Download ENGPHY1 QUIZ 3 • Kinetic Energy and Work • Potential Energy and

ENGPHY1 QUIZ 3
 Kinetic Energy and Work
 Potential Energy and Conservation of Energy
 Linear Momentum and Collisions
6.
A rock is lifted for a certain time by a force F that is
greater in magnitude than the rock's weight W. The
change in kinetic energy of the rock during this time is
equal to the
A. work done by the net force (F - W)
B. work done by F alone
C. work done by W alone
D. difference in the potential energy of the rock
before and after this time.
7.
An 80-N crate slides with constant speed a distance of
5.0 m downward along a rough slope that makes an
angle of 30◦ with the horizontal. The work done by the
force of gravity is:
A. −400 J
B. −200 J
C. −69 J
D. 200 J
E. 400 J
8.
A car of mass m slides across a patch of ice at a speed v
with its brakes locked. It the hits dry pavement and skids
to a stop in a distance d. The coefficient of kinetic
friction between the tires and the dry road is µ.
If the car has a mass of 2 m, it would have skidded a
distance of
A. 0.5d
B. d
C. 1.41d
D. 2d
E. 3d
9.
Three identical ideal springs (X,Y,Z) are arranged as
shown. When a 4.0-kg mass is hung on X, the mass
descends 3.0 cm. When a 6.0-kg mass is hung on Y, the
mass descends
MULTIPLE CHOICE
1.
Which of the following is NOT a correct unit for work?
A. erg
B. ft·lb
C. watt
D. newton·meter
E. joule
2.
A boy holds a 40-N weight at arm’s length for 10 s. His
arm is 1.5 m above the ground. The work done by the
force of the boy on the weight while he is holding it is:
A. 0
B. 6.1 J
C. 40 J
D. 60 J
E. 90 J
3.
Which of the following bodies has the largest kinetic
energy?
A. Mass 3M and speed V
B. Mass 3M and speed 2V
C. Mass 2M and speed 3V
D. Mass M and speed 4V
E. All four of the above have the same kinetic
energy
4.
A 2 kg ball is attached to a 0.80 m string and whirled in
a horizontal circle at a constant speed of 6 m/s. The work
done on the ball during each revolution is:
A. 90 J
B. 72 J
C. 16 J
D. 32 J
E. 0
5.
A block is attached to the end of an ideal spring and
moved from coordinate xi to coordinate xf. The relaxed
position is at x = 0. The work done by spring is positive
if:
A. xi = 2 cm and xf = 4 cm
B. xi = −2 cm and xf = 4 cm
C. xi = −2 cm and xf = −4 cm
D. xi = 2 cm and xf = −4 cm
E. xi = −4 cm and xf = −2 cm
A.
B.
C.
D.
E.
2.0 cm
4.0 cm
4.5 cm
6.0 cm
9.0 cm
10. The weight of an object on the moon is one-sixth of its
weight on Earth. The ratio of the kinetic energy of a
body on Earth moving with speed V to that of the same
body moving with speed V on the moon is:
A. 6:1
B. 36:1
C. 1:1
D. 1:6
E. 1:36
the mechanical energy E of the Earth-ball system as a
function of the altitude y of the ball?
11. The amount of work required to stop a moving object is
equal to:
A. the velocity of the object
B. the kinetic energy of the object
C. the mass of the object times its acceleration
D. the mass of the object times its velocity
E. the square of the velocity of the object
12. A 50-N force is the only force a 2-kg crate that starts
from rest. At the instant the object has gone 2 m the rate
at which the force is doing work is:
A. 2.5W
B. 25 W
C. 75 W
D. 100 W
E. 500 W
13. A force on a particle is conservative if:
A. its work equals the change in the kinetic energy of
the particle
B. it obeys Newton’s second law
C. it obeys Newton’s third law
D. its work depends on the end points of every
motion, not on the path between
E. it is not a frictional force
14. Two particles interact by conservative forces. In
addition, an external force acts on each particle. They
complete round trips, ending at their starting points.
Which must be the same for the two-particle system at the
start and end of this trip?
A.
B.
C.
D.
E.
total kinetic energy
potential energy
mechanical energy
total linear momentum
none of the above
15. The wound spring of a clock possesses:
A. kinetic but no potential energy
B. potential but no kinetic energy
C. both potential and kinetic energy in equal
amounts
D. neither potential nor kinetic energy
E. both potential and kinetic energy, but more
kinetic energy than potential energy
16. A ball is held at a height H above a floor. It is then
released and falls to the floor. If air resistance can be
ignored, which of the five graphs below correctly gives
17. A toy cork gun contains a spring with spring constant is
10.0 N/m. The spring is compressed 5.00 cm and then
used to propel a 6.00-g cork. The cork, however, sticks
to the spring for 1.00 cm beyond its unstretched length
before separation occurs. The muzzle velocity of the
cork is:
A.
B.
C.
D.
E.
