N3) Masses m1 and m2 are connected by a massless rope slung over a massless,

frictionless pulley. Assume m2>m1. The pulley and the masses are inside a vat containing

water, and each of the masses experiences a drag force equal in magnitude to |FDRAG| =

bv2; b is the same for both masses. The drag forces cause the masses to reach a terminal

velocity, vT. You may neglect any effects due to buoyancy.

1. When the terminal velocity is reached, what is the acceleration of mass m2?

a. The acceleration of m2 is upward. b. The acceleration of m2 is downward. c. The acceleration of m2 is zero. 2. Find an expression for the terminal velocity, vT.

a. gb

mmvT

22 12

b. gb

mmvT

2

12

c. gb

mmvT

2

12

d. gb

mmvT

12

e. gb

mmvT

12

N5) A block M1 with mass 3kg sits atop a frictionless inclined plane. The inclined plane is at an angle of =30 from the horizontal.

Block M1 is connected to block M2 (mass=2kg) through a massless string around an ideal, frictionless pulley.

1. Which way is block M2 accelerating?

A. upwards

B. downwards

C. it is not moving

2. With ‘a’ defined as the magnitude of the acceleration ( 0a ³ ) and g=+ 9.81 m/s2, which is the correct expression for the

magnitude of the tension in the string?

A. 0 N

B. M2(g-a)

C. M2(a+g)

D. M2ag/(a+g)

E. M1g sin

=30

M2=2kg

M1=3kg

N7) Two blocks A and B are connected by a string named string 2. A hand pulls string 1, which is attached to block A, so that the

blocks move upward and gradually slow down. The strings remain taut at all times.

Assume the strings are massless and do not stretch. The mass of block B is greater than that of block A.

1. Three students drew the free-body diagrams below for block A. Choose the diagram that is most nearly

correct.

Tension in string 1

Tension instring 2

Weight of A

Pulling forceof hand

Weight ofblock B

Weight of A

Tension instring 1

Weight of A

(a) (b) (c)

2. Is the upward force on block B by string 2 greater than, less than, or equal to the weight of block B? (a) greater than

(b) less than

(c) equal to

string 2

string 1

A

B

N8) Two masses m and 4m are connected by a string that runs over a massless pulley. The pulley can either be locked in place so

that it cannot rotate or unlocked to allow it to rotate freely. The pulley is suspended from a force probe, much like one used in Phys

211 Lab 2, which measures the upward force on the pulley. The force probe reads a positive force when it is pulled.

1. What will the force probe read when the pulley is locked and the whole system is motionless?

a. mg

b. 2mg

c. 3mg

d. 4mg

e. 5mg

2. Which of the following statements best describes the tension in the string T when the pulley rotates freely?

a. T > mg

b. T = mg

c. T < mg

x

y Force

probe pulley

4m m

string

N16) A satellite is put into a uniform circular orbit around the earth. The radius of the satellite’s orbit is Rs = 6.3 x107 m (measured

from the center of the earth). The satellite has a mass of 145 kg.

G=6.7x10-11 m3 kg-1 s-2

Me=6.0x1024 kg

Re=6.4x106 m

1. What is the period of the satellite’s orbit? (Note: 1 day = 86,400 s)

A. 0.2 days

B. 1.0 days

C. 1.8 days

D. 4.7 days

E. 27.0 days

2. Suppose the satellite were in orbit about the moon (Mmoon= Mearth /81 ). At what radius, compared to Rs above, would the

satellite have the same orbital period as in the previous problem?

A. R = 81Rs

B. R = Rs/9

C. R = 3

sR 81

Re

Rs Earth:

mass Me

satellite mass = 145 kg

N19) A roller coaster car of mass m is at the top of a loop-the-loop section of the track as shown in the diagram.

