation, the trapeze artist is brought gradually to a stop in the safety net, so the change in momentum takes place over a longer time than if the person hit the floor. The increase in time means that less force is required to acheive the same change in momentum, which makes the fall less damaging

How much power is required to lift a 30 kg object 2 meters in 60 seconds using this pulley system?

The pulley does not change the work, so it does not change the rate at which work is done. The power is work/time or mgh/t.

An eccentric pulley can be used on a compbound bow to increase the velocity of an arrow. The pulleys pivot around the dots. The tension in point A compared to point B is:

The eccentric pulley does not work on the principles of a normal pulley but, instead, works on the same principle as a lever. The lever arm for the string at point A is position 1 is greater than that for point B in position one. In position 2, the reverse is true. The lever is stationary, so the sum of the torques must equal zero or the clockwise torque equals the counter-clockwise torque. When the lever arm is greater, the tension force must be less.

A crate is to be lifted to a height of 3 meters with the assistance of an inclined plane. If the inclined plane is a non-ideal machine, which of the following statements is most likely true?

A) the non-ideal inclined plane increases the force required and decreases the work

B) the non-ideal inclined plane decreases the force required and increases the work

C) the non-ideal inclined plane increases the force required and increases the work

D) the non-ideal inclined plane decreases the force required and decreases the work

Machines are used because they decrease the force required to perform a task. An ideal requires the same work as would be done without the machine, but a non-ideal machine requires more work because frictional forces must be overcome.

A girl riding her bicycle up a steep hill decides to save energy by zigzagging rather than riding straight up. Ignoring friction, her strategy will require (same/less) energy and (less/same/more) force on the pedals.

By zigzagging, she is basically using a ramp. Her path is not as sleep, but it is longer. The work remains the same, but the force is lessened.

The pulley system operates as a modified lever. Pulley A and Pulley B turn together so when a person pulls on rope A, the mass attached to rope B will be lifted. Which of the following changes to the system will reduce the force needed to lift the mass?

A) increase the length of rope A

B) increase the length of rope B

C) increase the diameter of pulley A

D) increase the diameter of pulley B

For a lever, F_{i}L_{i} = F_{o}L_{o}. The radii of the two pulleys act as the lever arms for the system, so increasing the diameter of pulley A will decrease the force required to pull rope A. Changing the lengths of the rope will have no effect on the machine.

A wheelchair access ramp is to be designed so that 1000 N can be lifted to a height of 1 meter through the application of 50 N of force. The length of the ramp must be at least:

For an inclined plane, Fd = mgh so (50 N)d = (1000 N)(1 m) and d = 20 m.

The half-life of substance X is 45 years and it decomposes to substance Y. A sample from a meteorite was taken which contains 1.5% of X and 13.5% of Y by mass. If substance Y is not normally found on a meteorite, what is the approximate age of the meteorite?

Since Y is not normally found in the meteorite, we assume that all the Y came from the decomposition of X. The total amount of X originally, then, must have been 15%. The amount left is 10% of 15% or 1.5%. There have been about 3 half lives, so about 140.

When ^{224}Ra undergoes alpha decay an alpha particle is emitted at 1.0 x 10^{7} m/s. What is the velocity of the other particle?

This is a reverse collision. The initial momentum is zero; so, the final momentum must be zero. The momentum of the alpha particle is approximately mv = 4 x 10^{7}. The momentum of the other particle, Rn-220, must be equal in magnitude and opposite in direction. Thus, the velocity of Rn equals (4E7)/220. This quickly rounds to about 2000.

Two identical discs sit at the bottom of a 3 m pool of water whose surface is exposed to atmospheric pressure. The first dic acts as a plug to seal the drain. The second disc covers a container containing nearly a perfect vacuum. If each disc has an area of 1m2, what is the approximately difference in the force necessary to open the containers?

The only difference between the two discs is what they are covering. Ignoring everything else, the first disc has atmospheric pressure pushing upward, the second disc does not. This is the difference between the forces necessary to lift them. So it takes 101,300 N (which is equal to 1 atm = 101,300 Pa).

The brick displaces a volume of water equal to its own weight. Since its density is 1400 kg/m^{3}, its density is 1.4 times that of water and it must displace a volume of water 1.4 times its own volume. Since this is only 1/2 the volume of the sytrofoam, the full volume of the styrofoam must be 2.8 times larger than the volume of the brick

A child's bathtub toy has a density of 0.45 g/cm^{3}. What fraction of the toy floats above the water?

p_{water}V_{submerged fraction}g = p_{toy}V_{toy}g

V_{submerged fraction}/V_{toy} = p_{toy}/p_{water}

If the specific gravity was 0.999, the toy would be the same weight of the water and only 0.1% would be floating. The specific gravity must be how much is under the watr. 45% must be under water and so 55% must be above.

The pressure at the bottom of a cylindrical tube filled with water was measured to be 5000 Pa. If the water in the tube were replaced with ethyl alcohol, what would be the new pressure at the bottom of the tube given that the density of ethyl alcohol is 0.8 g/cm^{3}

The formula for fluid pressure is P = pgh. If the density is change, the pressure will change by the same ratio. Since the specific gravity of ethyl alcohol is 0.8, the pressure will decrease by a factor of 0.8. It will become 4000 Pa.

