Physics 2 Flashcards
(215 cards)
0
Q
Explain what a field is?
A
an invisible influence capable of exerting a force on a mass or charge.
1
Q
what is gravity?
A
Gravity is a field that exists between any two objects with mass.
2
Q
what is the equation for gravitational force between two objects with mass?
A
Fgravity= Gm1m2/r^2
This is often known as the inverse square law
The forces on both masses are equal in size but opposite in direction.
3
Q
whats the difference between gravity and the force of gravity?
How can we derive the value of g from the Force of gravity between two objects equation?
A
Gravity is the field that is will create a force on a object of mass.
mg= GMearthm/r^2 the m on both side of the equation leaving us with just g=G*Mearth/r^2
F=mg
4
Q
Is the Universal Law of Gravitation true everywhere?
A
Yes
5
Q
Two planets A and B, where the mass of B is two times that of A. What is the ratio of the forces between them? What is the ratio of acceleration between them?
A
Well they should have the same forces exerted between them due to Newtons 3rd Law. The acceleration of mass be will be half that of mass A.
6
Q
What force does the earth experience due to a rock falling?
A
The earth and the rock will experience the same force. The earth will just experience hardly any noticeable acceleration because its mass is so much greater than that of the rock.
7
Q
Important note
A
F=Gmm/r^2 gives the force due to gravity not gravity itself. Gravity itself, usually called “gravity” or “the strength of the gravitational field” or “acceleration due to gravity” is represented by lowercase g and is described by the formula g=Gm/r^2. Many students mistakenly reference the first formula when asked about gravity.
8
Q
What is the equation for gravitational potential energy? And what is it for liquids?
A
PE=mgh. Anything with mass can have gravitational potential energy. For example liquids have mass, so they can also have potential energy but we typically replace the mass term with density when dealing with fluids. So PE per unit of volume of fluid= pgh
9
Q
What is the equation we use for potential energy in space or near earth if NOT assuming g=10m/s/s?
A
PE= -Gmm/r
10
Q
Explain the difference between sliding friction and static friction?
A
Sliding friction is the force happening between to objects and there surface as it is moving. Static friction is the force when two surfaces are in contact with each other and a force is applied but the object doesn’t move. Think of a box sliding down across a surface and a box you’re trying to push but won’t move.
11
Q
In practice, the acceleration due to gravity is not a constant 9.8 m/s^2, but varies with distance from the center of the earth. Taking this into consideration, as a falling objects approaches the earth what will happen to its acceleration and velocity?
A
The object will exhibit an increasing rate of velocity change there for and increase in acceleration. Think of gravity equation.
12
Q
What two things are friction dependent upon?
A
Texture of the two surfaces
The amount of contact force (normal force) involved
13
Q
What does motion does friction always oppose?
A
It opposes SLIDING, NOT motion
14
Q
Which way does the friction force vector point for a car driving east? For a skidding car with locked breaks? For a gecko climbing a wall? For a car driving around a corner?
A
Vector will point east, will oppose the sliding of the car, point upwards, inwards towards the center of the circle because the car is trying to slide outward.
15
Q
What are the formulas for kinetic friction and static friction?
A
Ff= µsFn or Ff=µsmg*cosø
Ff= µkFn or Ff = µkmg*cosø
16
Q
What is the static friction for a box being applied with 20N or force? And 100N of force?
A
The static friction will oppose the applied force vector but will be equal to it so 20N and 100N
17
Q
500N is applied to an object and it does not move. 501N is applied and it just begins to slide. Describe the amount of force that must be applied to the object continuously to move it at a constant velocity across the surface?
A
For an object to be traveling at constant velocity the Net force must add up to 0 which will give no acceleration. We know that the normal force and weight force are the same if on a flat surface. So therefore the kinetic friction and the applied force must be the same in order for there to be no accel and remain at constant velocity.
18
Q
Why do objects accelerate down an inclined plane?
A
Forces are unbalanced because the normal force and the weight of the object aren’t the same due to the incline
19
Q
Explain how you should solve incline plane problems?
A
First resolve the weight or Force of gravity vector into components. Here you will then get a perpendicular and parallel vector and then solve for these two vectors. The parallel vector will give you force down the inclined plane and the perpendicular vector will give you the normal force. From here you can solve for the net force by adding all the forces acting upon the box.
20
Q
What are the equations used for incline plane problems and what do each do?
A
F= mgsinø this will give you the component that is parallel to the surface of the incline.
Fn = mgcosø this gives you the force that is perpendicular to the incline which is equal to the normal force because there is no acceleration in either of those directions
21
Q
How do you find the final velocity of an object at the bottom of an incline?
How do you find the acceleration of an object moving down an incline plane?
A
Use Vf = √(2gh)
Take the net for and divide it by the mass. You can derive the equation a= gsinø because mgsinø = m*a the mass cancel.
22
Q
Why does V = √(2gh) work for either incline or falling body problems?
A
The formula V = √2gh is derived from conservation of energy by equating mgh to 1/2mv2 and solving for v. As long as friction, air resistance, etc. are ignored, energy will be conserved in an identical way whether the object falls directly to the ground or rolls down a plane.
23
Q
As the angle of an incline increases, what happens to the value of a?
A
Well we know that a = gsinø so if the angle increases so does sine. (think of your triangle on a graph and what happens to sine as the angle increases). If sine increases therefore a will increase. As the angle increases sine increases cos decreases.
24
What happens to the normal force and the force down the plane as the angle increases for an inclined plane problem?
normal force decreases and force down the plane increases.
25
What are the min and max values for accel down an inclined plane?
Think of your triangle sin of 90 is 1 so that would give 10m/s/s
sin of 0 is just 0 which would give 0 accel.
26
Will a change in mass of a block on an incline cause it to slide down the plane if initially at rest?
No this will just increase the normal force and weight of the block.
