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Energy – Worksheet #3
Conservation of Energy – Energy cannot be created or destroyed. It may only change forms.
In equation form: For a closed system (a system where all the elements are isolated from the
rest of the universe):
TOTAL ENERGY BEFORE = TOTAL ENERGY AFTER
You must identify the types of energy present and what type of energy is changing into what
other types of energy! The basic types of mechanical energy that we are concerned with are:
KE (Kinetic Energy)
PE (Potential Energy – specific types shown below)
GPE (Gravitational Potential Energy )
EPE (Elastic Potential Energy)
HEAT – Work done against friction which produces random
vibration of molecules. Cannot be recovered into
KE or PE. Friction is a dissipative force!
Example:
A 1 Kg ball falls from a height of 50 meters. What is the GPE, KE and total
energy of the ball for each 10 meter interval in its fall?
Height (m)
50
40
30
20
10
0
GPE (J)
490
392
294
196
98
0
KE (J)
0
98
196
294
392
490
PE + KE (J)
490
490
490
490
490
490
Notice that the last column is always a constant 490 J! That is because the energy of the ball as
it falls is constant for every point in its flight! Also, note that we are ignorning air resistance,
which would “rob” the ball of some of its velocity (and some of its energy!)
1. A ball is thrown up into the sky vertically with an initial speed of 20 m/s. It has a
mass of 0.450 Kg.
a.
What is the KE of the ball as it leaves the thrower’s hands? (90 J)
b.
What will be the GPE of the ball at its highest point? (90 J)
c.
How high will the ball rise? (Use Conservation of Energy to solve!) (20.4 m)
2. A sled is at the top of a 40 meter high hill. The sled and its rider have a mass of 70 kg.
a. What is the GPE of sled and rider? (27,440 J)
b. How fast will the sled be moving at the bottom of the hill? (28 m/s)
c. If the length of the run down the hill is 200 meters and the average frictional force
is 110 N along the path, how much heat will be generated while the sled slides
down the hill? (22,000 J)
d. Write the equation for the energy states of the sled at the top of hill vs. the bottom
of the hill.
e. Solve the equation in letter d for the velocity of the sled at the bottom of the hill.
(12.5 m/s)
3. A roller coaster has an initial hill that has a height of 70 meters. The following hill
has a height of 40 meters. A car in the coaster has a mass of 250 Kg including riders.
a. What is the GPE of the car with respect to the ground below from the top of
the first hill? (171,500 J)
b. How fast will the car be moving at the bottom of the first hill? (37 m/s)
c. What is the GPE of the car at the top of the second hill? (98,000 J)
d. What is the GPE of the car with respect to the second hill from the first hill?
(73,500 J)
e. How fast will the car be moving at the top of the second hill? (24 m/s)
f. If the average frictional force on the car is 150 N and the distance from the top of
the first hill to the second hill is 200 meters along the track, how much energy will
be lost to the heat produced by friction in traveling this distance? (30,000 J)
g. What will the resulting speed be of this car at the top of the second hill given the
frictional heat loss in letter e above? (18.7 m/s)
Energy at top
= Energy at second hill
= Energy at bottom
4.
A car is traveling at 50 Km/Hr when the brakes lock and the car slides a distance of
60 meters. The car has a mass of 1800 Kg.
a. What is the amount of work done by friction in stopping the car? (-173,611 J)
b. What is the force of friction that existing between the tires of the car and the road
surface? (-2894 N)