Hour Exam 2 Review 9:00
Exam is Tomorrow (Wednesday)
at 7:00 pm
•
Hour Exam 2
xi mi

Center of Mass X cm 
 mi
• Work Energy
W
NC
• Impulse-Momentum
 KE  PE
 Ft  P
Two ice-skaters of mass 70 kg and 50 kg, each having an initial velocity
of 10 m/s in the directions shown, collide and fall and slide across the
ice together. The ice surface is horizontal & frictionless.
1. What is the speed of the skaters after the collision?
A)
B)
C)
D)
E)
V = 0 m/s
V = 1.7 m/s
V = 2.7 m/s
V = 10 m/s
V = 20 m/s
2. What is the angle q relative to the x axis that the two skaters travel after the collision?
A) q = 41 degrees
B) q = 28 degrees
C) q = 25 degrees
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
3. Which of the following remain constant as the pendulum swings down?
A) Horizontal component of the momentum of the ball
B) Horizontal component of the momentum of the cart
C) Horizontal component of the momentum of the ball + cart
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
4. What is the speed of the cart when the ball is at the bottom?
A)
B)
C)
D)
E)
Vcart = 1.17 m/s
Vcart = 1.75 m/s
Vcart = 2.44 m/s
Vcart = 2.91 m/s
Vcart = 3.37 m/s
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
5. What is the length L of the pendulum?
A) 0.59 m
B) 0.83 m
C) 1.18 m
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
6. How far to the right has the cart moved, when the ball is at the bottom?
A) L/2
B) L/3
C) L/4
7. A comet of mass 109 kg is observed at a distance from the sun of 8 x 1011 m
(mass of sun = 2 x 1030 kg) at a speed of 17000 m/s. Assuming no forces on it other than the
sun's gravity, how fast will it be going when it is a distance of 2.25 x 1011 m from the sun?
(The universal gravitational constant is G = 6.67x10-11 Nm2/kg2)
A)
B)
C)
D)
E)
12,900 m/s
18,300 m/s
23,700 m/s
29,200 m/s
33,800 m/s
8. Two fishermen, of masses 70 and 90 kg stand at opposite ends of their 20 meter boat. The
boat (without fishermen) has a mass of 400 kg. There is no wind or current and the boat can
move without friction on the water’s surface. The 90 kg fisherman walks to the left end of the
boat. How far has the boat moved when the fisherman reaches the left end?
A)
B)
C)
D)
E)
5.8 m to the right
3.2 m to the right
The boat does not move
3.2 m to left
5.8 m to left
9. The centers of three spheres having masses 1 kg, 2 kg, and 3 kg are placed at the corners of
an equilateral triangle whose sides are each 1 meter long, as shown below. What is the
horizontal position of the center of mass?
3 kg
y
A) xcm = 0.50 m
B) xcm = 0.58 m
C) xcm = 0.76 m
2 kg
1 kg
1m
x
An artillery shell of mass 20 kg is fired from a
rail car which is initially at rest on a horizontal
frictionless track. The combined mass of the
car and cannon is 2000kg. As viewed by
someone on the ground the shell moves with an
initial speed of 300 m/s at an angle of 27
degrees above the horizontal and the rail car
recoils to the right.
10. Relative to the ground, what is the speed of the rail car after the shell is fired?
A) 1.36 m/s
B) 2.67 m/s
C) 3.00 m/s
An artillery shell of mass 20 kg is fired from a
rail car which is initially at rest on a horizontal
frictionless track. The combined mass of the
car and cannon is 2000kg. As viewed by
someone on the ground the shell moves with an
initial speed of 300 m/s at an angle of 27
degrees above the horizontal and the rail car
recoils to the right.
11. If the shell was accelerated through the cannon for a time of 0.03 seconds, what was the
average force on the shell during this time?
A)
B)
C)
D)
E)
200 N
2,300 N
15,000 N
90,000 N
200,000 N
A block of mass m = 1.8 kg starts at rest on a
rough inclined plane a height H = 8m above the
ground. It slides down the plane, across a
frictionless horizontal floor, and then around a
frictionless loop-the-loop of radius R = 2.0 m.
On the floor the speed of the block is observed
to be 11 m/s.
12. What is the work done by friction on the block as it slides down the inclined plane?
A)
B)
C)
D)
E)
-49 J
-28 J
-78 J
-23 J
-32 J
A block of mass m = 1.8 kg starts at rest on a
rough inclined plane a height H = 8m above the
ground. It slides down the plane, across a
frictionless horizontal floor, and then around a
frictionless loop-the-loop of radius R = 2.0 m.
On the floor the speed of the block is observed
to be 11 m/s.
