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1. The following graph, shows the magnitude of a horizontal force applied to a 4.0 kg wagon as
its displacement changes. Construct a corresponding graph of work done on the wagon versus
the displacement of the wagon.
2. There are many situations when a force is exerted on an object and still no work is done.
Describe three such situations.
3. For each situation described below, determine the work done.
a) The locomotive of a train applies an average force of 5.4 X 104 N for 1.0 h in order to
pull the boxcars attached to it at a constant speed of 20 m/s.
b) A water buffalo pulls a boat upstream in a river. The rope attached to the boat makes
an angle of 15o with the shore of the river. The the distance the boat is pulled is 120 m,
and the tension in the rope is 500 N.
c) A fat cat of mass 30 kg climbs the stairs from one floor of a building to the next. The
higher floor is 5.0 m above the lower floor.
d) A business man carries an 8 kg briefcase for a horizontal distance of 150 m.
e) A sled of mass 8.0 kg has a force applied to it as illustrated in the following graph. The
sled is on a flat, friction less sheet of ice.
4. A utility wagon is being pulled at 10 m/s. The mass of the wagon is 40 kg.
a) Determine the amount of work needed to increase the speed to 20 m/s.
b) Calculate the amount of work needed to decrease the original speed to 5.0 m/s.
5. The graph below gives the horizontal force applied to a 10 kg crate when it is pushed from rest.
The crate sits on a horizontal, friction less surface.
a) In order to move the crate the first 2.0 m, how much work is done?
b) Determine the kinetic energy of the crate after it has moved 3.0 m.
c) Calculate the velocity of the the crate when it has moved 3.0 m.
6. A rock of mass 10.0 kg has the same momentum as a rock of mass 4.0 kg which is moving at
20 m/s.
a) Determine the 10.0 kg rock's velocity.
b) Calculate each rock's kinetic energy.
7. A suitcase of mass 5.0 kg has a kinetic energy of 5.0 X 102 J. What is its momentum?
8. A electron in a TV picture tube has a velocity of 1.0 X 107 m/s. The mass of such an electron
is 9.11 X 10-31 kg. Calculate the electron's kinetic energy.
9. The following graph displays the force on a pellet of mass 5.0 g, fired from a pellet gun which
has a barrel of length of 100 cm. Determine the velocity of the bullet (muzzle velocity) as it
leaves the gun.
10. A sled with a girl riding on it is moving at 12 m/s on smooth level ice. The sled slides onto a
rough patch of ice covered with snow. The mass of the sled is 20 kg, and the girl's mass is
40 kg.
a) Determine the starting kinetic energy of the sled with the girl on it.
b) Assuming the rough ice and snow apply an average frictional force of 540 N, calculate
the stopping distance of the sled and girl.
c) How much work is done in stopping the sled?
11. Explain why the gain in kinetic energy of an object as it falls towards the Earth, will not be
precisely equal to the decrease in gravitational potential energy in the object-Earth system.
12. Two objects slide in the same direction on a flat level friction less surface. The objects have
different mass, but the same kinetic energy. Assume that each has the same retarding force
applied to it. Compare their stopping distances.
13. A 2.5 kg fish is suspended from a spring scale attached to the ceiling of a room. The spring in
the spring scale has a force constant of 200 N/m.
a) How much will the spring stretch?
b) Calculate the elastic potential energy stored in the spring.
14. The equation which describes the force-compression relationship for a spring from a vehicle
is F = 50x. The spring is compressed 0.20 m.
a) Determine the elastic potential energy stored in the spring when compressed 0.20 m.
b) Calculate the change in elastic potential energy if the spring is further compressed to
0.60 m from 0.20 m.
c) The spring is used to propel a 0.40 kg car horizontally on a friction less plane. To do
this, the spring is compressed 60 cm, and the cart is placed against the compressed
spring. The system is then released. What will be the velocity of the cart when it leaves
the spring?
15. A person of mass 70 kg falls from rest off a 12 m diving tower.
a) How fast will the person be moving at when she hits the water?
b) Suppose the person dives off of the tower in stead of fall off. In the process of diving,
she gives herself an upward initial velocity of 5.0 m/s. What is her velocity at the
moment she enters the water? Do not calculate the maximum height she reaches!
16. A spring with a force constant of 800 N/m is used to propel a 2.0 kg mass along a friction less
horizontal surface, which directs the mass up a friction less sloped surface. The spring has been
compressed 0.22 m. Determine:
a) the initial potential energy stored in the spring.
b) how fast the mass moves immediately after leaving the spring.
c) the vertical height of the mass when it comes to rest on the slope.
17. By measuring the maximum vertical height a pendulum reaches when a bullet is fired into it
(The bullet stays lodged in the pendulum.), one can calculate the initial speed of the bullet.
