Mechanics III

Question 1

Equation for Work

Answer 1

W = FdCos(theta)

theta is the angle between F applied and d (displacement)

Question 2

You and your friend are at a waterpark. Your friend goes down a slide that has a straight path vertically down, whereas as you go down a slide that meanders (and therefore doesn’t have a straight path vertically downward). Which of you will reach the bottom first? Which will be going the fastest at the bottom of each slide?

Answer 2

The friend will reach the bottom first, but the both of you will have the same speed when you reach the bottom of the slides

Question 3

Work is the measure of how much force contributes to the ___ of an object

Answer 3

displacement

Question 4

Work:

1) if theta is between 0 and 90, work is _____
2) if theta is 90, work is _____
3) if theta is between 90 and 180, work is _____

Answer 4

1) positive (because cos(0º-90º) always be a positive value)
2) zero (because cos90º is zero)
3) negative (because cos(90º-180º) will always be a negative value)

Question 5

Why is the work done by kinetic friction always negative?

Answer 5

Because kinetic friction always acts against motion, theta has a value of 180 and cos180 = -1

Question 6

Why is the work done by centripetal force always zero?

Answer 6

Because centripetal force is always perpendicular to the motion: W = Fdcos90 = 0 (because cos90 = 0)

Question 7

Work done by the normal force is usually zero. When is it not zero?

Answer 7

Work done by F_N is zero when the F_N is perpendicular to the motion of the object (or in other words, when the object doesn’t move vertically). Therefore, the work done by normal force is not zero when the object moves vertically

Question 8

A tension in a rope of 200N directed 45º above the horizontal pulls a 50kg crate to the R for 5m. If u_k = 0.2, how would you find the work done by the tension force, the work done by the force of friction, and the net work?

Answer 8

W_T = Fdcos(theta) = 200N(5m)(cos45) = 700J

W_f = F_fdcos(theta) = (u_kmg)dcos(theta) = 0.2(50kg)(10)(5m)(cos180) = 500J

W_net = W_T + W_f + W_{normal force} + W_grav

W_{normal force} + W_grav cancel eachother, so W_net = W_T + W_f = 700 - 500 - 200J

Question 9

Is gravity a conservative or nonconservative force?

Answer 9

conservative

Question 10

Work done by gravity depends only on the initial and final __1__ of the object, not the __2__ it follows

Answer 10

1) heights
2) path

Question 11

Equation for Work done by gravity, W_grav

Answer 11

W_grav = mgh

Question 12

If an object is moved 5m horizontally, what is the work done by gravity?

Answer 12

zero, because there is no change vertical displacement (or vertical change in height) of the object

Question 13

Equation for Power

Answer 13

P = W/t = Fdcos(theta)/time

measured: J/s = (kg)(m²)/s³ = W (Watts)

In other words, this is the rate which work is done

For a constant force parallel to a constant velocity: P = Fv

Question 14

Equation for Power when a constant force is applied that is parallel to a constant velocity?

Answer 14

P = W/t = Fdcos(theta)/t = Fdcos0º/t = Fd/t = Fv

cos0º = 1 and d/t = velocity

Question 15

Object A and object B are released from the same position of height. Object A is allowed to fall straight to the floor, while object B falls along an inclined planed to the floor.

A) If the plane is frictionless, for which object is the net work greater?

B) If the plane has friction, in which case is the net work greater?

C) If the plane is frictionless, in which case is the power greater?

Answer 15

A) same (because the only force doing work is gravity, and gravity is a conservative force)

B) Object A (because friction will make a negative contribution to work)

C) Object A (W_net will be the same for both, but Object A reaches the ground first. The same amount of Work is done over less time, thus the Power exerted on Object A is greater)

Question 16

Equation for Kinetic Energy

Answer 16

KE = 1/2mv²

KE is the energy of motion, measured in Joules

For the MCAT, when you’re given m and v, you should solve for KE

Question 17

As long as there is no change in other forms of energy, the total work done on an object, W_total = _____

Answer 17

W_total = deltaKE = KE_f - KE_i

Question 18

Work can be thought of as a transfer of energy.

1) If W_total is positive, the object ____ KE
2) if the W_total is negative, the object ____ KE
3) if the W_total = 0, the object ____ KE

Answer 18

1) gains
2) loses
3) neither gains nor loses KE; KE remains the same

Question 19

Near the surface of the earth, the change in potential energy, deltaPE, is equal to _____

Answer 19

mg(deltaH) = mass x gravity x change in height

Question 20

Conservation of Mechanical Energy: when only _____ forces (like gravity) are doing work, total mechanical energy is conserved

Answer 20

conservative

(Total mechanical energy is conserved when the path taken by an object is frictionless, or if aerodynamics is ignored)

Question 21

How is PE related to KE (ignoring friction and aerodynamics)

Answer 21

W = deltaKE

W_grav = -deltaPE (W_grav = mgh_final - mgh_initial = mgdeltah)