27
Tension usually means you are going to be dealing with a force involving?
Rope cable string ect
28
what is the tension of a rope being pulled from opposite ends with identical forces of 50N?
The tension in the rope would be 50N
29
A 500kg elevator is being accelerated upward by a cable with a tension of 6000N. What force does the elevator exert on the cable?
The elevator is 500kg meaning that it weighs 5000 N. If there is 6000 N tension in the cable that means that the 1000 N is going into accelerating the elevator. So the force exerted on the cable iis 6000 N. Newtons 3rd law ??
30
What is hooks law?
F = k∆x springs and many other items such as resilient solids, rubber, and bonds between atoms follow this law.
∆x is the displacement from equilibrium, not length of spring
31
For a mass on a spring when is the velocity the greatest, the least, and acceleration is 0m/s/s
Velocity is greatest when spring is at equilibrium when oscillating, least when its furthest away and velocity is 0, and acceleration is 0 when spring is at equilibrium and even when it passes through equilibrium.
32
A ball rolls along a frictionless table and strikes a spring. Describe the force experienced by the ball due to the spring, the acceleration of the ball, and how both change with time?
As the ball hits the spring and compresses it, the spring then exerts a force in the opposite direction that the spring is compressing. As the spring compress further and further the ball is gaining a greater acceleration vector in the negative direction ( decelerating).
33
How do you solve for the spring constant?
use F=k∆x .. ∆x is the displacement from equilibrium or the difference in displacement between two trials. For F, use the force applied in one trial, or the difference in force between two trials. Remember to convert mass to weight (F=mg).
34
A student hangs a 4kg mass on a spring and it stretches 1m. What is the spring constant and how far will the spring stretch if he attaches a 2kg mass?
First solve for the spring constant using F=k∆x. After that plug in the spring constant and new force in the find out how far the spring will stretch.
35
What is the force of the spring directly proportional to?
The force required to stretch a spring will be directly proportional to the amount stretched
According to Hooke's law, the force required to stretch the spring will be directly proportional to the amount of stretch.
36
what is the equation for potential energy of a spring?
PE= 1/2 k∆x^2
Although the above formula can be used to solve for all of the variables in the equation, it is more likely to be used in connection with conservation of energy. If a mass with a velocity strikes a spring compressing it, all of its KE will turn into elastic PE. Setting the initial KE to the final PE allows you to predict how far the spring will compress.
37
True or False? A ball moving with twice the kinetic energy can compress a spring twice as far. A ball moving with three times the velocity can compress a spring three times as far.
False.. PE=KE. So KE=1/2kx^2.. If we double KE that will only increase x by √2.
True because 1/2mv^2 = 1/2kx^2 so if v increases by 3 times the left side of the equation equals nine so x will increase by 3.
38
What is a pendulum?
any weight (often called a bob) attached by a rob, string, wire ect. to a fixed overhead point and capable of freely swinging from side to side.
39
For a pendulum when is KE and PE at a max and a min?
PE is at a max at the max height of the bob and a min at the bottom of the pendulums arc. KE is at a max at the bottom of the pendulums arc and at a min at the max height of the bob.
40
When is gravitational PE assumed to be 0 for a pendulum bob?
At the lowest point of its arc. In other words, at the point we assume h=0
41
What value must be low for a pendulum to exhibit SHM? Why does the displacement of a pendulum slowly decrease over time?
The angle of displacement must be small for SHM on a pendulum because we are assuming sinø=ø and we are using this for the restoring force.
Displacement decreases over time due to non conservative forces like air resistance ect.
42
Describe how something can be moving fast but be moving infrequently?
Take the moon for example, the moon travels in orbit at about 10090m/s yet it takes about 27 days for it to complete that orbit and thats infrequent. Frequency is the amount of time it takes an object to complete one cycle.
43
For pendulum problems there are typically two forces acting upon the mass. ( and for incline problems). That is the tension force and the weight force. What force do we resolve into components and why?
We resolve the the weight force into two components because the tension ( normal force for incline) are perpendicular to the motion of the object.
44
For an object in pendulum motion. Why is the tension force greater than the perpendicular component of the Force of gravity? Imagine the two components in your head and what they contribute to.
The perpendicular one is smaller because the mass is moving along a circular path and this is for centripetal acceleration. The mgsinø component is the restoring force that lies tangent to the circular path.
There no need for centripital force at the max height because the mass is paused and not moving. And at the equilibrium position there is no restoring force. Only when the mass is displaced from the equilibrium will there be a restoring force.
45
Does mass have an effect on the period for a pendulum?
No it doesn't, only will mass on a spring.
46
what is simple harmonic motion?
Anything that oscillates back and forth and can be represented by a sine wave graphically constitutes SHM.
47
what are some examples of SHM?
Mass hanging on a spring and a pendulum
48
What is the formula for the period for a mass on a spring and for a pendulum?
T=2π√(m/k)
| T=2π√(L/g)
49
How would you find the frequency for a pendulum or mass on a spring? And what units is frequency in?
just do 1 divided by the period equations, or invert them. The units are Hz Hertz
50
How will increasing the following aspects of mass spring system change the frequency of oscillation? a) mass of object b) length of spring c) mass of spring d) gravity e) the spring constant
If mass is increased of object then frequency will go down. Length of spring wont have any effect. Mass of spring wont have any effect. Gravity wont have any effect. With a stiffer spring ie spring constant higher, then the frequency will be higher.
51
What will decreasing the following in a pendulum system do to its frequency? a) mass of bob b) length of pendulum c) gravity
the mass will have no effect, increasing the length will lower the frequency, lf you increase gravity frequency will go up, think about the restoring force and if gravity is increased the period will be less. mgsinø
52
when all the forces about an object are balanced what does this mean?
Object is in a state of equilibrium
53
what does in mean when an object is balanced?