13. What is the magnitude of the normal force exerted on the block at the top of the loop?
A)
B)
C)
D)
E)
0N
5.1 N
9.8 N
17.6 N
20.6 N
2.5 kg
k=250 N/m
h=1.5 m
 = 0.4
d = 0.50 m
A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a
frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5
meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with
spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.
14. What is the speed of the box at the bottom of the ramp?
A) 5.4 m/s
B) 3.7 m/s
C) 2.8 m/s
2.5 kg
k=250 N/m
h=1.5 m
 = 0.4
d = 0.50 m
A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a
frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5
meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with
spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.
15. What is the maximum distance the spring is compressed by the box?
A)
B)
C)
D)
E)
0.50 m
0.66 m
0.83 m
0.94 m
1.21 m
2.5 kg
k=250 N/m
h=1.5 m
 = 0.4
d = 0.50 m
A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a
frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5
meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with
spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.
16. What is the maximum height to which the box returns on the ramp?
A) 1.1 m
B) 1.3 m
C) 1.5 m
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.
17. In which case is the change in momentum of the ball the biggest?
A) Case 1
B) Case 2
C) The change in momentum of the ball is the same in both cases.
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.
18. Which of the following statements best describes V1 and V2?
A) V1 < V2
B) V1 = V2
C) V1 > V2
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.
19. In case 2 it is observed that V2 = v0/3. What is the ratio of masses M/m?
A)
B)
C)
D)
E)
M/m = 1/2
M/m = 3/4
M/m = 4/3
M/m = 3/2
M/m = 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.
20. In case 1 it is observed that vf = v0/2. What V1/v0?
A)
B)
C)
D)
E)
V1/v0 = 3M/2m
V1/v0 = 2M/3m
V1/v0 = 3m/2M
V1/v0 = 2m/3M
V1/v0 = m/2M
Two blocks of mass mA and mB are placed side by side on a
frictionless horizontal 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).
21. How do the momenta of the two blocks compare 5 seconds after t0?
A) pA < pB
B) pA > pB
C) pA = pB
22. How do the kinetic energies of the two blocks compare 5 seconds after t0?
A) KA < KB
B) KA > KB
C) KA = KB
Two blocks of mass mA and mB are placed side by side on a
frictionless horizontal 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).
23. After each block has traveled the distance of 1 m, which is correct?
A) pA = pB
B) KA = KB
C) Both of the above
Hour Exam 2 Review 11:00
Exam is Tomorrow (Wednesday)
at 7:00 pm
•
Hour Exam 2
xi mi

Center of Mass X cm 
 mi
• Work Energy
W
NC
• Impulse-Momentum
 KE  PE
 Ft  P
Two ice-skaters of mass 70 kg and 50 kg, each having an initial velocity
of 10 m/s in the directions shown, collide and fall and slide across the
ice together. The ice surface is horizontal & frictionless.
1. What is the speed of the skaters after the collision?
A)
B)
C)
D)
E)
V = 0 m/s
V = 1.7 m/s
V = 2.7 m/s
V = 10 m/s
V = 20 m/s
2. What is the angle q relative to the x axis that the two skaters travel after the collision?
A) q = 41 degrees
B) q = 28 degrees
C) q = 25 degrees
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
3. Which of the following remain constant as the pendulum swings down?
A) Horizontal component of the momentum of the ball
B) Horizontal component of the momentum of the cart
C) Horizontal component of the momentum of the ball + cart
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
4. What is the speed of the cart when the ball is at the bottom?
A)
B)
C)
D)
E)
Vcart = 1.17 m/s
Vcart = 1.75 m/s
Vcart = 2.44 m/s
Vcart = 2.91 m/s
Vcart = 3.37 m/s
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
5. What is the length L of the pendulum?
A) 0.59 m
B) 0.83 m
C) 1.18 m
A cart of mass M = 9 kg rolls without friction on a horizontal surface.
It is attached through a freely pivoting initially-horizontal massless rod
of length L to a ball of mass m = 3 kg. The system is initially at rest
when the ball is released. The pendulum swings down and to the left,
and at the bottom of its swing the ball is observed to have a velocity of
3.5 m/sec to the left.
6. How far to the right has the cart moved, when the ball is at the bottom?
A) L/2
B) L/3
C) L/4
7. A comet of mass 109 kg is observed at a distance from the sun of 8 x 1011 m
(mass of sun = 2 x 1030 kg) at a speed of 17000 m/s. Assuming no forces on it other than the
sun's gravity, how fast will it be going when it is a distance of 2.25 x 1011 m from the sun?
(The universal gravitational constant is G = 6.67x10-11 Nm2/kg2)
A)
B)
C)
D)
E)
12,900 m/s
18,300 m/s
23,700 m/s
29,200 m/s
33,800 m/s
8. Two fishermen, of masses 70 and 90 kg stand at opposite ends of their 20 meter boat. The
boat (without fishermen) has a mass of 400 kg. There is no wind or current and the boat can
move without friction on the water’s surface. The 90 kg fisherman walks to the left end of the
boat. How far has the boat moved when the fisherman reaches the left end?