Three containers are filled with water to a depth of 1 meter. At the bottom of which container is the pressure the greatest?

Pressure only depends on depth and density ,not the shape of the container. They are all the same.

If the container pictured below

The fluid at A, C, and D is at atmospheric pressure. The fluid at B is at atmospheric pressure plus pgh.

Water in moist soil rises through capillary action. The intermolecular forces between water molecules are:

(weaker/stronger/equal) to the intermolecular forces between water and soil molecules.

Since the molecules are more attracted to the soil than to the other water molecules, the shape of the meniscus is concave. The surface tension creates a net force which pulls the water upward.

(Adhesion > Cohesion = concave)

(Cohesion > Adhesion = convex)

A spigot is to be placed on a water tank

The equation for velocity of fluid from a spigot is derived from Bernoulli's equation. The relationship is 2gh = v^{2} and h is proportional to v^{2}, which is reflected in the graph in D.

Two drops of equal volume of different substances were placed on the same flat surface. A side view of drop A and drop B is shown below:

Compared to drop B, drop A has:

(stronger/weaker/equal) intermolecular forces and (greater/lesser/equal) surface tension.

The drop with stronger intermolecular forces will have greater surface tension, which will cause it to bead up more.

A spigot was opened at the bottom of a barrel full of water and the water was allowed to run through the spigot until the barrel was empty. Was the speed of water flowing through the spigot as the barrel emptied always decreasing, increasing, constant, or was it decreasing then increasing?

The equation governing the speed is v = sqrt(2gh). As h decreases, so does v.

The pressure at the bottom of the column is given by pgh. Setting this equal to maximum pressure, we get 12 x 10^{5} = 400 x 10 x h.

(D)

The Young's modulus for any susbtance is a constant.

(A)

Using the formula for Young's modulus:

strain = (5.4 x 10^{3} / 6 x 10^{-4}) / 9 x 10^{9}.

Strain equals 10^{-3} or 0.1%.

(B)

The weight per unit area cannot exceed one fifth of the yield strength. Convert 1.5 x 10^{8} kg to 1.5 x 10^{9} N. Divide the yield strength by 5, and set it equal to weight per unit area:

(0.5 x 108 N/m^{2}) = (1.5 x 10^{9} N) / A

A = 30 m^{2}.

(D)

The strain must remain the same. The deformity of the shoe will double with the height because F/A does not change. This keeps the strain (Δx/h_{o}) the same.

(B)

Copper has the largest value for Young's modulus, so it will undergo the least strain for a given stress.

(A)

Young's modulus for lead is one-fourth the modulus for glass. So the fractional change in lead will be four times the change for glass.

(D)

The bulk modulus describes a substance's resistance to pressure applied from all sides, which is the same as the stress encountered under water.

(A)

One end of a string is shaken each second, sending a wave with an amplitude of 10 cm toward the other end. The string is 5 meters long, and the wavelength of each wave is 50 cm. How many waves reach the other end of the string in each 10 second interval?

The frequency of the waves being sent is equal to the frequency of the waves being received. Everything else is irrelevant. Every one second, a wave is sent. In 10 seconds, 10 waves are sent.

The sound level of the chirping made by a bird at a distance of 5 meters is measured at 30 dB. When the same bird is 50 meters away the sound level is measured at 10 dB. How many times greater is the amplitude of the sound wave at 5 meters away compared to 50 meters away?

B = 10log(I/I_{o}). A change in 20 dB means that I is 100 times greater at 5 meters. The intensity of the sound wave is proportional to square amplitude, so to change the intensity by a factor of 100 requires a change in amplitude by a factor of only 10.

Sound waves are an example of:

A) longitudinal waves because the medium moves perpendicularly to the propagation of the wave

B) longitudinal waves because the medium moves parallel to the propagation of the wave

C) transverse waves because the medium moves perpendicularly to the propagation of the wave

D) transverse waves because the medium moves parallel to the propagation of the wave.

(B). Sound waves are longitudinal waves because the medium waves move parallel to the propagation of the wave.

If the intensity of a sound is doubled, the decibel level it will increase by is:

A 10 dB increase means that the intensity is increasing by a factor of 10, so if the intensity is only doubled, there will be less than a 10 dB increase (actually, it's about a 3 dB increase).

A vibrating string has consecutive harmonic wavelengths of 2.0 m and 4.0 m. What is the length of the string?

The first and second harmonies are the only consecutive harmonies that have a ratio of 1 to 2. The second harmonic is the length of the string. L = nλ/2. To find n:

n(4.0)/2 = ((n+1)*2.0)/2

n = 1. To find L:

L = (1)(4.0)/2) = 2.0

Two violinists are playing together, slightly out of tune. One violoinist produces a frequency of 883 Hz and the other produces a frequency of 879 Hz. Beats would be heard with a frequency of:

When two slightly different frequencies are sounded at the same time, they wil create beats with a frequency equal to the difference: 4 Hz.

If a guitar string is 0.5 m long, what is the wavelength of its third harmonic?

L = 3λ/2 because L = nλ/2 so 0.5 = 3λ / 2

λ = 0.33 m

In order for two sound waves to have an audible beat frequency, the two waves must be:

A) in phase

B) out of phase

C) close in frequency

D) of the same wavelength

(C). An audible beat frequency requires that the two sound waves have close frequencies.