The net force is 0 which means 0 acceleration Fnet=ma
54
what does static equilibrium mean?
At rest stationary, if you add all forces acting on the object together by the head toe method ect. The resultant vector should equal 0
55
Explain how you would solve for say a sign that is hanging by two strings at different angles attached to a roof?
First, find all the forces acting about the sign, the two tension forces and the weight force. Resolve them into components and solve for both the horizontal and vertical components of each force. Then add up all the horizontal components and vertical components and they should balance each other out and be 0 in the horz and vert
56
For equilibrium problems as the angle with the horizontal increases. say for a sign being held by two wires. What happens to the tension?
Decreases, tension for two ropes holding a sign at 30 degrees will be greater than at 60 degrees
57
Conclusion of Equilibrium
In conclusion, equilibrium is the state of an object in which all the forces acting upon it are balanced. In such cases, the net force is 0 Newton. Knowing the forces acting upon an object, trigonometric functions can be utilized to determine the horizontal and vertical components of each force. If at equilibrium, then all the vertical components must balance and all the horizontal components must balance.
58
Static vs Dynamic Equilibrium?
Static not moving, Dynamic at a constant velocity. Both there is no acceleration.
59
What are some examples when objects are in a state of Equilibrium?
Terminal Velocity, Constant Velocity, Objects are at rest, Balanced fulcrums or boards hanging, Objects floating in liquids
60
How should you solve for equilibrium problems?
Set forces equal to each other: Fleft=Fright Fup=Fdown Tclockwise=Tcounterclockwise. Recommended to make a T on your paper. Right all the forces that would push the object to the right in the right column and all the forces that will push it to the left in the left column. Always draw a free body diagram.
61
A 15kg toy rocket is falling toward earth with a constant velocity of 20m/s. A small amount of fuel still present in the cone creates a downward force of 30 N. What is the force due to air resistance?
The force due to the rockets weight is 150 N and the fuel is also a 30 N force in the downward direction. The rocket is at terminal velocity (no acceleration and in dynamic equilibrium) so the force of air resistance must be equal to the force down ward resulting in 0 net force.
62
What are the formulas for Torque?
T= Fr or T= Frsinø
63
When do you need to use T= Frsinø
You use this when the force applied is not a perpendicular force and is at an angle.
64
How do you solve fulcrum and board on string problems?
These are simple equilibrium problems. Just find the torques exerted on the balanced board or a board attached to a string. Determine if its rotating the board clockwise (-) or counterclockwise (+) and if there is no net torque these will be come out to be 0.. if not there will be a greater torque in one of the directions which will cause an acceleration. DONT FORGET TO FIND TORQUE AND NO JUST THE FORCES
65
Do forces or tension created directly at the rotating position of the board or fulcrum create a torque?
No, this is because the ( r=0). For example a mass right over the center of the fulcrum.
66
If 20 kg hangs exactly 3 meters from the fulcrum, what mass should hang on the other end, 5 meters from the fulcrum, to balance the board?
The 20 kg mass exerts a 200 N force, this means that it exerts a 600 Nm torque. Now all we have to do is set 600 equal to 5*10*m. This would give us a 12kg mass.
67
What does it mean for a system to not be in equilibrium?
This is when an object has an acceleration due to a net force. ( aka translational acceleration problems)
68
How would you solve for the equilibrium of an object on an incline plane?
Use the T method. Call all the forces acting down on the plan "down" forces and all the forces acting up the plan "up forces". The force down the plane due to gravity is always F=mgsinθ. The force of friction is always parallel to the plane opposite the direction of motion. There will never be acceleration perpendicular to the plane, so you can ignore these forces.
69
A 120kg rocket is accelerating toward the at 8m/s/s. The engine creates a downward force of 200 N. A small parachute is attached to the rocket and slows its decent. What is the force due to air resistance against the parachute. ( assume all air resistance is due to the parachute)
The forces acting down on the rocket are: mg (1200N) + 200N = 1400N. The forces acting up on the rocket are: Fair + ma (120kg*8m/s2) = Fair + 960N. Therefore: Fair + 960 = 1400 and Fair = 440N.
70
For circular motion at constant speed can you derive centripetal acceleration?
Yes
71
For circular motion which way is the change in velocity vector (∆v) pointing?
The change in velocity vector is pointing toward the middle. Think about the khan academy video of how he cut out each tangental velocity vector and put the tails of each vector together and saw how each one changed.
72
So if an object has a constant velocity and is going around in a circle is the velocity changing?
Yes, the magnitude isn't but the direction of the vector is changing. So this means that there is a net force which is going to cause an acceleration.
73
Just a note
If the velocity of an object is changing in anyway ( magnitude or direction) this means that there is an acceleration taking place meaning that there is a net force acting on the object. This net force is acting in the direction of the acceleration which is causing the change in velocity. This net force is centripetal force.
74
What is the centripetal force, when a yoyo on a string is swung around in a circle? When a satellite orbits the earth? when a car drives around a corner?
The tension in the string, gravity, and the frictional force. These are all pointing inward toward the center of the circle which the object is orbiting around
75
whats the equation for the circumference of a circle?
Circumference= 2π*r
76
if a car is moving at constant speed around a track, is it accelerating?
Yes even though the magnitude of the velocity may not be changing the direction of the velocity vector is changing indicating acceleration. Acceleration is any change in velocity
77
What way is the acceleration vector pointing, for an object traveling around in a circle at constant speed?
The acceleration vector points towards the middle of the circle, the same way as the change in velocity vector (∆v)
78
What is inertia, explain when a car is going around a corner and a person is in it.
Inertia can be described as a resist to accelerate, so when a car is going around a corner at constant speed the person is resisting acceleration and wanting to still move in the same path as the tangent velocity vector. Sometimes as you go around a corner you think your body is accelerating but really its just maintaining the motion of the tangent velocity and resisting a change in acceleration.