1.02 m/s
1.41 m/s
2.00 m/s
2.04 m/s
4.00 m/s
18. The string in the figure is 50 cm long. When the ball is
released from rest, it swings along the dotted arc. How fast
is it going at the lowest point in its swing?
A.
B.
C.
D.
E.
2.0 m/s
2.2 m/s
3.1 m/s
4.4 m/s
6.0 m/s
19. A block slides across a rough horizontal table top. The
work done by friction changes:
A. only the kinetic energy
B. only the potential energy
C. only the internal energy
D. the kinetic and potential energies
E. the kinetic and internal energies
20. The x and y coordinates of the center of mass of the
three-particle system shown below are:
A.
B.
C.
D.
E.
0, 0
1.3 m, 1.7m
1.4 m, 1.9m
1.9 m, 2.5m
1.4 m, 2.5m
21. The center of mass of Earth’s atmosphere is:
A. a little less than halfway between Earth’s surface
and the outer boundary of the atmosphere
B. near the surface of Earth
C. near the outer boundary of the atmosphere
D. near the center of Earth
E. none of the above
22. The center of mass of a system of particles has a
constant velocity if:
A. the forces exerted by the particles on each other
sum to zero
B. the external forces acting on particles of the
system sum to zero
C. the velocity of the center of mass is initially zero
D. the particles are distributed symmetrically
around the center of mass
E. the center of mass is at the geometric center of
the system
23. A man sits in the back of a canoe in still water. He then
moves to the front of the canoe and sits there.
Afterwards the canoe:
A. is forward of its original position and moving
forward
B. is forward of its original position and moving
backward
C. is rearward of its original position and moving
forward
D. is rearward of its original position and moving
backward
E. is rearward of its original position and not
moving
24. Two objects, P and Q, have the same momentum. Q has
more kinetic energy than P if it:
A. weighs more than P
B. is moving faster than P
C. weighs the same as P
D. is moving slower than P
E. is moving at the same speed as P
25. A 1.0-kg ball moving at 2.0 m/s perpendicular to a wall
rebounds from the wall at 1.5 m/s. The change in the
momentum of the ball is:
A. zero
B. 0.5N·s away from wall
C. 0.5N·s toward wall
D. 3.5N·s away from wall
E. 3.5N·s toward wall
26. A man is marooned at rest on level frictionless ice. In
desperation, he hurls his shoe to the right at 15 m/s. If
the man weighs 720 N and the shoe weighs 4.0 N, the
man moves to the left with a speed of:
A. 0
B. 2.1 × 10−2 m/s
C. 8.3 × 10−2 m/s
D. 15 m/s
E. 2.7 × 103 m/s
27. A projectile in flight explodes into several fragments.
The total momentum of the fragments immediately after
this explosion:
A. is the same as the momentum of the projectile
immediately before the explosion
B. has been changed into kinetic energy of the
fragments
C. is less than the momentum of the projectile
immediately before the explosion
D. is more than the momentum of the projectile
immediately before the explosion
E. has been changed into radiant energy
28. Force:
A. equals the negative integral (with respect to
B.
C.
D.
E.
distance) of the potential energy function
is the ability to do work
is the rate of change of doing work
equals the time rate of change of momentum
has dimensions of momentum multiplied by
time
29. A rocket exhausts fuel with a velocity of 1500 m/s,
relative to the rocket. It starts from rest in outer space
with fuel comprising 80 per cent of the total mass. When
all the fuel has been exhausted its speed is:
A. 3600 m/s
B. 2400 m/s
C. 1200 m/s
D. 880 m/s
E. 400 m/s
30. The law of conservation of momentum applies to a
system of colliding objects only if:
A. there is no change in kinetic energy of the
system
B. the coefficient of restitution is one
C. the coefficient of restitution is zero
D. the net external impulse is zero
E. the collisions are all elastic
31. Sphere X, of mass 2 kg, is moving to the right at 10 m/s.
Sphere Y, of mass 4 kg, is moving to the left at 10 m/s.
They collide head-on. The magnitude of the impulse of
X on Y is ____ the magnitude of the impulse of Y on X.
A. twice
B. half
C. one-fourth
D. four times
E. the same as
32. Two bodies of unequal mass, placed at rest on a
frictionless surface, are acted on by equal horizontal
forces for equal times. Just after these forces are
removed, the body of greater mass will have:
A. the greater speed
B. the greater acceleration
C. the smaller momentum
D. the greater momentum
E. the same momentum as the other body
33. A 4.0-N puck is traveling at 3.0 m/s. It strikes an 8.0-N
puck, which is stationary. The two pucks stick together.
Their common final speed is:
A. 1.0 m/s
B. 1.5 m/s
C. 2.0 m/s
D. 2.3 m/s
E. 3.0 m/s
35. How does an air mattress protect a stunt person landing
on the ground after a stunt?
A. It reduces the kinetic energy loss of the stunt
person.
B. It reduces the momentum change of the stunt
person.