1. What speed, v, is required for the roller coaster car

to have a normal force exerted on it by the track which

is equal to the car’s weight? Note that this normal

force acts in the direction of g.

a. m/grv

b. grv

c. grv 2

d. 2/grv

e. 0v

2. If the speed of the car is twice as large as v calculated above, the magnitude of the normal force is

a. larger than the car’s weight.

b. equal to the car’s weight.

c. smaller than the car’s weight.

g

v

r

N27) A block of mass m = 0.5 kg rests on top of a block of mass M = 2.0 kg. A string attached to the block of mass M is pulled so that

its tension is T = 6.0 N at a 20o angle to the horizontal as shown. The blocks move together. The coefficient of static friction at the

surface between the blocks is s = 0.4; there is no friction at the surface between block M and the floor.

1. What is the acceleration, a, of the two-block system?

a. a = 1.63 m/s2

b. a = 2.26 m/s2

c. a = 3.18 m/s2

d. a = 3.72 m/s2

e. a = 4.89 m/s2

2. The tension T is now increased - what is the maximum tension, Tmax, with which the string can be pulled such that the blocks

continue to move together (i.e. that the block of mass m does not start to slide on top of the block of mass M)?

a. Tmax = 7.67 N

b. Tmax = 8.31 N

c. Tmax = 8.94 N

d. Tmax = 9.36 N

e. Tmax = 10.44 N

20o M

m T s = 0.4

= 0

g

30o

M

m

s = 0.6

= 0 g

N28) Two blocks of mass m = 2 kg and M = 5 kg are

positioned as shown on top of an inclined plane. There is

no friction at the surface between the two blocks, but there

is friction on the surface between the large block and the

incline. The string attached to the block of mass m is

parallel to the incline. The system is in equilibrium with

both blocks stationary.

1. What are the forces exerted on each block?

a. Forces on m: Tension, weight

Forces on M: Weight, friction, normal force due to

incline, normal force due to m

b. Forces on m: Tension, weight, friction

Forces on M: Weight, friction, normal force due to incline, normal force due to m

c. Forces on m: Tension, weight, normal force due to M

Forces on M: Weight, friction, normal force due to incline, normal force due to m

d. Forces on m: Tension, weight, normal force due to M

Forces on M: Weight, friction, normal force due to incline

e. There are no forces on either mass because they are both in equilibrium

2. What is the magnitude of the net force, Fnet, on the block of mass m?

a. Fnet = 0 N

b. Fnet = 9.8 N

c. Fnet = 12.3 N

d. Fnet = 19.6 N

e. Fnet = 47.3 N

E3) The next two questions relate to the following situation

In lab 4 a cart of mass M = 700 g is attached to a spring with force

constant k = 3 N/m and suspended on a frictionless incline plane that

makes a 30° angle with respect to the horizontal. With the spring in

the unstretched position, the cart is released from rest at x = 0.

1. What is the maximum extension of the spring when the cart is at

its lowest point on the incline?

a. 1.1 m

b. 3.8 m

c. 4.5 m

d. 1.7 m

e. 2.3 m

2. For what value of x does the cart have the largest kinetic energy?

a. 1.1 m

b. 0.5 m

c. 2.3 m

d. 5.2 m

e. 0.9 m

30°

M

k

x x=0

motion detector

g

E8) The next two questions refer to the following situation.

A block is on a plane inclined at an angle = 30 from the horizontal. The coefficient of the kinetic friction between the block and

the incline is k = 0.12. A force is applied along the incline to a block of mass m = 2 kg as shown in the figure, and the mass moves up

the incline at constant velocity v = 2 m/s.

1. How much work does force F do in 0.6 seconds?

a. 24.43 J

b. 14.22 J

c. 18.94 J

d. 22.82 J

e. 30.03 J

2. Considering all forces acting on the block, which force does zero work on the block?

a. The normal force of the incline

b. The gravitational force of the Earth

c. The friction force between the block and the incline

g

E11) The next two problems concern identical blocks that initially have the same velocity V at the bottom of two ramps. The first

ramp inclined at a shallower angle (1 ) with respect to the horizontal than the second ramp (2 ). The maximum heights reached by

the blocks are h1 and h2, respectively.

