Kinds of Energy
| Kinetic Energy K | Gravitational Potential Energy  |
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Elastic Potential Energy  |
Thermal Energy  |
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Chemical Energy  |
Nuclear Energy  |
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Energy Transformations
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Energy Transfers: Work and Heat
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The Law of Conservation of Energy
Alternate form
Systems
Work
Positive vs. Negative Work video
Example 1
An intern pushes
a 72 kg patient on a 15 kg gurney, producing an acceleration of 
.
How much work does the intern do by pushing the patient and gurney through
a distance of 2.5 m? Assume the gurney moves without friction.
Example 2
A 75.0 kg person slides a distance of 5.00 m on a straight water slide, dropping through a vertical height of 2.50 m. How much work does gravity do on the person?
Kinetic Energy
Example 3
A 4.1 kg box of books is lifted vertically from rest a distance of 1.6 m by an upward applied force of 60.0 N.
Find (a) the work done by the applied force,
(b) the work done by gravity, and
(c) the final speed of the box.
Example 4
The figure shows two industrial spies sliding an initially stationary 225 kg floor safe a displacement d of magnitude 8.50 m, straight toward their truck. The push F1 of Spy 001 is 12.0 N, directed at an angle of 30˚ downward from the horizontal: the pull F2 of Spy 002 is 10.0 N, directed at 40˚ above the horizontal. The magnitudes and directions of these forces do not change as the safe moves, and the floor and safe make frictionless contact.
(a) What is the net work done on the safe by forces F1 and F2 during the displacement d?
(b) During the displacement, what is the work Wg done on the safe by the gravitational force Fg and what is the work Wn done on the safe by the normal force N from the floor?
(c) The safe is initially stationary. What is its speed vf at the end of the 8.50 m displacement?
Example 5
A boy exerts a force of 11.0 N at 29˚ above the horizontal on a 6.40 kg sled. Find the work done by the boy and the final speed of the sled after it moves 2.00 m, assuming the sled starts with an initial speed of 0.500 m/s and slides horizontally without friction.
Rotational Kinetic Energy
Example 6
The turntable in a microwave oven has a
moment of inertia of 
and
is rotating once every 4.0 s. What is its kinetic energy?
Potential Energy
Example 7
Find the gravitational potential energy of a 65 kg person on a 3.0 m high diving board. Let U = 0 be at water level.
Example 8
An 82 kg mountain climber is in the final stage of the ascent of 4301 m high Pikes Peak. What is the change in gravitational potential energy as the climber gains the last 100 m of altitude? Let Ug = 0 be (a) at sea level or (b) at the top of the peak.
Example 9
A candy bar called
the Mountain Bar has a calorie content of 210.0 Cal = 210.0 kcal, which
is equivalent to an energy of 
.
If an 82 kg mountain climber eats a Mountain Bar and magically converts
it all to potential energy, what gain of altitude would be possible?
Example 10
The figure shows a 2.0 kg block of slippery cheese that slides along a frictionless track from point a to point b. The cheese travels through a total distance of 2.0 m along the track, and a net vertical distance of 0.80 m. How much work is done on the cheese by the gravitational force during the slide?
Example 11
A 2.0 kg sloth
hangs 5.0 m above the ground. See figure.
(a) What is the gravitational potential energy U of the sloth-Earth
system if we take the reference point y = 0 to be (1) at the ground, (2) at a
balcony floor that is 3.0 m above the ground, (3) at the limb, and (4) 1.0 m
above the limb? Take the gravitational potential energy to be zero at y = 0.
(b) The sloth drops to the ground. For each choice of reference point, what is
the change in
the potential energy of the sloth-Earth system due to the fall?
Elastic Potential Energy
Example 12
An
object of mass m = 0.200 kg is vibrating on a horizontal frictionless
table.The spring has a spring constant k = 545 N/m. It is stretched initially
to 
and
then released from rest. Determine the final translational speed 
of
the object when the final displacement of the spring is (a) 
and (b)
.
Thermal Energy
When two objects slide against each other with friction present, mechanical energy is always transformed into thermal energy.
Example 13
In
the figure, a circus beagle of mass m = 6.0 kg runs onto the
left end of a curved ramp with speed 
at
the initial height of 8.5 m above the floor. It then slides to the right
and comes to a momentary stop when it reaches a height y = 11.1 m from
the floor. The ramp is not frictionless. What is the increase 
in
the thermal energy of the beagle and ramp because of the sliding?
Example 14
The figure shows a contest in which a sphere,
a cylinder, and a circular hoop, each with mass M and radius R, are placed
at height h on a slope of angle 
.
All three are simultaneously released from rest and roll down the ramp
without slipping. Which one will win the race at the bottom of the hill?
Energy in Collisions
Example 15
A 90 kg signal relay floating in space is struck by a 1000 g meteoroid. The latter imbeds itself in the craft and the two sail away at 5.0 m/s.
(a) What was the initial speed of the meteoroid?
(b) What was the change in kinetic energy?
Elastic Collisions
A collision for which mechanical energy is conserved is called a perfectly elastic collision.
Example 16
At an amusement park, a 96.0 kg bumper car moving with a speed of 1.24 m/s bounces elastically off a 135 kg bumper car at rest. Find the final velocities of the cars.
Example 17
In
a ballistic pendulum, an object of mass m is fired with an initial speed
at
the bob of a pendulum. The bob has a mass M, and is suspended by a rod
of negligible mass. After the collision, the object and the bob stick
together and swing through an arc, eventually gaining a height h. Find
the height h in terms of m, M, ,
and g.
Example 18
The ballistic pendulum was used to measure the speeds of bullets before electronic timing devises were developed. The version shown in the figure consists of a large block of wood of mass M = 5.4 kg, hanging from two long cords. A bullet of mass m = 9.5 g is fired into the block, coming quickly to rest. The block +bullet then swing upward, their center of mass rising a vertical distance h = 6.3 cm before the pendulum comes momentarily to rest at the end of its arc. What is the speed of the bullet just prior to the collision?
Power
The rate at which energy is transformed is called the power, P.
Example 19
To
pass a slow-moving truck, you want your fancy 
,
car to accelerate from 13.4 m/s to 17.9 m/s in 3.00 s. What is the minimum
power required for this pass?
Example 20
It takes a force of 1280 N to keep a 1500 kg car moving with a constant speed up a slope of 5.00˚. If the engine delivers 50.0 hp to the drive wheels, what is the maximum speed of the car?