All of the following statements are true about a resonating string EXCEPT:

A) A resonating string forms a standing wave

B) The wavelength of a resonating string must coincide with one of its harmonics

C) Some spots on a resonating string will not move at all

D) If left alone, the amplitude of a wave on a resonating string will grow infinitely large

(D). When energy is added to a structure at one of its natural frequencies, the amplitude reaches some maximum value. At this point, damping effects create energy loss produces at the same rate at which energy is absorbed, and the total energy of the structure is constant in this standing wave.

How many wavelengths are produced between the dotted lines?

The pattern repeats twice between the dotted lines.

If the amplitude of a sine wave is doubled, the intensity:

The square of the the amplitude is proportional to its intensity. So it will increase by a factor of 4.

Which of the following factors by itself will increase the frequency at which an observer hears a sound emanating from a source?

A) A wind blows from the source to the observer

B) The source and the observer move away from each other at the same speed

C) The source and the observer move in the same direction at the same speed

D) The source moves away from the observer more slowly than the observer moves toward the source

(D). For a frequency to increase, the relative velocity must move the source and the observer toward each other. The relative velocity does not dictate at what frequency the sound is heard. A wind can also change the frequency by changing the velocity of the sound, but even with the wind, the source and the observer must have a relative velocity.

A clock uses the motion of a pendulum to keep time. If the clock were placed at a height several thousand kilometers above the earth's surface, it would run (faster/slower/at the same speed) that it would at the surface of the earth.

(B). Frequency of a pendulum is related to the square root of g/L. High above the earth, the acceleration due to gravity will decrease. If g decrases the frequency will decrease. If the frequency of the time keeper decreases, the clock will slow down.

Bremsstrahlung is produced when electrons are accelerated during collisions with ions. Bremsstrahlung will not be produced by collisions between electrons and:

A) He

B) He^{2+}

C) Li^{1=}

D) protons

(A) All of the choices are ions except for He, which is a neutral atoms.

A rectangular sheet of material has a width of 3 m and a length of 4 m. Forces with magnitudes of 3 N and 4 N, respectively, are applied parallel to two edges of the sheet, as shown in the figure below:

A third force is applied to the center of the sheet, along a line in the plane of the sheet, at an angle θ = arctan 0.75 with respect to the horizontal direction. The sheet will be in translational equilibrium when F has what value?

A) 3 N

B) 4 N

C) 5 N

D) 7 N

A body is in transitional equilibrium when the components of all external forces cancel. F^{2} = 4^{2} + 3^{2} = 5 N. Since the F vector points in the proper direction (tan θ = ¾), answer choice C is the best answer.

The period of the waveform in Figure 1c is the:

A) same as the period of the first harmonic

B) same as the period of the second harmonic

C) same as the period of the third harmonic

D) sum of the periods of the first, second, and third harmonics.

(A) same as the period of the first harmonic.

A receiver is in a jet flying alongside another jet that is emitting 2.0 x 10^{6 }Hz radio waves. If the jets fly at 268 m/s, what is the change in frequency detected at the receiver?

A) 0 Hz

B) 0.90 Hz

C) 1.79 Hz

D) 3.58 Hz

(A) There is no relative motion between the jets, so there is no frequency shift.

An object with 15 grams mass is immersed in benzene and suffers an apparent loss of mass of 5 grams. What is the approximate specific gravity of the object? (Specific gravity of benzene is 0.7

A) 1.4

B) 1.8

C) 2.1

D) 3.0

(C) The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. There were 5 g of liquid displaced, so the ratio of object mass to fluid mass is 15/5 = 3. The specific gravity of the object is three times the specific gravity of benzene because the volumes of the object and displaced liquid are equal.

The fundamental, resonant wavelength of a pipe open at both ends that is 1 m long and 0.1 m in diameter is:

A) 0.1 m

B) 0.2 m

C) 1.0 m

D) 2.0 m

(D) Pipes and tubes have their resonant wavelengths when standing waves develop. An open pipe has its fundamental, resonant wavelength at twice the length of the pipe. The resonant wavelength is independent of the diameter of the pipe.

Mechanical waves in a medium such as water function to transport:

A) matter only

B) energy only

C) both matter and energy

D) neither matter nor energy

(B) Mechanical waves, such as sound waves and water waves, are a local oscillation of material. Only the energy propagates; the oscillation material does not move far from its initial equilibrium position.

In radioactive dating, the age of a rock can be determined by measuring the amount of radioactive potassium (^{40}K, half life = 2.4 x 10^{8} years) in the rock and the amount of its decay product, argon gas (^{40}Ar) in the sample. What kind of object is emitted in the decay of ^{40}K?

A) a gamma ray

B) an alpha particle

C) an electron

D) a positron

(D) The ^{40}K to ^{40}Ar radioactive decay does not change the atomic mass (40) of the nucleus, but changes its atomic number (19 to 18). These conditions point to a positron as the emitted object in the radioactive decay.

Suppose a certain far-sighed person can see objects clearly no closer than 300 cm away. What is the minimum distance from a plane mirror such a person must be to see his reflection clearly?