C. It shortens the stopping time of the stunt person
and increases the force applied during the landing.
D. It lengthens the stopping time of the stunt person
and reduces the force applied during the landing.
PROBLEM SOLVING
1. A box is sliding with a speed of 4.50 m/s on a horizontal
surface when, at point P, it encounters a rough section.
On the rough section, the coefficient of friction is not
constant, but starts at 0.100 at P and increases linearly
with distance past P, reaching a value of 0.600 at 12.5 m
past point P.
(a) Use the work–energy theorem to find how far this
box slides before stopping.
(b) What is the coefficient of friction at the stopping
point?
(c) How far would the box have slid if the friction
coefficient didn’t increase but instead had the constant
value of 0.100?
2. A 10.0kg block is released from rest at point A. The
track is frictionless except for the portion between points
B and C, which has a length of 6.00 m. The block travels
down the track, hits a spring of force constant 2 250
N/m, and compresses the spring 0.300 m from its
equilibrium position before coming to rest momentarily.
Determine the coefficient of kinetic friction between the
block and the rough surface between points B and C.
34. An open cart on a level surface is rolling without
frictional loss through a vertical downpour of rain, as
shown above. As the cart rolls, an appreciable amount of
rainwater accumulates in the cart. The speed of the cart
will
A. increase because of conservation of mechanical
energy
B. decrease because of conservation of momentum
C. decrease because of conservation of mechanical
energy
D. remain the same because the raindrops are falling
perpendicular to the direction of the cart's motion
3. A 1500-kg sedan goes through a wide intersection
traveling from north to south when it is hit by a 2200-kg
SUV traveling from east to west. The two cars become
enmeshed due to the impact and slide as one thereafter.
On-the-scene measurements show that the coefficient of
kinetic friction between the tires of these cars and the
pavement is 0.75, and the cars slide to a halt at a point
5.39 m west and 6.43 m south of the impact point. How
fast was each car traveling just before the collision?
ANSWER KEY (including explanations to selected problems)
1.
C
2.
A
3.
C
4.
E
5.
E
6.
A
7.
D
8.
B
9.
E
10.
C
11.
B
12.
E
13.
D
14.
B
15.
B
16.
E
No air resistance = no nonconservative force = ME is conserved
17.
C
1
18.
C
𝑚𝑔ℎ = 2 𝑚𝑣 2
19.
E
20.
C
21.
D
22.
B
23.
E
24.
B
25.
D
∆𝑝 = 𝑚∆𝑣 = 1.0 [2.0 − (−1.5)]
26.
C
𝑚1 (0) + 𝑚2 (0) = 𝑚1 𝑣1𝑓 + 𝑚2 𝑣2𝑓
27.
A
28.
D
Work done is zero since the Force is always perpendicular to the distance moved as you move incrementally around
the circle.
𝑊 = 𝐹⃗ ∙ 𝑑⃗
𝐹⃗ 𝑎𝑛𝑑 𝑑⃗ are in the same direction (positive 𝑊) if 𝑑⃗ is towards equilibrium (x = 0).
𝑊 = 𝐹𝑔 𝑑𝑠𝑖𝑛𝜃
1
𝑚𝑣 2 − µ𝑘 𝑚𝑔𝑑 = 0
2
KE is dependent on mass, not weight.
2
1
1
𝑘𝑥𝑖 2 = 2 𝑘𝑥𝑓 2 + 2 𝑚𝑣 2
1
Initial momentum = 0 = final momentum
𝑚𝑚𝑎𝑛 (0) + 𝑚𝑐𝑎𝑛𝑜𝑒 (0) = 0 = 𝑚𝑚𝑎𝑛 𝑣𝑓𝑜𝑟𝑤𝑎𝑟𝑑 + 𝑚𝑐𝑎𝑛𝑜𝑒 𝑣𝑟𝑒𝑎𝑟𝑤𝑎𝑟𝑑
The canoe compensates for the forward motion of the man so that the center of mass of the system doesn’t move
(momentum doesn’t change).
𝐼 = ∆𝑝 = 𝐹∆𝑡
𝐹=
∆𝑝
∆𝑡
29.
B
30.
D
31.
E
Same force (𝐹𝑋𝑌 = 𝐹𝑌𝑋 ) and time of contact (∆𝑡 ). Same impulse.
32.
E
Same force (𝐹𝑋𝑌 = 𝐹𝑌𝑋 ) and time of contact (∆𝑡 ). Same momentum change.
33.
A
𝑚1 𝑣1𝑖 + 𝑚2 (0) = 𝑚1 𝑣𝑓 + 𝑚2 𝑣𝑓
34.
B
𝑚𝑖 𝑣𝑖 = 𝑚𝑓 𝑣𝑓
35.
D
∆𝑝 = 𝐹∆𝑡 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
As 𝑚 increase, 𝑣 decrease.
∆𝑡 increases, so 𝐹 decreases.
Study hard!
God Bless! 