Therefore:

delta KE = -deltaPE → deltaKE + delta PE = 0

KE_f - KE_i = PE_f - PE_i → KE_i + PE_i = KE_f + PE_f

Question 22

Name 3 conservative forces and 2 nonconservative forces

Answer 22

conservative: gravity, electrostatic force, spring force
nonconservative: kinetic friction, drag

Question 23

What is the equation for the total work done when the nonconservative force (friction) is considered

Answer 23

KE_i + PE_i + W_nc = KE_f + PE_f → W_nc = deltaE

E: total mechanical energy

The value should be negative, because friction always does negative work

Question 24

Finding the forces of an inclined plane: What is the formula used to find each of the following forces:

1) gravity
2) normal force
3) friction
4) force parallel to the plane

Answer 24

1) F_grav = mgsin(theta) → this specifically refers to the force by gravity that pulls an object down an inclined plane
2) F_N = mgcos(theta)
3) F_f = umgcos(theta)

Question 25

What is mechanical advantage?

Answer 25

Refers to the factor by which a force can be reduced when using a simple machine

The mechanical advantage gained by using a machine will always be greater than 1

MA = F_resistance / F_effort

MA = mg/mgsin(theta) (the weight alone divided by moving the weight up an incline with a theta)

sin(theta) is always a decimal, and its value will always increase as the angle increases. This means that as the angle of the incline plane increases, the amount of Force required to move that object up that ramp increases.

Question 26

number of pulleys needs is equal to _________

Answer 26

the force you need to lift an object divided by the force you yourself can lift

i.e. You want to lift a block with mass, m, that requires 200N to be lifted, and you can only lift 50N: 200/50 = 4. You need 4 pulleys to lift that block. The force in one pulley is equal to the force you can lift. The tension force in the rope is the tension force produced by one pulley (which is also the force you yourself can lift)

Question 27

If a block with mass requires 200N of force to pull up, and you can only lift 50N, how many pulleys will you need to lift the block? What is the mechanical advantage?

Answer 27

200/50 = 4 pulleys to lift the block

MA = 4pulleys/1me = 4:1

Question 28

What’s the efficiency of all pulleys?

Answer 28

~80%-85%

Question 29

It requires 60J of work to lift a box. A pulley system that has 75% efficiency is used to lift this box. How much work will have to be performed by the pulleys in order to lift the box?

Answer 29

If the pulleys had 100% efficiency, they would only have to do 60J of work to lift the box; however, since there is only 75% efficiency, the pulleys will have to do more work in order to lift the box.

60J = 0.75W_pulleys

W_pulleys = 60J/0.75 = (60)4/3 = 240/3 = 80J

Thus, the pulleys must do at least 80J of work to be able to lift the box.

Question 30

Equation for conservation of total momentum?

Answer 30

m₁v₁ + m₂v₂ … = m₁v₁’ + m₂v₂’ …

Question 31

Distinguish between elastic, inelastic collisions, and perfectly inelastic collisions

Answer 31

Elastic collisions conserve KE

Inelastic collisions do NOT conserve KE (and therefore some KE is lost as another form of energy)

Perfectly inelastic collisions lose the most KE (objects stick together after collision)

Question 32

A ball is positioned at the bottom of an incline. The ball is pushed up an incline with an initial velocity of 2m/s, travels a certain distance up the hill, and then rolls back down. What is the velocity of the ball once it reaches back down to the bottom of the incline?

Answer 32

2m/s

Question 33

Object A is traveling at 2m/s when it collides into object B, which is stationary. They bounce off each other in a perfectly elastic collision and speed off in different directions. If object A is moving with a speed of 2/3 m/s post collision, how fast is object B moving?

Answer 33

4/3 m/s

no KE is lost, therefore 2 - 2/3 = 4/3

Question 34

If Alice did 10J of work while pushing Jeff in 5 seconds, and the force of friction did -2J of work, how much power did Alice exert?

Answer 34

P = 10/5 = 2W

The work done by friction doesn’t matter in this question. The power exerted by Alice is the work she does divided by the time it takes her.

Question 35

The main reason to use a simple machine to accomplish a task is:
A) to reduce the total work done

B) to increase power

C) to minimize the work done by friction

D) to reduce the amount of force that must be applied

Answer 35

D) to reduce the amount of force that must be applied

Note that the same amount of work will be done, but the force required to do that work is less.

Question 36

An object traveling in a circular path at a constant speed undergoes a continuously ___1__ (changing or constant) acceleration of ___2__ magnitude (changing or constant)

Answer 36

1) changing
2) constant

Question 37

The potential energy of a mass relative to the Earth is:
A) always proportional to height above the Earth

B) proportional to height above the Earth for heights much smaller than the radius of the earth

C) equal to its kinetic energy

D) inversely proportional to the square of the distance from the center of the Earth

Answer 37

B

Question 38

You lift 100kg from the ground to a 1m high table in 1hr. Your friend lifts 100kg to the same table in 15min. How much work and power did you exert compared to your friend?

Answer 38

Same amount of work was done by both you and your friend, but your friend exerted more power.