A) 75 cm

B) 150 cm

C) 300 cm

D) 600 cm

(B) A plane mirror produces an image behind its plane at a distance equal to the object distance in front of the plane. If the object plus image distances must be at least 300 cm, then the plane of the mirror must be half this distance, 150 cm.

In the circuit shown below, the current in the 2-ohm resistance is 2 A. What is the current in the 3-ohm resistance?

A) 2 A

B) 3 A

C) 4 A

D) 6 A

(B) Currents in parallel resistors are inversely proportional to their individual resistances since they have the same voltage drop across them. Since the 2 ohm resistor has 2 A, the parallel 4 ohm resistor has 1 A through it. The currents add to 3 A, as they combine to pass through the 3 ohm resistor.

As the pressure on a gas increases without affecting its temperature, how is the ideality of the gas affected?

**A** The gas becomes more ideal due to the increase in density of the gas.

**B** The gas becomes more ideal due to the increase in pressure.

**C** The gas becomes less ideal due to the increase in density of the gas.

**D** The gas becomes less ideal due to the increase in pressure.

Ideal gases assume negligible volume of the gas molecules, and therefore account for all the space between the molecules. As the density of a gas increases, the total percentage of the volume taken up by molecules increases compared to the empty space, so the ideality of the gas would therefore decrease due to the increase in the density of the gas (C)

A 5m massless string is set up with a mass of 5 kg on the end. The mass is swung like a pendulum and at its maximum amplitude reaches 90° to either side of its resting position. What is the maximum tension generated on the string during its swing?

A) 50 N

B) 100 N

C) 150 N

D) 500 N

(C) To calculate the answer we must realize that there are two forces acting on the string at its highest tension: the force of gravity and the centripetal force due to its circular motion. Its maximum tension will be reached at its resting position (think about being in a swing - the greatest force you feel is at the bottom of the arc). The force of gravity will simply be mg so 50 N. Add to this the force due to the circular motion: F = mv^{2}/r. We have all the variables except for velocity. Since we know the mass reaches 90° during its swing, it reaches a maximum height of 5 m above its resting position (see the diagram below). This means its potential energy at either amplitude is mgh = 5 x 10 x 5 = 250 J. This gets converted to kinetic energy at the bottom of the swing, so 250 = (1/2)mv^{2}. Solving for v, we get 10 m/s. Plug this back into the equation F = mv^{2}/r and we get F = (5)(100)/5 = 100 N. Therefore the total force at the bottom of the swing (and therefore the maximum force on the mass) is 50 + 100 = 150 N.

An upright wave is traveling along a thin rope. Upon merging onto a thicker portion of the same rope, which of the following would happen?

A) The wave is reflected upright on the thin portion of the rope.

B) The wave is transmitted upside-down on the thicker portion of the rope.

C) The wave is both reflected (on the thin portion) and transmitted (on the thicker portion) upright on the rope.

D) The wave is reflected (on the thin portion) upside-down and transmitted upright (on the thicker portion) on the rope.

(D) When a wave meets a denser medium the wave is reflected upside-down. The wave is also transmitted in the denser medium but maintains its position. The wavelength of the wave is reduced in the denser medium, but frequency is unchanged.

If ocean waves strike the shore every 3.0 s, and the horizontal distance between adjacent crests and troughs is 1.0 m, what is the average speed of the waves?

A) 0.33 m/s

B) 0.67 m/s

C) 1.5 m/s

D) 3.0 m/s

(B) The speed of a wave is given by the product of its frequency times its wavelength: v = fλ. The frequency is 1/3 s and the wavelength is 2 x 1 m because the crest and an adjacent trough are a half wavelength apart. Therefore the wave speed is 2 m / 3 s = 0.67 m/s.

When a sound source moves away from an observer, the observer has the impression that the sound source is:

A) rotating

B) louder than it actually is

C) lower in frequency than it actually is

D) higher in frequency than it actually is

(C) A sound source moving away from an observer appears to have its source frequency shifted to a lower frequency when detected.

A 54-kg child with a 6-kg toboggan slide down the ice-covered hill. Point A and Point B are the top and the bottom of the hill, and are a distance *l* apart along the slope. Between these points, the toboggan and rider are opposed by a constant 60-N frictional force. Which of the following expressions gives the amount of energy lost to friction by the toboggan and rider between points A and B?

A) (60 N)(20 m)

B) (60 N)(*l*)

C) (60 kg)(g)(20 m)

D) (60 kg)(g)(*l*)

(B) Frictional force dissipates an amount of energy given by the product of force times the distance over which the force acts.

The sled (3 kg) and rider (47 kg) are travelling at 10 m/s when they have a completely inelastic collision with the stationary toboggan (6 kg) and rider (54 kg). How fast do the sled and toboggan travel immediately after the collision?

A) 4.6 m/s

B) 5.0 m/s

C) 8.3 m/s

D) 10 m/s

(A) In a completely inelastic collision, the two objects stick together and have a common final velocity:

V_{final} = V_{initial} x m_{initial}/m_{final}. This is equal to: V_{final} = (10 m/s) x (50 kg)/(110 kg) = 4.55 m/s

From the ground level, a person at point A throws a snowball horizontally to the right at 25 m/s. Where does the snowball land?

