x

yA

B

a) (length of ) (component of parallel to )

b) (length of ) (component of parallel to )

c) d) cos

e) all of the above

x x y y

A B A

B A B

A B A B AB

Which of the following is the best description of the dot product ?

A B

Dot Product

x

y

ˆ3A x

ˆ ˆ2B x y

26.60

Which of the following is the best description of the dot product ?

A B

ˆ ˆ(a) 3 5 cos 26.6 (b) 6 3

ˆ(c) 6 (d) 6 0

(e) (a) and (d)

x y

x y

�

Suppose you want to ride your mountain bike up a steep hill. Two paths lead from the base to the top, one twice as long as the other. Compared to the average force you would exert if you took the short path, the average force you exert along the longer path is

(a) four times as small.

(b) three times as small.

(c) half as small.

(d) the same.

(e) undetermined—it depends on the time taken.

Work

v

A

B CThe platform on the right pushes the blocks up at a constant velocity

1. Does the block A do work on block B ?

a) yes b) no

2. Is the work done by block A on block B

a) negative b) positive c) zero

3. Is the work done by block B on block A

a) negative b) positive c) zero

4. Is the work done by the earth on block C

a) negative b) positive c) zero

5. Is the net work done on the block C

a) negative b) positive c) zero

Gravitational Potential Energy

In the expressions below, h is a height and m is a mass

Which of the expressions below is the gravitational potential energy of a body?

Recall:

(1) Energy is measured in joules

1 J = 1 N m = 1 kg m2s-2

(2) W= F·s = m·a·s

(a) mg (b) mh (c) gh

(d) mgh (e) ½mh2

Use dimensional analysis and any other arguments to prove to a colleague that your answers are correct.

hm

If we choose the gravitational potential energy to be zero for an object sitting on the table, what is its potential energy when on the floor?

a) positive

b) negative

c) zero

Thermal Energy Due to Kinetic Friction

In the expressions below, x is a change in length, N is a normal force between two surfaces in contact, m is a mass, µk is a coefficient of kinetic friction

Which of the expressions below is the thermal energy due to kinetic friction?

Recall: 1 J = 1 N m = 1 kg m2s-2 and W= F·s = m·a·s

(a) µkN (b) µkgx (c) µkNx

(d) Nx (e) ½µkmgx 2

Use dimensional analysis and any other arguments to prove to a colleague that your answers are correct.

Kinetic Energy

In the expressions below, v is a speed, v is a change in speed and m is a mass

Which of the expressions below is the kinetic energy of a moving body?

Recall:

Energy is measured in joules: 1 J = 1 N m = 1 kg m2s-2

(a) mv (b) mv

(c) ½mv2 (d) ½m(v)2

Use dimensional analysis and any other arguments to prove to a colleague that your answers are correct.

Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has

(a) as much kinetic energy as the lighter one.

(b) twice as much kinetic energy as the lighter one.

(c) half as much kinetic energy as the lighter one.

(d) four times as much kinetic energy as the lighter one.

(e) impossible to determine

Potential Energy of a Spring

In the expressions below, x is a position, x is a change in length and k is a spring constant in N/m.

Which of the expressions below is the potential energy of a spring?

Recall:

Energy is measured in joules: 1 J = 1 N m = 1 kg m2s-2

(a) kx (b) kx (c) -kx

(d) ½kx2 (e) ½kx2

Use dimensional analysis and any other arguments to prove to a colleague that your answers are correct.

A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring?

(a) 96 m

(b) 48 m

(c) 24 m

(d) 12 m

(e) 6 m

Work & Energy

A cart on an air track is moving at 0.5 m/s when the air is suddenly turned off. The cart comes to rest after traveling 1 m. The experiment is repeated, but now the cart is moving at 1 m/s when the air is turned off. How far does the cart travel before coming to rest?

(a) 1 m

(b) 2 m

(c) 3 m

(d) 4 m

(e) impossible to determine

A block initially at rest is allowed to slide down a frictionless ramp and attains a speed v at the bottom. To achieve a speed 2v at the bottom, how many times as high must a new ramp be?

(a) 1

(b) 2

(c) 3

(d) 4

(e) 6

Suppose you drop a 1-kg rock from a height of 5 m above the ground. When it hits, how much force does the rock exert on the ground?

