# Supplemental Material Physics ```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.
m2  m1
g
2b
m2  m1
b. vT 
g
2b
m2  m1
c. vT 
g
2b
m2  m1
d. vT 
g
b
m2  m1
e. vT 
g
b
a. vT  2
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.
M1=3kg
1. Which way is block M2 accelerating?
A.
upwards
B.
downwards
C.
it is not moving
M2=2kg
=30
2. With ‘a’ defined as the magnitude of the acceleration ( a ³ 0 ) and g=+ 9.81 m/s2, which is the correct expression for the
magnitude of the tension in the string?
A.
0N
B.
M2(g-a)
C.
M2(a+g)
D.
M2ag/(a+g)
E.
M1g sin
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.
string 1
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 in
string 2
Pulling force
of hand
(a)
Weight of
block B
B
Weight of 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
Tension in
string 1
Weight of A
Weight of A
A
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.
y
Force
probe
pulley
x
string
4m
m
1.
a.
b.
c.
d.
e.
What will the force probe read when the pulley is locked and the whole system is motionless?
mg
2mg
3mg
4mg
5mg
2.
a.
b.
c.
Which of the following statements best describes the tension in the string T when the pulley rotates freely?
T > mg
T = mg
T < mg
N16) A satellite is put into a uniform circular orbit around the earth. The radius of the satellite’s orbit is R s = 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
Re
satellite mass = 145 kg
24
Me=6.0x10 kg
Re=6.4x106 m
Earth:
Rs
mass Me
1. What is the period of the satellite’s orbit? (Note: 1 day = 86,400 s)
A.
B.
C.
D.
E.
0.2 days
1.0 days
1.8 days
4.7 days
27.0 days
2. Suppose the satellite were in orbit about the moon (M moon= 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 = R s
3
81
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.
v
r
a. v  gr / m
b. v  gr
c. v  2 gr
d. v  gr / 2
e. v  0
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
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.
s = 0.4
T
m
M
20
g
o
= 0
1.
a.
b.
c.
d.
e.
What is the acceleration, a, of the two-block system?
a = 1.63 m/s2
a = 2.26 m/s2
a = 3.18 m/s2
a = 3.72 m/s2
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
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.
= 0
m
s = 0.6
1. What are the forces exerted on each block?
a. Forces on m: Tension, weight
Forces on M: Weight, friction, normal force due to
30o
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
g
M
E3) The next two questions relate to the following situation
motion detector
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.
b.
c.
d.
e.
1.1 m
3.8 m
4.5 m
1.7 m
2.3 m
2. For what value of x does the cart have the largest kinetic energy?
a.
b.
c.
d.
e.
1.1 m
0.5 m
2.3 m
5.2 m
0.9 m
k
g
M
x=0
x
30°
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.
g
1.
a.
b.
c.
d.
e.
How much work does force F do in 0.6 seconds?
24.43 J
14.22 J
18.94 J
22.82 J
30.03 J
2.
a.
b.
c.
Considering all forces acting on the block, which force does zero work on the block?
The normal force of the incline
The gravitational force of the Earth
The friction force between the block and the incline
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.
V
V
1
h1
2
h2
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
E13) The next two questions are about the following situation:
2m

h?
1m
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.
b.
c.
d.
e.
2 meters
1.75 meters
1.50 meters
1.25 meters
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
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.
v
T
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.
b.
c.
d.
e.
-4.83 J
-6.91 J
-8.11 J
-9.25 J
-14.83 J
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.
v
T
1. If the floor is frictionless, how far has the box moved?
a.
b.
c.
d.
e.
0.47 m
0.97 m
1.21 m
1.50 m
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.
b.
c.
d.
e.
–4.83 Joules
–5.17 Joules
–8.11 Joules
–9.25 Joules
–14.83 Joules
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.
M
6R
R
R/2
1. Where is the center of mass of this two-body system with respect to the center of the larger planet?
a.
b.
c.
d.
e.
R/3
R/2
2R/3
5R/6
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 <
b. V =
c. V >
2GM
R
2GM
R
2GM
R
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.
g
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.
b.
c.
d.
e.
12cm
33cm
67cm
93cm
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
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?
g
A.
3h
1 gh
6
B.
1 gh
3
C.
g
D.
6h
1 gh
2
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
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.
a.
b.
c.
d.
e.
At the instant the spring is maximally compressed, both masses will be traveling with a common velocity of
0.25 m/s
0.5 m/s
1 m/s
1.5 m/s
2 m/s
2.
a.
b.
c.
When the spring is maximally compressed, how do the magnitudes of the acceleration of the two blocks compare?
The acceleration of the 5 kg block is 3 times the acceleration of the 15 kg block.
The acceleration of the 15 kg block is 3 times the acceleration of the 5 kg block.
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.
B.
C.
D.
E.
2.
10/13
13/20
23/10
13/23
10/23
What is the speed, in km/hr, of the two cars (stuck together) immediately after the collision?
A.
B.
C.
D.
E.
46.2
33.9
26.1
19.8
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.
L=1 m
1. What is the kinetic energy, K, of the pendulum just before it strikes the
putty resting on the ground?
m=0 .2 4 Kg
a.
b.
c.
d.
e.
K = 0.34 J
K = 0.39 J
K = 0.47 J
K = 0.53 J
K = 0.87 J
h=0 ,2 m
m=0 .3 6 Kg
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.
b.
c.
d.
e.
H = (0.16)h
H = (0.24)h
H = (0.08)h
H = (0.44)h
H = (0.12)h
P14) The next four questions refer to the following situation. Consider the following two cases:
v0
v0
m
vf
M
V1
m
M
V2
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 V 2. 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.
a.
b.
c.
d.
e.
In case 1 it is observed that vf = v0/2. What V1/v0?
V1/v0 = 3M/2m
V1/v0 = 2M/3m
V1/v0 = 3m/2M
V1/v0 = 2m/3M
V1/v0 = m/2M
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.
x
1. What is the speed of the steel ball just before the collision?
a.
b.
c.
d.
e.
2.27 m/s
2.88 m/s
3.13 m/s
3.72 m/s
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.
b.
c.
d.
e.
4v/9
2v/3
3v/4
3v/2
v
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?
1
P
2
a. p x 
b. p x 
1
P
2
c. p x 
3
P
4
d. p x 
3
P
5
e. p x  P
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).
top view
mA
mB
F
F
1. How do the momenta of the two blocks compare 5 seconds after t 0?
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
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.
m
A
3R
60 
R
R
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
5 g
c.
d. 4g
17 g
e.
 
 
M8) The next two problems to the following situation:
top
A skier is on top of a frictionless, spherical mountain of radius R=300m.
cos  = (R-h)/R
R-h

g
R
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
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.
m
A
3R
60 
R
R
1. What is the magnitude of the net acceleration on the block just before the block leaves the track?
a. g
b. 2g
5 g
c.
d. 4g
17 g
e.
 
 
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
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