A) 10 m to the left of Point B

B) At Point B

C) 12.5 m to the right of Point B

D) 50 m to the right of Point B

(B) t = (2h/g)^{1/2} = (2 x 20 m/ 10m/s^{2})^{1/2} = 2 s. The horizontal distance covered is: x = vt = (25 m/s)(2 s) = 50 m. This is the distance of Point B.

The sled and rider start from a location on the hill that is 10 m lower than Point A. How does the speed of the sled and rider at Point B, starting from this location, compare to the speed of the sled and rider at Point B when starting from the top of the hill?

A) It is slower by a factor of 4

B) It is slower by a factor of 2*sqrt(2)

C) It is slower by a factor of 2

D) It is slower by a factor of sqrt(2)

(D) Set mgh = mv^{2}/2. The ratio of the speeds at the bottom of the hill when starting at h = 10 m and h = 20 m is: v^{2}_{10}/v^{2}_{20} = 10/20. Taking the square root of: (1/2)^{1/2} means that v_{10} is slower by a factor of 2^{1/2}.

For a given laser-cavity mode, the standing wave pattern within a laser cavity can be viewed as a superposition of two travelling waves. Their amplitudes and directions are described by which of the following:

A) equal amplitudes, opposite directions

B) equal amplitudes, same direction

C) different amplitudes, same direction

D) different amplitudes, opposite direction

(A) Two traveling waves that make up a standing wave must have equal amplitudes and move in opposite directions otherwise the wave superposition does not produce a stationary wave envelope.

In a nearsighted individual, the image of a distant object is focused:

A) in front of the retina, requiring divergent lens correction

B) in front of the retina, requiring convergent lens correction

D) behind the retina, requiring divergent lens correction

D) behind the retina, requiring convergent lens correction

(A) A near sighed myopic person can focus on nearby objects but cannot see clearly objects far away .Thus, this eye has a shorter focal length. This condition is corrected by glasses with a divergent lenses.

At the moment when the driver takes his foot off the gas, the car travels at a speed v. The car takes t seconds in order to come to a halt. The car has mass M, the coefficient of friction for the road is μ, and the gravity in the system is g.

What is the acceleration of the car as the driver presses the brakes?

A) g*μ

B) -g*μ

C) g*M*μ

D) -g*M*μ

(B) The acceleration is negative, because the car is decelerating. We know that the only force acting on the car is friction. The force from friction is μ*N, where N is the normal force, which is Mg. We also know that F = M*a, where F is the vector sum of all the forces on the car. Thus, F = M*a = -μ*M*g, which can be simplified to give us the answer.

Lead acid batteries, like those typically found in vehicles, are composed primarily of lead and sulfuric acid. An individual cell of the battery has a voltage of 2 V, but batteries for cars typically will have a voltage of 12 V. This increase in voltage can be accomplished in which of the following ways?

A) placing the cells in series

B) placing the cells in parallel

C) adding more lead to the cells

D) increasing the concentration of sulfuric acid in the cells

Placing cells or batteries in series will add their voltage, while placing them in parallel will keep the voltage the same. Because electric potential is an intensive property, the amount of either of the half-reaction components will not affect the voltage; adding more lead or sulfuric acid may increase the capacity rating (in Amp-hours) but will not increase the voltage (potential difference) of the cell or battery.

The sum of all of the external forces on a group of particles is zero. Which is true of this system?

A) The system is in static equilibrium

B) Linear momentum of the system is constant

C) Total kinetic energy of the system is constant

D) Total potential energy of the system is constant

(B) Since all external forces on the group of particles is zero, the system can not be accelerating. It is possible that there is potential and kinetic energy in the system, but it is not possible for velocity to be changing, because that would mean that the system was accelerating. Since linear momentum can be calculated as mass*velocity, and we know that both of those are constant, we can say that the linear momentum of the system is constant. Static equilibrium exists only when the particles of a system are unmoving. This condition is not true in the question since it does not preclude movement; an object can be in motion and still have no forces acting on it, making (A) incorrect.

Which of the following expressions describes the work done by air resistance on a falling object between the time when it reaches its terminal velocity and the time when it impacts the ground?

A) mgh

B) m(gh - (1/2)v_{terminal}^{2})

C) √2gh

D) (1/2)v_{terminal}^{2}

(A) For this object that has reached its terminal velocity (no acceleration), we know that the force of gravity is equal to the force of air resistance (F_{g} = F_{terminal}). Since F_{g} = mg, we know F_{terminal} = mg. We also know W = Fd, so therefore W = mgd where d is the height fallen, also known as h. The work done on the object is equal to the gravitational potential energy of that object from the height at which it falls because air resistance counteracts all the force that is acting on the object due to gravity. None of the other expressions properly sets up this relationship.

When a light wave and a sound wave pass from air to glass, what changes occur in their speeds?

A) both speed up

B) both slow down

C) light speeds up; sound slows down

D) light slows down; sound speeds up

[D] Light slows down because the index of refraction in the glass is greater than in the air. The index is a measure of the ratio of the velocity in air to the velocity in the medium. For sound, the speed becomes greater because the speed of sound in a solid is much greater than in air.

Cell-phone channels operate at frequencies ranging between 824 MHz and 894 MHz. Each channel requires a finite amount of frequency space called the bandwidth of the channel and is set at 30 kHz. What is the total frequency range available for cellular phone communications?