(a) 0.2 N

(b) 5 N

(c) 49 N

(d) 9.8 N

(e) impossible to determine

(a) The thermal energy produced in the sliding surfaces equals the work done by gravity (the gravitational force of the earth on the block).

The block is accelerating as it moves down the plane. Which of the following statements is (are) correct?

av=0 m/s

hv

(b) The total work done by gravity on the block equals the total amount of kinetic and thermal energy at the bottom.

(c) The kinetic energy of the block at the end is equal to the potential energy of the block at the start.

(d) The total work done by gravity equals the decrease in the block’s potential energy.

(e) Answers (b) and (d)

If the block is accelerating and K is the change in the block’s kinetic energy, the work done by the constant applied force is

(a) Fs

(b) Fs + K

(c) F cos s

(d) + K

(e) (b) and (d)

F s

F

s

F

s

If the block is accelerating and K is the change in the block’s kinetic energy, the work done by the constant applied force is

F

(a) F cos s + K + thermal energy in the rubbing surfaces

(b) K + thermal energy in the rubbing surfaces

(c) Fs + K

(d) F cos s

(e) Fs

Nmg

f k

F

s

coefficientof friction

k

The block below is pulled to the right by the force at a constant velocity

F

What is the work done by the ‘puller’ to move it through displacement

s

a) b)

c) cos d) sin

e) cos

k

k

Fs f s

F s F s

F f s

Nmg

f k

F

s

coefficientof friction

k

The block below is pulled to the right by the force at a constant velocity

F

What is the work done by friction as the block is pulled a displacement ?

s

a) b)

c) cos d) cos

e) cos

k k

k

k

f s f s

F s F s f s

F s f s

A box is pulled up a hill a distance s by a rope under tension T. The FBD of the box is shown on the right

1. The work done by the rope is

(a) T s (b) (T - fk) s (c) (T - fk - mg sin) s (d) zero

2. The work done by the friction is

(a) fk s (b) -fk s (c) fk cos s (d) zero

3. The work done by the normal force is

(a) Nsin s (b) Ncos s (c) -Nsin s

(d) -Ncos s (e) zero

4. The work done by gravity is

(a) mg sin s (b) -mg sin s (c) mg cos s

(d) -mg cos s (e) zero

Nmgfk

TsT

Sketch the graph of the force F required to stretch the spring a distance x.

Which of the following is most correct?

x

F

(b)

x

F

x

F

x

F

(d)

(a)

(c)

Work and F(x) Graphs

A spring has a force constant k = 8 N/m. Therefore, the plot of force vs. extension of the spring looks like

What is the work required to extend the spring a distance of 0.2 m?

(a) (1.6 N)(0.2 m) (b) ½(1.6 N)(0.2 m)

(c) (8 N/m) (0.2m) (d) None of the above.

x

Fslope = 8 N/m

0.2 m

A boy pulls a cart across flat ground with a force parallel to the ground which varies with distance as sketched below

How much work has the boy done in this time?

F

20 N

20 2510x(m)

F

a) zero b) 250 N

c) 350 N m d) 500 J

e) Can’t tell because the time is not given

The figure below is a potential-energy diagram U(x) of a ball on a frictionless track.

Starts from rest

CA

D

B

x

U

Which of points A B C D is (are)…

(a) …the point of maximum velocity

(b) …a point of zero velocity

(c) …a point of unstable equilibrium

(d) …a point of stable equilibrium

Potential-Energy Diagrams

The figure on the right following is potential-energy diagram for a mass vibrating horizontally on the end of a spring.

U=1/2 kx2U

x

Massed released

0Neglecting friction, which of the following diagrams best represents the kinetic energy of the mass?

K

x0

(B)K

x0

(A)

K

x0

(C)

A sports car accelerates from zero to 30 mph in 1.5 s. How long does it take for it to accelerate from zero to 60 mph, assuming the power of the engine to be independent of velocity and neglecting friction?

(a) 1.5 s

(b) 3 s

(c) 4.5 s

(d) 6 s

(e) 9 s

Power

System = Earth + box

Earth

A person pulls a box along the ground at a constant speed. If we consider Earth and the box as our system, what can we say about the net external force on the system?

(a) It is zero because the system is isolated.

(b) It is nonzero because the system is not isolated.

(c) It is zero even though the system is not isolated.

(d) It is nonzero even though the system is isolated.

(e) none of the above