1. Assume that both ramps are frictionless. Which statement is most correct concerning the maximum heights reached by the

blocks?

a. h2 = h1

b. h2 > h1

c. h2 < h1

2. Now assume instead that in both cases there is the same (non-zero) kinetic coefficient of friction between the blocks and the

ramps. Which statement is most correct concerning the maximum heights reached by the blocks?

a. h2 = h1

b. h2 > h1

c. h2 < h1

2 1

h1

V

V

h2

E13) The next two questions are about the following situation:

A small box of mass M=10 kg is released from rest at a height of 2 meters on a frictionless incline as shown. At the bottom of the

ramp, it encounters a 1 meter long rough surface with k=0.25, and then a frictionless circular rise.

1. At what height, h, does the box stop on the circular rise?

a. 2 meters

b. 1.75 meters

c. 1.50 meters

d. 1.25 meters

e. 1.0 meters

2. Compare the magnitude of the work done by gravity to the magnitude of the work done by friction in the above problem at the

moment when the mass has reached its maximum height, h, on the circular rise.

a. Wgravity > Wfriction

b. Wgravity < Wfriction

c. Wgravity = Wfriction

2m h?

1m

E14) The next two questions are about the following situation:

A 6 kg box is pulled across a rough floor by a rope. There is friction between the box and the floor. The tension in the rope is T=5 N.

Consider a time interval during which the box moves a distance of 2 m, and its velocity decreases from 1.5 m/s to 0.8 m/s.

1. How much work is done on the box by the rope?

a. 0 J

b. 10 J

c. -10 J

2. How much work is done on the box by friction?

a. -4.83 J

b. -6.91 J

c. -8.11 J

d. -9.25 J

e. -14.83 J

T

v

E15) The next two questions are about the following situation:

A 6 kg box is pulled across a horizontal floor by a rope. The tension in the rope is

T = 5 N. Consider a time interval during which the velocity of the box increases from

0.8 m/s to 1.5 m/s.

1. If the floor is frictionless, how far has the box moved?

a. 0.47 m

b. 0.97 m

c. 1.21 m

d. 1.50 m

e. 1.77 m

2. Suppose now that there is friction between the box and the floor. The box now has to be pulled for 2 m to increase its speed

from 0.8 m/s to 1.5 m/s (still with tension T = 5N). How much work is done on the box by friction?

a. –4.83 Joules

b. –5.17 Joules

c. –8.11 Joules

d. –9.25 Joules

e. –14.83 Joules

T

v

E17) The next two questions are about the following situation:

A planet of mass M and radius R and a smaller planet of radius R/2 and mass M/8 are separated by a distance 6R between their

centers.

1. Where is the center of mass of this two-body system with respect to the center of the larger planet?

a. R/3

b. R/2

c. 2R/3

d. 5R/6

e. R

2. If a missile is launched from the north pole of the larger planet, what is the escape velocity, V, for the missile (taking into account

the gravitational force from both planets)?

a. V < 2GM

R

b. V = 2GM

R

c. V > 2GM

R

M

R R/2

6R

E20) The next two problems refer to the following situation:

A block of mass m=100g is launched horizontally on a frictionless track by compressing a spring of constant k=78N/m. After 1m

(from the position of the spring at equilibrium) the track turns upward at a 30° angle as shown in the figure below. The height

difference between the lower and upper level is 1.4m.

1. If you compress the spring by a distance of 20cm, what is the horizontal range of the block x shown in the figure?

a. 12cm

b. 33cm

c. 67cm

d. 93cm

e. 123cm

2. Let x be the answer to the previous question. If there is friction between the track and the block, the horizontal range of the

block is now:

a. greater than x

b. equal to x

c. smaller than x

g

P1) The next three questions refer to

the following situation

A frictionless ramp of mass 3m is initially at rest on a horizontal frictionless floor. A small box of mass m is placed at the top of the

ramp and then released from rest. After the box is released, it slides down the ramp and onto the horizontal floor, where it is

measured to have a speed v, having fallen a total distance h.

1. What is the speed V of the ramp after the box has left the ramp?

A.

B.

C.

D.

E.