A) 30 kHz

B) 894 MHz

C) 70 MHz

D) 894.03 MHz

[C] 894 – 824 = 70 MHz

Surface waves are associated with elastic oscillations in the crust of about 10-s periodicity and cause little lasting deformation. The wavelength of surface waves is about 20 km. The propagation speed of these waves is estimated as:

a) hundreds of m/s

b) thousands of m/s

c) tens of thousands of m/s

d) hundreds of thousands of m/s

[B] The speed of a wave is given by its wavelength λ divided by its period T.

A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. A cannon ball is launched with an initial speed of 50 m/s. The red cannon ball is launched horizontally. About how long will it take the red cannon ball to strike the canyon floor?

A) 3.5 seconds

B) 4.5 seconds

C) 5.5 seconds

D) 6.0 seconds

(B) ∆y = ½at^{2}. (100 m) = ½(10 m/s^{2})t^{2}. 20 = t^{2}. t = 4.5 seconds.

A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. Three cannon balls are launched with an initial speed of 50 m/s. The red cannon ball is launched horizontally. The white ball is launched at a 30º angle above the horizontal, and a blue ball is launched at a 60º angle above the horizontal. If all balls were launched simultaneously, in which order would they hit the ground?

A) White, blue, red

B) Blue, white, red

C) Red, white ,blue

D) Red, blue, white

(C) The angles will tell us the order in which the balls fall. The red ball will fall to the canyon first, and the white ball (with a lower max height) will fall the canyon second. The blue ball (with the largest max height) will fall to the canyon third.

A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. Three cannon balls are launched with an initial speed of 50 m/s. The red cannon ball is launched horizontally. The white ball is launched at a 30º angle above the horizontal, and a blue ball is launched at a 60º angle above the horizontal. In comparing the maximum heights and ranges for the white and blue cannon balls, which of the following statements is true?

A) The blue ball has a smaller maximum height but a longer range

B) The blue ball has a larger maximum height and a longer range

C) The white ball has a smaller maximum height and a shorter range

D) The white ball has a smaller maximum height but a longer range

(D) B and C are saying the same exact thing. Because the blue ball was launched at a higher angle, it will have a larger maximum height. Therefore D is the best answer.

A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. Three cannon balls are launched with an initial speed of 50 m/s. The red cannon ball is launched horizontally. The white ball is launched at a 30º angle above the horizontal, and a blue ball is launched at a 60º angle above the horizontal. Approximately how far above the canyon will the white ball be when it reaches its apex?

A) 30 m

B) 120 m

C) 130 m

D) 225 m

(C) You can think about it like this: v^{2} / 2g = ∆y. This works in dimensional analysis: (m^{2}/s^{2}) x (s^{2}/m) = m. The “2” factor comes in here because there is an incline and a decline in the parabola. So: (50sin30)^{2} = 625/20 = 31.25 m. We have to add this to our initial 100 m.

A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. Three cannon balls are launched with an initial speed of 50 m/s. The red cannon ball is launched horizontally. The white ball is launched at a 30º angle above the horizontal, and a blue ball is launched at a 60º angle above the horizontal. When the white cannon ball reaches its apex:

A) acceleration is zero and its velocity is not zero

B) acceleration is zero and is speed is zero

C) acceleration is not zero and its velocity is zero

D) acceleration is not zero and its speed is not zero

(D) The projectile always has an acceleration. The projectile still has speed in the x-direction.

A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. Three cannon balls are launched with an initial speed of 50 m/s. The red cannon ball is launched horizontally. The white ball is launched at a 30º angle above the horizontal, and a blue ball is launched at a 60º angle above the horizontal. What is the acceleration of the red cannon ball while it is inside the cannon barrel is the barrel is 1m?

A) 25 m/s^{2}

B) 125 m/s^{2}

C) 250 m/s^{2}

D) 1250 m/s^{2}

(D) Dimensional analysis: a = v^{2} / 2x = (m^{2}/s^{2}) x (1 / m) = (m/s^{2}). So: (2500 m^{2}/s^{2})/(2 x 1 m) = 1250 m/s^{2}

A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. Three cannon balls are launched with an initial speed of 50 m/s. The red cannon ball is launched horizontally. The white ball is launched at a 30º angle above the horizontal, and a blue ball is launched at a 60º angle above the horizontal. Which of the three balls hits the ground with the greatest kinetic energy?

A) Red

B) White

C) Blue

D) They all hit the ground with the same kinetic energy

(D) Since all three balls start at the same height and finish, they all have the same initial potential energy and the same final potential energy so they will all have the same kinetic energy.

For the first ten seconds, a moving car with a mass of 1500 kg accelerates uniformly along a straight horizontal road from rest to maximum velocity of 15 m/s. How far will the car have traveled?

A) 7.5 m

B) 15 m

C) 75 m

D) 225 m

(C) x = t(v_{f} +v_{1})/2 = (10)(15)/2 = 75 m. Alternatively: x = ½at^{2}. Our acceleration is (15)/(10) = 1.5 m/s^{2}. So: ½(1.5 m/s^{2})(100 s^{2}) = 75 m.