79
what is centripetal force?
Centripetal force is the net force ( friction, tension, gravity ect) that causes and object to change in velocity and have an inward acceleration.
80
Centripetal Force
To summarize, an object in uniform circular motion experiences an inward net force. This inward force is sometimes referred to as a centripetal force, where centripetal describes its direction. Without this centripetal force, an object could never alter its direction. The fact that the centripetal force is directed perpendicular to the tangential velocity means that the force can alter the direction of the object's velocity vector without altering its magnitude.
81
what are the 3 mathematic quantities when analyzing circular motion?
Force, acceleration , speed
82
How do you solve for centripetal force?
Fc=mv^2/r or Fc can be thought of as net force which will always be the centripetal foce.
83
Is centripetal force an actual force?
No, when you see centripetal force think that is always caused by some other responsible force. ( tension, friction, gravitational ect). Centripetal force is just a category name for forces that act to pull things into circular motion.
84
What is centrifugal force?
this forms an action reaction pair with centripetal force. Like when a ball on a string is swung around in a circle. It the string is pulling the ball into the center, the ball must also be pulling on the string ( Newtons 3rd Law). The strings force on the ball is centripetal and the balls force on the string is centrifugal.
85
For a ball in circular motion does the centrifugal force act on the ball or on the string?
the centrifugal force acts on the string. The strings force on the ball is centripetal and the balls force on the string is centrifugal.
The string. In this system a centripetal force upon the ball provided by the string maintains the circular motion, and the reaction to it, usually called the reactive centrifugal force acts upon the string.
86
what is the equation of centripetal acceleration?
ac= v^2/r centripetal acceleration
87
What is the direction of the centripetal acceleration vector?
towards the center, both the centripetal acceleration and centripetal force (ie tension, friction ect) point toward the center.
88
how can a lot of centripetal force questions be solved?
we can just set what force is causing the centripetal force, like for a satellite gravitational force . So mv^2/r=Gmm/r^2 We can do this because that force is the net force on the object which is going to cause the acceleration. Like for a car friction is the centripetal force, and the weight and normal force cancel each other.
89
What force equation should be set equal to the centripetal force in each situation?
- a car going around a corner? µ*Fn = mv^2/r
- a satellite orbiting earth? Gmm/r^2 = mv^2/r
- a ball on a string? Tension= mv^2/r
- a charged particle in a magnetic field? qvßsinø = mv^2/r
90
so what would be the velocity of a satellite orbiting the moon?
Gmm/r^2 = mv^2/r so v= √Gm/r m=mass of earth
91
Derive a formula for the minimum coefficient of static friction between a car and the road to keep a car going around a circular track?
µFn = mv^2/r and the Normal force= mg
so µ = v^2/rg
92
what is the equation for angular velocity? and what are the units?
w = v/r
w = 2πf
rad/sec
v= tangential velocity
93
what is the difference between angular frequency and angular velocity?
You can use these interchangeably for the MCAT. Because angular frequency is just the magnitude of velocity ( scalar)
94
in what direction does the angular velocity ( omega w ) point?
-It either points straight up or straight down. Whatever way the wheel or object is rotating ( clockwise or counterclockwise) will tell you up or down.
-
The angular velocity vector points along the axis of rotation. Use the right hand rule to decide if it is up or down. Curl the fingers of your right hand around the axis of rotation such that your fingers point in the direction of rotation and your thumb will be pointing in the direction of the vector.
95
how in many cases, can we solve angular momentum problems linearly?
Take the circumference of the circle as a translational distance:
C= 2πr or C=πd and use this distance just like you would along a straight path.
96
A ball with a radius of 11cm is spinning at a rate of 24 rad/s. How far does the particle on the equator of the ball travel?
We know that there are 6 radians for every 1 revolution. Therefore in 1 second we know that the ball spins 4 times. So now we can find the circumference of the ball and multiply this by 4 which will give us the distance. C= π*d C= about 66 cm 66*4= 264 cm
97
If you see something in radians how do you convert it to degrees and vice versa
use the conversion factor π/180
98
How do you know if an object is in rotational equilibrium?
If it is NOT rotating... or it is rotating with a constant angular velocity
99
When a sports team is on the move and is going to take some effort to stop?
The sports team has the momentum
100
All objects have mass, so if an object is in motion then it has what?
Momentum
101
What is momentum dependent upon?
The amount of mass of the object and how fast it's traveling
102
Momentum is a vector. There was be a direction in which way the object has the momentum in.
Just a note
103
The more momentum an object has the harder it is going to be to stop which means?
There is going to have to be a force involved. And the larger the momentum the larger the amount if force it is going to take or longer period of time or both in order to bring the object to a hault. We have witnessed this in our cars. When we come to a stop the brakes apply a force for a given amount of time to bring the car to a stop. The more momentum the larger the force its going to take or will take a longer amount of time.
104
What is always the causing factor of accelerating an object?
An unbalanced force. Either speed up the object or slow it down. which in turn increases or decreases the momentum.
105
what does impulse equal?
The change in momentum
106
Say a half back experienced a force of 800N for 0.9 seconds. What would be the impulse?
The impulse is 800 * 0.9. This is also equal to the half backs change in momentum
107
Just a note.
Observe that each of the collisions above involve the rebound of a ball off a wall. Observe that the greater the rebound effect, the greater the acceleration, momentum change, and impulse. When a ball is rebounded off a wall if is initial velocity is 25 m/s and it comes of at 20 m/s that has a greater v change a change momentum change and impulse than something that is 10 m/s to 5 m/s. You have 25 and -20 vs 10 and -5.
108
Just a note
In a collision, an object experiences a force for a given amount of time ( impulse) that results in its mass undergoing a change in velocity (i.e., that results in a momentum change).