2. If there were kinetic friction between the ramp and the floor, but none between the block and the ramp, the speed V of the

ramp after the box has left the ramp, compared to its speed when both the ramp and the floor are frictionless, would be

A. Less

B. The same

C. More

g

3h

16

gh

13

gh

g

6h

12

gh

P3) The next three questions are about the following situation:

A 5 kg block slides on a horizontal, frictionless surface with a velocity of 2 m/s. It collides with an ideal, massless spring which is

attached to a 15 kg block which is initially at rest. The spring has a spring constant of k = 50 N/m.

1. At the instant the spring is maximally compressed, both masses will be traveling with a common velocity of

a. 0.25 m/s

b. 0.5 m/s

c. 1 m/s

d. 1.5 m/s

e. 2 m/s

2. When the spring is maximally compressed, how do the magnitudes of the acceleration of the two blocks compare?

a. The acceleration of the 5 kg block is 3 times the acceleration of the 15 kg block.

b. The acceleration of the 15 kg block is 3 times the acceleration of the 5 kg block.

c. The acceleration of the 5 kg block equals the acceleration of the 15 kg block.

P7) The next two questions are about the following situation:

A block of mass M1 slides on a horizontal, frictionless surface with a velocity of V1. It collides with an ideal, massless spring which is

attached to a block of mass M2 which is initially at rest. The spring has a spring constant of k = 20 N/m.

1. At the instant the spring is maximally compressed, both masses will be traveling with a common velocity, V, of

a. M1V1 / M2

b. M1V1 / (M1+M2)

c. (M1+M2)V1 / M1

2. Assuming M1 = 5 kg, M2 = 25 kg, and V1 = 3 m/s, what is the maximal compression of the spring during the collision?

a. 0.55 m

b. 0.74 m

c. 1.37 m

P11) The next two questions refer to the following situation

A car of mass 2000 kg is travelling along a straight road at 60 km/hr. It collides completely inelastically with another car, of mass

2600 kg, that is initially stationary in the middle of the road.

1. What is the ratio of the final kinetic energy of the two-car system after the collision to its initial kinetic energy?

A. 10/13

B. 13/20

C. 23/10

D. 13/23

E. 10/23

2. What is the speed, in km/hr, of the two cars (stuck together) immediately after the collision?

A. 46.2

B. 33.9

C. 26.1

D. 19.8

E. 15.3

P13) The next two questions refer to the following situation:

A pendulum is made by attaching a piece of putty of mass 0.24 kg to the end

of a massless string of length L = 1 m. The putty is swung out until it is at a

height h = 0.2 m above the ground and released from rest. When the putty is

at the lowest point in the swing, it collides with and sticks to another,

stationary piece of putty of mass 0.36 kg, and the resulting mass of putty

continues swinging to the right.

1. What is the kinetic energy, K, of the pendulum just before it strikes the

putty resting on the ground?

a. K = 0.34 J

b. K = 0.39 J

c. K = 0.47 J

d. K = 0.53 J

e. K = 0.87 J

2. How does the new maximum height reached by the center of mass of the two-putty system, H, compare to the original height h?

a. H = (0.16)h

b. H = (0.24)h

c. H = (0.08)h

d. H = (0.44)h

e. H = (0.12)h

m=0.24 Kg

m=0.36 Kg

L=1 m

h=0,2 m

P14) The next four questions refer to the following situation. Consider the following two cases:

Case 1 Case 2

In case 1 a ball of mass m is thrown horizontally with speed v0 at a stationary box of mass M. The ball bounces off the box and after

the collision the box is moving to the right with V1 and the ball is moving to the left with speed vf.

In case 2 a ball of mass m is thrown horizontally with speed v0 at a stationary box of mass M. The ball sticks to the box and after the

collision the box (with the ball stuck to it) is moving to the right with speed V2. In both cases the box slides without friction. Assume

all motion is horizontal.

1. In case 2 it is observed that V2 = v0/3. What is the ratio of masses M/m?

a. M/m = 1/2

b. M/m = 3/4

c. M/m = 4/3

d. M/m = 3/2

e. M/m = 2

2. In case 1 it is observed that vf = v0/2. What V1/v0?

a. V1/v0 = 3M/2m

b. V1/v0 = 2M/3m

c. V1/v0 = 3m/2M

d. V1/v0 = 2m/3M

e. V1/v0 = m/2M

v0 v0

M M m m vf

V1 V2

P15) The next two questions are about the following

situation:

A small steel ball of mass 2 kg is attached to the end of a

massless string of length 0.5 m which is fixed at the

opposite end. The string is pulled taut and held

horizontally, as shown above. The ball is then released

from rest. At the bottom of the path, the ball strikes a

steel block of mass 6 kg initially at rest on a horizontal frictionless surface.