In order to change the maximum velocity obtained by a vehicle, the driver should:

A) allow the car to travel a greater distance during the first acceleration period

B) use a car with a larger mass

C) allow the car to coast before decelerating

D) drive with a reduced force of gravity

(A) Think about velocity: v^{2} = 2ax. If we keep the acceleration the same, but increase the distance, we’ll get a greater velocity.

Which could explain the frequently bluish color of earthquake lights?

A) sodium salts are common in the earth’s crust and sodium emissions can be quite bright

B) in transparent substances, dispersion effects are in general greater for longer wavelengths

C) the ultraviolet radiation is absorbed by molecules that then fluoresce at yet shorter wavelengths

D) the ultraviolet radiation is absorbed by molecules that then fluoresce at yet longer wavelengths

[D] C cannot occur (energy is not conserved). Sodium emits yellow, not blue. Shorter wavelengths, not longer, are more affected.

Visible light travels more slowly through an optically dense medium than through a vacuum. A possible explanation for this could be that the light:

A) is absorbed and re-emitted by the atomic structure of the optically dense medium

B) is absorbed and re-emitted by the nucleus of the material in the optically dense medium

C) bounces around randomly inside of the optically dense medium before emerging

D) loses amplitude as it passes through the optically dense medium

[A] This is the reason for the slowing down of light. The nucleus is involved. The motion of photons is certainly not random.

A 7-N force and an 11-N force act on an object at the same time. Which of the following cannot be the magnitude of the sum of these forces?

A) 2 N

B) 8 N

C) 12 N

D) 18 N

[A] The largest net force occurs when the forces point in the same direction (18 N). When the values are subtracted, the result is at 4 N. 2 N is excluded from this.

Which of the following graphs best illustrates how charge accumulates on the plates of a capacitor after the switch is closed?

[B] As time increases, charging must increase as well. Furthermore, the charging of a capacitor is an exponentially decreasing process that must reach a constant value after a long time.

A 1.00 kg projectile with an applied force of 19.6 N through a distance of 0.50 m is propelled straight upward. The projectile explodes at its peak height. What is the total momentum carried by all the fragments immediately after the explosion?

A) 19.6 kg m/s

B) 9.80 kg m/s

C) 0.50 kg m/s

D) 0 kg m/s

[D] At the moment of the explosion, the object is not moving so its momentum is moving. After the explosion, by conversation of momentum, the total momentum of the fragments must again sum to zero.

Ionization detectors contain two parallel electrodes that are typically separated by 3 cm with a 5-V potential difference across them. What is the magnitude of the electric field between the two electrodes?

A) 1.5 N/C

B) 1.66 N/C

C) 15 N/C

D) 166 N/C

[D] An electric field is volts/meter. So 5/0.03 is 166.7 V/m.

Destructive interference occurs in photodiode detectors when direct and scattered light rays take path in the photocell that differ in phase by:

A) 0 degrees

B) 90 degrees

C) 180 degrees

D) 360 degrees

[C] The phase difference corresponding to a half of a wave is 180º. Half a wave difference in phase between two waves corresponds to destructive interference.

Why are curved particle trajectories through stacks of ionization chambers preferable to straight ones?

A) Curves trajectories require longer, providing more time for data analysis

B) Straight-line trajectories would produce too few anode signals to define tracks precisely

C) The radius of curvature can be used to help identify the particle that produced the track

D) Neutron trajectories can be immediately distinguished form those of other particles

[C] Charged particles in motion constitute a current, and freely moving charges are deflected by a magnetic field into a curved path. The amount of curvature depends on the charge and mass of each incoming particle and can be used to distinguish species of particle from one another.

In a healthy person standing at rest, a comparison of arterial blood pressure is measured in the arm with that measured in the leg shows that the pressure in the leg is:

A) lower, because the blood flow rate is less

B) greater, because the column of blood between the arm and the leg has a hydrostatic pressure

C) the same, because vicious pressure loss precisely compensates the hydrostatic pressure increase

D) lower, because viscous flow resistance causes pressure loss

[B] Pressure in a liquid is proportional to the height of the liquid above it (P = ρgh) so the blood pressure is increased because of the force of gravity.

The intensity level in decibels is defined as 10 log_{10}(I/I_{o}) where I_{o} is a reference intensity equal to the human threshold of hearing, 10^{-12} W/m^{2}. What is the intensity of the threshold of pain, 120 decibels?

A) 10^{12} W/m^{2}

B) 10^{0} W/m^{2}

C) 10^{-2} W/m^{2}

D) 10^{-12} W/m^{2}

[B] Because the intensity level is 120 dB = 10 log (I/I_{o}), log(I/I_{o}) must equal 12 and to equal 12, I/I_{o} must equal 10^{12}. I = 10^{0} W/m^{2}

A ball is thrown vertically upward. When the ball reaches its maximum height, which of the following describes its velocity *v* and its acceleration *a*.

A) v = 0, a = 0

B) v ≠ 0, a = 0

C) v = 0, a ≠ 0

D) v ≠ 0, a ≠ 0

[C] The maximum height defines the point where v_{y} is zero. For a free falling object, the acceleration is always –g. There is no horizontal velocity.

The primary mirror of the hubble space telescope is approximately spherical and has a focal length of 5.8 m and a diameter of 2.4 m. The secondary mirror is flat and 0.3 m in diameter. If incoming parallel lines, when reflected by the mirrors, converge 2 m to the left of the reflective side of the primary mirror, what is the approximate distance between the two mirrors?