A)
B)
C)
D)
E)
5.8 m to the right
3.2 m to the right
The boat does not move
3.2 m to left
5.8 m to left
9. The centers of three spheres having masses 1 kg, 2 kg, and 3 kg are placed at the corners of
an equilateral triangle whose sides are each 1 meter long, as shown below. What is the
horizontal position of the center of mass?
3 kg
y
A) xcm = 0.50 m
B) xcm = 0.58 m
C) xcm = 0.76 m
2 kg
1 kg
1m
x
An artillery shell of mass 20 kg is fired from a
rail car which is initially at rest on a horizontal
frictionless track. The combined mass of the
car and cannon is 2000kg. As viewed by
someone on the ground the shell moves with an
initial speed of 300 m/s at an angle of 27
degrees above the horizontal and the rail car
recoils to the right.
10. Relative to the ground, what is the speed of the rail car after the shell is fired?
A) 1.36 m/s
B) 2.67 m/s
C) 3.00 m/s
An artillery shell of mass 20 kg is fired from a
rail car which is initially at rest on a horizontal
frictionless track. The combined mass of the
car and cannon is 2000kg. As viewed by
someone on the ground the shell moves with an
initial speed of 300 m/s at an angle of 27
degrees above the horizontal and the rail car
recoils to the right.
11. If the shell was accelerated through the cannon for a time of 0.03 seconds, what was the
average force on the shell during this time?
A)
B)
C)
D)
E)
200 N
2,300 N
15,000 N
90,000 N
200,000 N
A block of mass m = 1.8 kg starts at rest on a
rough inclined plane a height H = 8m above the
ground. It slides down the plane, across a
frictionless horizontal floor, and then around a
frictionless loop-the-loop of radius R = 2.0 m.
On the floor the speed of the block is observed
to be 11 m/s.
12. What is the work done by friction on the block as it slides down the inclined plane?
A)
B)
C)
D)
E)
-49 J
-28 J
-78 J
-23 J
-32 J
A block of mass m = 1.8 kg starts at rest on a
rough inclined plane a height H = 8m above the
ground. It slides down the plane, across a
frictionless horizontal floor, and then around a
frictionless loop-the-loop of radius R = 2.0 m.
On the floor the speed of the block is observed
to be 11 m/s.
13. What is the magnitude of the normal force exerted on the block at the top of the loop?
A)
B)
C)
D)
E)
0N
5.1 N
9.8 N
17.6 N
20.6 N
2.5 kg
k=250 N/m
h=1.5 m
 = 0.4
d = 0.50 m
A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a
frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5
meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with
spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.
14. What is the speed of the box at the bottom of the ramp?
A) 5.4 m/s
B) 3.7 m/s
C) 2.8 m/s
2.5 kg
k=250 N/m
h=1.5 m
 = 0.4
d = 0.50 m
A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a
frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5
meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with
spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.
15. What is the maximum distance the spring is compressed by the box?
A)
B)
C)
D)
E)
0.50 m
0.66 m
0.83 m
0.94 m
1.21 m
2.5 kg
k=250 N/m
h=1.5 m
 = 0.4
d = 0.50 m
A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a
frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5
meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with
spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.
16. What is the maximum height to which the box returns on the ramp?
A) 1.1 m
B) 1.3 m
C) 1.5 m
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.
17. In which case is the change in momentum of the ball the biggest?
A) Case 1
B) Case 2
C) The change in momentum of the ball is the same in both cases.
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.
18. Which of the following statements best describes V1 and V2?
A) V1 < V2
B) V1 = V2
C) V1 > V2
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.
19. In case 2 it is observed that V2 = v0/3. What is the ratio of masses M/m?
A)
B)
C)
D)
E)
M/m = 1/2
M/m = 3/4
M/m = 4/3
M/m = 3/2
M/m = 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.
20. In case 1 it is observed that vf = v0/2. What V1/v0?
A)
B)
C)
D)
E)
V1/v0 = 3M/2m
V1/v0 = 2M/3m
V1/v0 = 3m/2M
V1/v0 = 2m/3M
V1/v0 = m/2M
Two blocks of mass mA and mB are placed side by side on a
frictionless horizontal 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).
21. How do the momenta of the two blocks compare 5 seconds after t0?
A) pA < pB
B) pA > pB
C) pA = pB
22. How do the kinetic energies of the two blocks compare 5 seconds after t0?
A) KA < KB
B) KA > KB
C) KA = KB
Two blocks of mass mA and mB are placed side by side on a
frictionless horizontal 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).
23. After each block has traveled the distance of 1 m, which is correct?
A) pA = pB
B) KA = KB
C) Both of the above