1. What is the speed of the steel ball just before the collision?

a. 2.27 m/s

b. 2.88 m/s

c. 3.13 m/s

d. 3.72 m/s

e. 4.65 m/s

2. In the x-direction, if the velocity of the ball just before the collision is v and the velocity of the ball just after the collision is -v/3,

what is the velocity of the block just after the collision?

a. 4v/9

b. 2v/3

c. 3v/4

d. 3v/2

e. v

x

P20) The next two questions are about the following situation.

A spherical object of mass M, initially at rest, explodes into 3 pieces with masses M/2, M/4 and M/4. After the explosion, the pieces

move in the x-y plane.

1. Suppose the final velocity of the large piece is v = v j. In this case, after the explosion, the total momentum of the two smaller

pieces, Psmall, is

a. Psmall = 0

b. Psmall = (Mv/2) j

c. Psmall = - (Mv/2) j

2. Suppose in a different situation that the magnitudes of the final momenta of all three pieces were the same – all equal P. If the

final momentum of the larger piece is again in the j direction, what is the component, px, of the final momentum of one of the

smaller fragments in the i direction?

a. Ppx2

1

b. Ppx2

1

c. Ppx4

3

d. Ppx5

3

e. Ppx

M3) The next three questions refer to the following situation.

Two blocks of mass mA and mB are placed side by side on a frictionless table. At time t0 both blocks are at rest and a constant force of

the same magnitude is applied to each of the blocks. Block A has a smaller mass than block B (mA < mB).

1. How do the momenta of the two blocks compare 5 seconds after t0?

a. pA < pB

b. pA > pB

c. pA = pB

2. After each block has traveled the distance of 1 m, which is correct?

a. pA = pB

b. KA = KB

c. all of the above

mA

mB

F

F

top view

M7) The next three questions refer to the following situation:

A small block of mass m slides down a frictionless ramp that makes an angle of 60 º with the horizontal. The ramp joins smoothly

onto a circular track of radius R which ends where it is vertical, as shown in the figure. The block is released from rest at a distance

3R above the horizontal and leaves the track at point A.

1. After the block leaves the track, how high above the lowest point of the track does the block rise?

a. 3 3 R

b. 3R/2

c. 3R

2. What is the magnitude of the net acceleration on the block just before the block leaves the track?

a. g

b. 2g

c. 5 g

d. 4g

e. 17 g

R R

A 3R

60

m

M8) The next two problems to the following situation:

A skier is on top of a frictionless, spherical mountain of radius R=300m.

1. From rest, she begins to slide down the hill. What is the vertical distance between the top of the mountain and the place where

she leaves the ground?

a. 10m

b. 40m

c. 100m

d. 166m

e. 300m

2. Let h be the answer to the previous problem. If the skier had a non-zero initial velocity, the vertical distance between the top of

the mountain and the spot where she would leave the ground would be

a. smaller than h

b. equal to h

c. greater than h

g

cos = (R-h)/R R R-h

top

M9) The next three questions refer to the following situation:

A small block of mass m slides down a frictionless ramp that makes an angle of 60 º with the horizontal. The ramp joins smoothly

onto a circular track of radius R which ends where it is vertical, as shown in the figure. The block is released from rest at a distance

3R above the horizontal and leaves the track at point A.

1. What is the magnitude of the net acceleration on the block just before the block leaves the track?

a. g

b. 2g

c. 5 g

d. 4g

e. 17 g

2. If the flat section had a coefficient of kinetic friction μk =0.2 (and all other surfaces are frictionless), what is the maximal length of

the flat section in order for the block to reach point A?

a. 3R

b. 6R

c. 10R

R R

A 3R

60

m