A) 14 m

B) 28 m

C) 58 m

D) 116 m

[B] Our equation will essentially be:

2d + 2 = 58 m

This is because we know the focal length of the primary mirror is 58 m and that the light rays go 2 m beyond the primary mirror. The "2" before the "d" for distance is there because the light rays go forth once and then bounce back the same distance. So, when we calculate this, we get d = 28 m.

Which of the following energy conversions best describes what takes place in a battery-powered resistive circuit when the current is flowing?

A) Electric to thermal to chemical

B) Chemical to thermal to electric

C) Electric to chemical to thermal

D) Chemical to electric to thermal

[D] The battery (chemical) creates an electric current in a resistive circuit. The current creates thermal energy in the resistors.

The compressive strength of human bone is about 2.0 x 10^{8} N/m^{2}. What crushing mass, supported by an upright forearm, would cause a 1% change in length of a 5-cm^{2} cross-sectional area of forearm bone?

A) 10^{2} kg

B) 10^{3} kg

C) 10^{4} kg

D) 10^{5} kg

[A] F = (∆L/L) x A x E = mg. Solving for m gives: (0.01 x 5 x 10^{-4} x 2 x 10^{8}) / (10) = 10 kg

Which of the following graphs shows the relationship between the distance fallen form rest as a function of time for an object experiencing air resistance?

[B] Air resistance causes a constant terminal velocity. This gives a distance versus time a linear graph. However the portion of the fall starting from rest is proportional to the square of time. Graph B shows this.

How much gravitational potential energy is transformed during the 2-km fall of a 75 kg parachutist?

A) 1.5 x 10^{3} J

B) 3.0 x 10^{3} J

C) 6.0 x 10^{5} J

D) 1.5 x 10^{6} J

[D] E = 75 kg x 10 m/s^{2} x 2000 m = 1.5 x 10^{6} J

When the speed of a car is a constant 20m/s, the period if its circular motion along a track is:

A) 0.50 s

B) 1.00 s

C) 1.57 s

D) 3.14 s

[D] The period is given by T = 2π/ω. The rotational angular velocity is given by ω = v/r. With v = 20 m/s, and r = 10 m, then ω = 20/10 = 2 rad/s giving: 2π/2 = π

At which point in Figure 2 does the human riding in the centrifuge car experience the strongest sense of gravity?

A) A

B) B

C) C

D) D

[C] The centripetal acceleration a = v^{2}/r is closest the acceleration of gravity g when the velocity is the greatest.

Which of the following constraints applies to the suspension angle θ (in radians) of the car shown in Figure 1?

A) 0 ≤ θ ≤ π/4

B) 0 ≤ θ < π/2

C) 0 ≤ θ ≤ 3π/4

D) -π/4 ≤ θ ≤ π/4

[B] The angle shown in Figure 1 is zero when centrifuge is at rest. When the centrifuge is rotating at high angular velocity, the angle increases at most to 90º.

If the centrifuge in Figure 1 emitted a sound as it moved, a stationary observer standing just outside the radius of the centrifuge would hear:

A) a frequency that oscillates about that emitted by the car

B) the same frequency as that emitted by the car

C) a higher frequency than that emitted by the car

D) a lower frequency than that emitted by the car

[A] A stationary observer will hear the sound when the sound is approaching and when it is receding. A higher frequency will appear as the source approaches, and a lower frequency as the source recedes.

Which of the following best explains what happens at the molecular level to the supporting pillars as the water level in the storage tank rises?

A) The increasing mass of the tank causes a greater gravitational pull between the tank and the molecules in the pillars, making the pillars shorter.

B) The increasing pressure force on the pillars causes some of the kinetic energy of the molecules to be turned into potential energy, making the pillars colder

C) The increasing weight of the tank pushes the molecules in the pillars closer together along the vertical direction, making the pillars shorter

D) The increasing repulsion between the molecules in the pillars releases some of their electrons, making the surface of the pillars electrically charged

[C] The pressure on the pillars increases as the tank is filled with water. The pressure forces on the molecules in the solid to be closer together.

The change in gravitational potential energy of 4 x 10^{-4} m^{3} of water that falls 0.2 m from the inlet in the side of the storage tank to the water surface would be:

A) 0.08 J

B) 0.8 J

C) 4 J

D) 2000 J

[B] The potential energy is *mgh*, with *m* = 4 x 10^{-4} m^{3} x 10^{3} kg/m^{3} = 0.4 kg, g = 10 m/s^{2}, and h = 0.2 m. The result is 0.8 J.

A hockey puck of mass 0.16 kg is slapped so that its velocity is 50 m/sec. It slides 40 meters across the ice before coming to rest. How much work is done by friction on the puck?

(A) +4 J

(B) –60 J

(C) –200 J

(D) –340 J

(C)

he work-energy theorem relates the change in kinetic energy to the work done on the puck:

_{}

Since the force of gravity is vertical and the displacement of the puck is horizontal, the force of gravity does no work. Since the only horizontal force on the puck is the friction force, all of the work on the puck is done by friction:

_{}

or

Since friction always exerts a force opposite to the velocity, the work done by friction is expected to be negative, as calculated.