Impulse=change in momentum
109
Describe why we use air bags in cars?
When the driver gets in a wreck he will continue to move will his momentum. Since change of momentum is = to impulse. The longer it takes for the driver to come to a stop the less force has been exerted on the driver. This is because F*t are inversely related and = to the change in momentum
110
explain situations of rebound?
when something rebounds it undergoes a big velocity change compared to something that say just hits a wall and stops. This is because the direction of the velocity is also changing. Will a big velocity change this also means that there was a big change in momentum which means that there was a large impulse.
111
Explain how momentum is conserved?
Think about it, say a car runs into a car that is stationary. The second car will experience a force from the first car, and the first car will experience the same force in the opposite direction ( 3rd law ). So we have F*t= -F*t and this is equal to impulse which is equal to change in momentum.
112
In a system what is the only way momentum change?
Momentum can only change if there is a net force acting on the system (basically reacts with its souroundings) . Because net force= ∆p/∆t
113
What is the equation for momentum?
p=mv
114
What should we think of momentum as?
Momentum= inertia increased by velocity
115
is momentum always conserved in a ISOLATED system?
yes. you will see this most in collision problems (including reverse collision). Isolated means that there are no external forces acting on the system. Friction and drag are common external forces.
116
what are the units of momentum?
kg*m/s
117
A 10kg block falls from a height of 10m onto a table that is 5m high. Was momentum conserved during the fall? Was momentum conserved during the collision with the table?
If you define the ball as your system, then gravity is an external force so momentum will not be conserved. However, if you defined your system to include the earth and the ball then momentum would be conserved. At rest the ball had no momentum and whatever momentum it gains as it increases in velocity will be matched by an increase in momentum of the earth. Because they will be vectors in opposite directions they will cancel to zero and momentum will have been conserved: zero before, zero after. In the collision with the table, momentum will be conserved for the ball-table-earth system, but not the ball-table system. All of this, of course, assumes no external forces.
118
What is the definition of impulse?
Impulse is the change in an objects momentum.
119
what is impulse equal to?
=∆p
=m∆v
=Favg*t
120
If there is no change in velocity can there be an impulse?
No,
however, the greater the change in velocity, the greater the impulse (assuming constant mass)
121
How is impulse= m∆v the same as impulse= Favg*t
We know that F=ma which is the same as F=m*∆v/t. So if we multiply t over, we get F*t=m*∆v and this gives us impulse is equal to momentum.
122
Car collision problems are frequently used to test your understanding of impulse.
-Air bags increase the time during which the driver comes to rest during a collision. How or why would this prevent injury?
The driver is going to have some momentum when it comes in contact with whatever is causing the collision. So when this happens the driver is going to have some velocity and (mass) this means that he has momentum. F•t = m∆v so by increasing the time it takes for him to come to a stop there will be less force acting upon him. F•t are inversely related
123
A 1kg rubber ball falls from some heigh, and strikes the cement at a final velocity of 10m/s. If the ball experiences a completely elastic collision, what will be the velocity of the ball after the collision and the impulse experienced by the ball, respectively?
10m/s and 20kg*m/s
124
what is the difference between elastic and inelastic collisions? what is conserved and what is not
in an elastic collision momentum and kinetic energy is conserved.
in a inelastic collision momentum is conserved but NOT kinetic.
125
If an object is deformed during a collision it must have undergone what type of collision?
inelastic, when an object undergoes deformation this means that you are loosing energy and in elastic collisions no energy is lost.
126
what equation should we use for elastic collisions?
Just use conservation of energy equation because no energy is lost in elastic collisions 1/2mv^2+1/2mv^2 = 1/2mv^2 + 1/2mv^2
127
Conservation of relative speed
For completely elastic collisions ONLY, the relative speed before will equal the relative speed after.
128
why must the collision be elastic for conservation of relative speed?
Because in order to for the relative speed to be conserved there must be conservation of energy.
129
Objects exchange velocities: If the objects of equal mass and the collision is perfectly elastic, the two objects will exchange velocities before and after the collision. Why? Describe conceptually why/how the objects exchange their initial velocities?
For a head-on collision with a stationary object of equal mass, the projectile will come to rest and the target will move off with equal velocity, like a head-on shot with the cue ball on a pool table. This may be generalized to say that for a head-on elastic collision of equal masses, the velocities will always exchange. mv=mv
130
For inelastic collisions what equation should we use?
Use the conservation of momentum. You MUST USE SIGNS. any velocity vectors left or down must be given a negative sign.
mv+mv = mv+mv and this equation becomes mv+mv = (m + m)v this is because the objects stick together.
131
What is a reverse collision?
| Provide at least 3 examples?
- This is when two objects are together and they come apart.
- A bomb. Two ice skaters pushing off each other. Radio active decay
132
Swuppose an atom of 56Fe undergoes alpha decay. The velocity of the exiting alpha particle is 2.0*10^3 m/s. What is the identity and ejection velocity of the decay product?
The new particle formed has 52amu (Cr-52). This can be determined by subtracting the A and Z number for Helium from Fe-56. The momentum of the ejected particle must equal the momentum of the decay product, therefore: (2 x 103 m/s)(4 amu) = (v)(52 amu). This simplifies to 8 x 103/5.2 x 101 = 154 m/s.
133
What is the formula for stress?
Stress = Force/Area
134
What is the formula for Strain?
Strain = ∆dimension/ original dimension
135
What is the formula for moduli of elasticity?
ME = stress/strain
136
What is Young's modulus?
Youngs Modulus = tensile or compressive stress/strain modulus (simultaneous pushing or pulling forces on both sides of an object; the two forces must be exactly aligned in both vertical or horizontal planes)
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What is Shear Modulus?
shear stress/strain modulus ( simultaneous pushing or pulling forces; tow forces are NOT aligned)
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What is Bulk Modulus?