Consider the situation where the bullet has mass of 20 g, and the pendulum has a mass of
10.00 kg. Assuming the pendulum rises to a height of 0.040 m after it is hit by the bullet,
a) how much does the gravitational potential energy of the pendulum and bullet change by
during the swing?
b) calculate the velocity of the pendulum and bullet immediately after impact.
c) determine the initial velocity of the bullet just before it strikes the pendulum.
d) is the collision elastic or inelastic?
18. A 1500 kg pile driver is used to drive a pile 0.50 m into the ground. The average opposing
force is 3.5 X 105 N. What height must the pile driver be dropped from in order to do the
job?
19. A 5.0 m long cord is used to suspend a 1.0 kg steel ball. The ball is pulled sideways and
upwards, so that the cord is in a horizontal position. Once in the described position, the ball is
allowed to fall. What is
a) the ball's maximum velocity?
b) the tension in the cord when the ball reaches maximum velocity?
20. A toy truck has a velocity of 6.0 m/s when it begins to role freely up a ramp inclined at 30o.
The toy has a mass of 5.0 kg, and the frictional forces present are 4.0 N. What distance does
the truck travel before stopping, and what is its change in gravitational potential energy once it
has stopped?
21. A 1200 kg booster for a rocket is ejected when the rocket is 2000 km above the Earth. The
ejected booster momentarily is at rest with respect to the Earth. If we neglect the effects of
atmospheric resistance, calculate
a) the work done by gravity in pulling the booster back to the Earth.
b) the velocity of the booster when it strikes the Earth's surface.
22. A rocket reaches a point in its path where it has kinetic energy of 5.0 X 109 J, and potential
energy of -6.4 X 109 J. Calculate the rocket's binding energy.
23. A satellite is 200 km above the surface of the Earth. The orbit is circular, and the mass of the
satellite is 500 kg. What is
a) the satellite's gravitational potential energy?
b) the satellite's kinetic energy?
c) the binding energy of the satellite?
d) the percentage increase in launching energy needed so that the satellite will escape
the Earth?
24. The sun has a mass of 1.98 X 1020 kg, and a radius of 6.96 X 108 m. What is the sun's
escape velocity?
25. A wooden block of mass 490 g rests against a spring with a force constant of 100 N/m. The
wooden block also sits on a horizontal, friction less surface. A bullet of mass 10.0 g is fired at
the wooden block. The bullet, after striking the block, becomes embedded in the block. As
a result of the impact, the spring momentarily is compressed 0.20 m.
a) Calculate the potential energy stored in the spring at maximum compression.
b) What will be the velocity of the block and bullet immediately after impact?
c) Determine the bullet's velocity just before impact.
d) Calculate the bullet's initial kinetic energy.
e) Why are the answers for (a) and (d) different?
26. A cart of mass 2.0 kg moving at 2.0 m/s [right], is struck from behind by a second cart of
mass 6.0 kg moving at 6.0 m/s [right]. The collision is a perfectly elastic.
a) What is the velocity of each cart after collision?
b) The collision is elastic because one of the carts has a spring bumper on it. What is the
largest amount of elastic potential energy stored in this bumper during collision?
27. Object A of mass 0.40 kg is at rest. Object B of mass 0.80 kg moves directly at object A
with a speed of 8.0 m/s. If the collision is head-on, and perfectly elastic, what are the
velocities of the objects after collision?
28. Two magnetic air pucks of mass 1.0 kg and 0.50 kg collide in a head-on collision on a level
table. The speed of the 1.0 kg puck is 0.24 m/s, while the other puck is stationary. If the
collision is repulsive in nature, calculate
a) each puck's velocity after collision.
b) what the velocity of each puck would be at minimum separation.
c) at minimum separation, the total kinetic energy.
d) what the maximum potential energy stored in the magnetic field would be, during the
collision.
29. An air track glider of mass 0.30 kg moves at 0.40 m/s [right], while a second glider of mass
0.80 kg moves at 0.15 m/s [left]. The resulting collision is perfectly elastic.
a) Calculate the velocities of the gliders after collision.
b) During the collision, what would be the minimum amount of kinetic energy present?
c) During the collision, where does the kinetic energy go to?
30. A bullet of mass 4.0 g is fired horizontally at a wooden block. The bullet enters the block with
a speed of 500 m/s, and leaves the other side with a speed of 100 m/s. The wooden block
has mass 2.0 kg, and is in contact with the bullet for a negligible period of time. As a result
of the collision, the block slides across the rough surface it sits on, for a distance of 40 cm
before coming to rest.
a) Determine the block's velocity just after the bullet exits.
b) Calculate the kinetic energy of the block just after the bullet exits.
c) Determine the magnitude of the average frictional force on the block.
e) As the bullet passes through the block, it loses kinetic energy. Also, as the bullet
passes through the block, the wooden block's kinetic energy increases to a maximum
at the time when the bullet exits. Explain why these two changes in kinetic energy are
not equal. Where does the missing energy go to?
December 18, 2013
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