Bulk Modulus = bulk stress/strain modulus (simultaneous compression from all sides)
139
Which object has the highest ME a marsh mellow or a rock?
The higher the Modulus Elasticity the better the object is able to keep its shape. So the rock would have the higher ME
140
What happens when solids are heated or cooled?
When heated they expand, when cooled they shrink
141
What is the equation for thermal expansion?
∆L = alphaL*∆T
142
Why is water weird?
Water exhibits some notable exceptions to the thermal expansion rules above. As long as water remains a liquid, it follows trends we would expect, with volume increasing as temperature rises and decreasing as temperature falls.
However, once water gets very near to its freezing point, ice crystals begin to form and it actually begins expanding.
This is due to the highly ordered lattice structure of the solid (ice), which includes regularly alternating hydrogen bonds.
Water is one of very few substances for which the solid phase will float in the liquid phase.
143
Several ice cubes are added to a drinking glass. Water is then added until the glass is just on the verge of overflowing. All of the ice cubes are floating at the top of the water. When viewed from the side, it can be seen that the ice cubes are sticking up out of the water and above the rim of the glass. If the glass is left to equilibrate to room temperature will the glass overflow?
Will the water level be higher or lower once all of the ice cubes have melted?
?
144
what is energy?
Energy = the capacity to do work
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whats the equation for KE?
KE = 1/2mv^2
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What is the equation for PEgravitational?
PEgrav = mgh (near earth)
PEgrav = -Gmm/r (away from earth)
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What is equation for PEelastic?
PEelastic= 1/2k∆x^2
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What is the equation for PEelectrical?
PEelectrical=qv
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What is the equation PEcapacitor?
PEcapacitor = 1/2QV or 1/2CV2 or 1/2Q2/C
150
What is internal energy?
The energy of the internal vibrations and random motions of molecules and/or atoms within a system. Non conservative forces such as friction or drag acting on a moving object results in the transfer of kinetic energy into internal energy.
151
What is heat energy?
Energy dissipated as heat. On the MCAT this is usually heat dissipated from a collision, or from a current-carrying wire. The terms heat energy and internal energy are used almost interchangeably.
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What is chemical energy?
The energy contained within chemical bonds, or the energy stored/released due to the separation and/or flow of electrons. ( ie a battery)
153
What is mechanical energy?
It is the total of KE+PE = ME
154
In the absence of non conservative forces ( friction , drag ect) is mechanical energy always conserved?
Yes, mechanical energy the total energy
155
Name the type of energy possessed or created by each of the following? 1) an explosion 2) a chemical reaction 3) a collision 4) any moving object 5) any object with height 6) a spring 7) a battery 8) two positive charges 9) water in a tank
Name the type of energy possessed or created by each of the following:
• An explosion = Chemical energy turns into heat energy and the kinetic energy of any flying debris;
• A chemical reaction = In a chemical reaction chemical energy is transferred between reactants and products—in an exothermic reaction heat is released
• A collision = in a collision the KE of the objects before the collision is transferred into heat energy used to create damage/deformity/etc.
• Any moving object = any moving object has kinetic energy
• Any object with height = potential energy, any object with height has gravitational potential energy
• A spring = mechanical energy, elastic potential energy, a spring stores elastic potential energy
• A battery = chemical energy, a battery stores chemical energy
• Two positive charges = electrical potential energy, two separated charges contain electrical potential energy
• Water in a tank = potential energy, water in a tank has gravitational potential energy and kinetic energy of the molecules
156
Describe the energy transformations that take place as a rocket ignites and combusts its rocket fuel, launches into the air, rises to a max height, then falls back to earth and strikes the ground..
48. Chemical energy stored in the bonds of the rocket fuel is transferred into kinetic and gravitational potential energy as the rocket rises. If air resistance is taken into account some energy will also be dissipated as heat due to drag. Gravitational PE reaches a max at the max height and is then transferred back into kinetic energy (and heat if considering air resistance) as the rocket falls back to earth. When the rocket strikes the ground its kinetic energy is transferred into heat energy.
157
What is the law of conservation of energy?
Energy is an ISOLATED system is always conserved. Energy is frequently transferred back and forth between forms, but never lost.
158
Provide conceptual definitions for open, closed and isolated systems?
Open System = both mass and energy can be exchanged with the surroundings; Closed System = energy, but not mass, can be exchanged. Isolated System = neither mass nor energy can be exchanged.
159
In order for a force to be qualify as have done work on an object...?
There must be a displacement and the force must have caused this.
160
for the work equation. there is cosø. how do you determine the angle?
the angle is the angle between the displacement vector and force vector.
161
what does work equal?
W=∆Energy
Think of work this way first! Be on the look out for any changes to the total energy of an object or system- IF ENERGY CHANGED, THINK WORK! Most students tend not to recognize or think about work when it appears on the MCAT.
162
When there is a change in velocity has work been done?
Yes, this means a change in KE. ( this is the most common example of how the MCAT might trick ya)
163
Changing in height has work been done?
Yes, this is a change in PEgrav which means a change in energy which means work.
164
is work done when there are changes in masses/planets/ect in space?
Yes, this is a change in PEgrav which = work
165
Change in position of charge means work?
yes this is a change in electrical PE which would be equal to the work done.
166
compression of a spring has work been done?
yes there has been a change in elastic potential energy which would equal work.
167
change in Friction or air resistance what should you think of?
Work, work=∆E
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What is the equation of work?
W= Fdcosø think of work this way second
Any time a force is applied across a displacement, work has been done. Students ten to think of this only as something like pushing a block across a table. Howeber, if a ball falls from a height, a force (mg) has been applied across a displacement . All of the examples of energy change listed above fir within the formula above
169
What is the units of work?
Joules. But this can be broken down into kg*m^2/s^2. This comes from F=ma
170
When is work positive? when is work negative?
There are two conventions for the sign of work. In physics, we say that if the force and the displacement are in the same direction, work is positive (e.g., pushing a barbell up). If force and displacement are in opposite directions we say work is negative (e.g., lowering a barbell). In both physics and chemistry a common convention is used that says: If work is done on the system it is positive; if it is done by the system it is negative.
171
what does the 1st law of thermo and what is the equation?
energy change is not always completely due to work; some energy is often lost to heat. Work and heat are the only ways energy can be transferred in and out of a system. The 1st Law of Thermodynamics
Work = energy transfer via a force
Heat = energy transfer via friction or energy flow from hot to cold
ΔE=W+q
172
What is the Work-Energy Theorem?
If a net force does work on a rigid object, the work done on that object is equal to the change in the KE of the object.
W = KEfinal - KEinitial
Focus on ∆E though because this means the same thing just will other types of energy as well.
173
Describe the work done when a force, applied at an angle of 45 degrees to the horizontal, is used to push a box across the floor. Describe the work done when a box is moved at a constant velocity across a frictionless table. Describe the work done by the string when a ball on a sting is swung in a circular motion.
When the force is not in the same direction as the displacement, only that component of the force that is aligned with the displacement does work. Thus the work done is Fdcos(45degrees). If the angle between force and displacement vectors is 90 degrees then no work can be done by that force. If a box is moved at constant velocity horizontally no work is done because there was no net force and the energy of the box was the same before and after the motion (ignoring some net force necessary to get the box moving). For a ball on a string no work is done by the centripetal force created by the string because this force is exactly 90 degrees to the tangential displacement vector at any instant.
174
how much work is done when a 1000kg car traveling at 40 m/s applies its brakes and comes to a stop?
just plug in and find kinetic energy. Should be 0 - 800,000 J =
-800,000
175
what is the work done on a spring compressed by 0.5 meters?
| k=10 N/m
use PE= 1/2k∆x^2 and W= ∆E 0-1.25= -1.25 Nm
176
can a simple machine out put more force than was put into it?
No, it follows the conservation of energy
177
what are machines?
machines are things that reduce the amount of force necessary to perform a given amount of work
178
Does a machine ever reduce or change the amount of work?
No machines NEVER reduce or change the amount of work
179
what is helpful thing to do when working a machine problem?
Sometimes its useful to first find the force needed to lift or move an object without a machine. With that you then can compare that to the force necessary with the machine. These values will differ by an exact ratio. ( h/d, L1/L2 ect)
180
What is the equation to find the force necessary to lift a mass without a machine?
Fnecessary = mg
181
Whats the equation that give force necessary to do work with a ramp type of machine?
Fm= mg(h/d) h is the height of the ramp and d is the distance of the hypotenuse. This force needed to do work will be less than without the machine. But remember you still do the same amount of work with or without the machine. When MCAT says a ramp is 5m long this means that hyp is 5m
182
A worker must move a 50kg block onto a table that is 2m off the floor. How much work will be required without the use of a machine? If a worker constructs a ramp that is 2m high and 8m long, how much force will be required? How much work will be required with the use of the machine?
-1000 J of work will be required with and without the machine. 125 N of force with using the machine
183
what is the equation for the force necessary when dealing with a lever? Remember work will still be the same amount of force required is the only thing that will decrese
Fm = mg(L1/L2) where L1 and L2 refer to the lever arms for the mass and the applied force, respectively.
184
what is the equation for the force necessary for pullys to do a certain amount of work with the machine?
Fm = mg(# of vertical ropes directly lifting the mass)
CAUTION not every rope that is vertically oriented should be counted and entered into the above equation. To be counted, a vertical section of rope must lift the mass directly, either by being attached to the mass, or by lifting a pulley that is attached to the mass. To test this, imagine grabbing only that rope and tugging it upward. Would it lift the mass?
185
whats the equation for the force required to do a amount of work with a machine using a hydraulic?
Fm= mg(h1/h2) or F=mg(A1/A2) where h1 and h2 refer to the distance traveled by the large plunger and the small plunger, respectively; and A1 and A2 refer to the cross sectional areas of the small plunger and the large plunger, respectively
186
Draw schematic plans for a ramp, lever, pulley and hydraulic lift that each provide a mechanical advantage of 5. Show these to your tutor and check if they are viable.
?
187
how can power be defined?
The rate of doing work or the rate of using energy. These are equivalent because one unit of energy must be required to do 1 unit of work
188
Describe what power is?
The quantity that has to do with a rate which a certain amount of work is done.
Work has to do with a force causing a displacement but it has nothing to do with the amount of time this force acts to cause the displacement.
189
if someone or something does the same amount of work in less time. Like a 2 weight lifters shoulder press the same amount of weight but one does it in less amount of time. Who is more powerful?
The weight lifter that does the same amount of work in less time does more work.
190
what is the unit of power?
Power is in Watts which is also = Joules/s
191
When you first see power what should you think of? (what is power=to?)
P = ∆E/t and this the same as P = W/t because W=∆E also
P = Fdcosø/t because W= Fdcosø
192
when you see instantaneous power what equation should you use?
P= Fvcosø this is only used for instantaneous power!
193
Truck engine A has twice the power of truck engine B.
True or False?
a) Truck A can accelerate the same trailer from zero to 50m/s in half the time
b) Truck A can accelerate a trailer to a velocity v, in a time t, that is twice as massive as the trailer truck B can accelerate to the same velocity in the same time period.
c) Truck A can accelerate the same trailer to twice the velocity in the same amount of time.
True if you break down the equation where W= ma*dcosø you can see the acceleration will double if the power has doubled.
True just as above this question is regarding mass
194
How are work energy and power all related?
Work- refers to an activity involving a force and movement in the directon of the force. A force of 20 newtons pushing an object 5 meters in the direction of the force does 100 joules of work.
Energy- is the capacity for doing work. You must have energy to accomplish work - it is like the "currency" for performing work. To do 100 joules of work, you must expend 100 joules of energy.
Power-is the rate of doing work or the rate of using energy, which are numerically the same. If you do 100 joules of work in one second (using 100 joules of energy), the power is 100 watts.
195
what equation is used for the force of gravity between two objects?
F=Gmm/r^2
196
when an object is hung from a spring and then you put a heavier object on the spring how would you find the spring constant?
take the difference of the forces and the difference of the lengths stretched and then use these values for ∆x and F. You can only find the spring constant if the same spring is used for both masses.
197
How would you find the instantaneous velocity of something in orbit?
When an object is in circular motion even though it may be at constant magnitude of velocity, the direction of the velocity vector is changing. So this indicates that there is an acceleration which means there is a net force. Centripetal acceleration to be exact, is caused by some force pointing inward toward the middle of the circular path. this is Centripetal Force. So we know that this Force tension gravity ect is equal to the Centripetal force so we can set lets say Gmm/r^2 = mv^2/r and then solve for v
198
If something is pressed against a spring. When does that object have the greatest force on it. When this object rebounds from the spring when is acceleration greatest?
When something hits a spring the force is greatest when the spring is fully compressed. The acceleration of the object is greatest right when you let go of the spring because the force is greatest at that point a= F/m .
199
what way is the friction vector point for a car driving east why?
Its pointing to the east because this vector opposes the sliding of the tire.
200
if an object is going 40 m/s and friction accelerates it (decelerate) at a rate of 4m/s/s. how far does the sled go?
v=d/t so the sled will take 10s to stop. Then we find the average velocity of 20m/s and then multiply to get 200m.
201
if you have a net force ( say for instance centripetal force) of something how can you solve for the instantaneous velocity?
well when an object is in circular motion we know that there is a net force acting toward the center (centripetal foce). which is just the force of gravity. So we can set mv^2/r= Gmm/r^2
202
if a rock is falling downward at an acceleration of 8m/s/s. What is the net force due to air resistance? mass of 10kg
Draw a free body. We know that there is a weight force point straight down at 100 N. We know if an object is accelerating there has to be a net force involved and here the net force will be in the downward direction because thats the way the object is accelerating. So add ma to the loosing side which is the Fup side and then solve 100 = Fup + (10)(8) 20N
203
If an object is accelerating upward what way is the net force pointing?
There is a net force in the upward direction. so an 1000 kg elevator being accelerated upward at 2m/s/s find the tension in the rope. 10000 + ma = Fup 12000
204
If an object say on a fulcrum is perfectly balanced. Is there a net toque on the object?
No, there is no net torque on the object it is in equalibrium. If there were a net torque the object would accelerate some amount in the clockwise or counterclockwise direction.
205
if a mass is attached to one end of a board with a fulcrum under it. what mass would have to be attatched to the other end to balance it.?
all you do in a question like this is set the TORQUES equal to each other and solve Tclockwise=Tcounterclockwise T=F*d*sineø
206
when you see average force on the mcat what is this a dead giveaway of what you'll be dealing with?
This is a dead giveaway that you'll be dealing with Work or Impulse. Remember the ∆E is equal to the amount of work. So if someone has a KE of 120 and then gets stopped. How much work was done? 120 then we can just divide this by the distance traveled and it will give us average force.
207
if there are two objects and one of them as 2 times as much power of the other. the first can pull a trailer with twice the weight in the same amount of time up a hill? Do twice the work in the same amount of time? Accelerate a trailer from rest with the same weight to twice the speed in the same amount of time?
True, True, False.
When solving questions dealing with power. Think about what power equals (∆E, and works over time) So its the amount of work done over a period of time. Two people can do the same amount of work but one may do it twice as fast meaning double the power. Also think about energy like KE=1/2mv^2 and how much power it would take to double the speed. It would take 4 times as much power.
208
for what type of collision do you have to worry about the signs?
inelastic conservation of momentum you have to keep track of signs but conservation of energy you dont. thats why for elastic collisions we use KE+KE=KE+KE
209
for pully problems what has the exceed number of ropes be pulled either by the box or by a person (2). The number of vertical ropes directly lifting the mass.
Note.
210
For any question that machine question that asks how long the ramp must be or how long the board is on the fulcrum ect. Or to figure out how much a person could lift using the aid of a machine what should you do?
First find how much the object would take to lift without the machine or how much the person can lift without the machine.
In this case, the crate requires 1,000 N of force, but the worker is only capable of 200 N. So he must magnify the distance by a factor of 5 to keep the work the same. A machine doesn't change the amount of work done ever.
211
when are velocities exchanged in an elastic collision?
When the masses are the same
212
When is ME the highest for an object? what is the equation for stress?
When it doesn't distort or strain as much under a given stress.
stress = Force/area
213
rotational equilibrium vs translational equilibrium
external forces must sum to 0, with rotational external torques must sum to 0
214
conservation of momentum and energy
Remember that momentum is ALWAYS conserved in a collision! Whether it is angular or linear momentum, elastic or inelastic collision, momentum is always conserved! This makes A and B clearly false because the stem asks for entities that are NOT conserved. Mechanical energy is the sum of potential and kinetic energy. The wrench had potential energy when it was dropped, but we are told by the stem to focus only on the collision itself. At the moment the collision occurs the wrench has no potential energy. Immediately after the collision it will have no potential energy either, and so it can be said that potential energy was conserved, or “remained constant” across the collision. These observations combined make C the correct answer. KE is conserved only in perfectly elastic collisions. One of the hallmarks of a perfectly elastic collision is no deformity or damage to the two objects. It is almost certain the wrench and/or the turbine blade will be scuffed, scratched, bent or broken in some way as a result of the collision.
