ENERGY

1
ENERGY

• Chapter 5

2
Definitions

• Kinetic energy energy of an object due to
  motion
• Chemical energy energy stored in the form of
  chemical bonds
• Gravitational Potential Energy PEg the stored
  energy in a system resulting from gravitational
  interaction between masses
• Elastic Potential Energy PEs the stored energy
  in an object due to stretching or bending

3
Calculating Kinetic Energy

• KE ½ m v2

4
Ex.

• A 1600 kg. car travels at a speed of 12.5 m/s.
  What is its kinetic energy?

5
Answer

• KE ½ m v2
• ½ (1600 kg) (12.5 m/s)2
• 125,000 J
• 1.3 x 105 J

6
Example continued

• Given the previous car with KE1.3 x 105 J and
  m1600 kg
• If µ0.6, what is the force of friction when the
  driver applies the brakes?
• Using the work-energy theorem, how far does it
  skid before stopping?

7
Answer

• FkµkFN
• 0.6 x 1600 x 9.8
• 9400 N

8
Answer cont

• W?K
• FdKf Ki
• -9400 d0 - 1.3 x 105
• d14 meters

9
Potential Energy

• Potential energy is stored energy
• It has the potential to convert into usable
  energy.
• Energy can be stored in the gravitational field
  or in the stretch of a spring.

10
Gravitational Potential Energy

• PEg mgh
• where m is mass of object
• g9.8 m/s2
• h is height of the object above some reference
  level that has zero PEg

11
Elastic Potential Energy

• The stretchiness of a rubber band is called its
  spring constant, k
• PEs ½ kx2
• where x is the distance stretched

12
Mechanical Energy

• ME is the sum of kinetic and potential energies
• MEKE PEg PEs
• Mechanical energy is conserved if there is no
  applied force or friction.

13
Conservation of Energy

• MEbefore ME after
• To solve an energy problem, pick a before and
  after and set the total energy before to the
  energy after.
• PEg1 PEs1 KE1 PEg2 PEs2 KE2

14
Ex. with PEg

• A 20 kg rock is on the edge of a 100-m cliff.
• A. What potential energy does the rock possess
  relative to the base of the cliff?
• B. The rock falls from the cliff. What is its
  kinetic energy just before it strikes the ground?
• C. What speed does the rock have as it strikes
  the ground?

15
Answer to a

• PEg mgh
• 20 x 9.8 x 100
• 19,600 Joules

16
Answer to b

• PEg1KE2
• KE19,600 J

17
Answer to c

• KE1/2 mv2
• 19,600 ½ x 20 x v2
• v44 m/s

18
Elastic PE Example

• An archer puts a 0.30 kg arrow to the bowstring.
  The bowstring has a force constant of 309 N/m.
  The bow is drawn back 1.3 meters and then
  released.
• What is the elastic potential energy of the bow?
• With what speed does the arrow leave the bow?
  v42 m/s
• If the arrow is shot straight up, how high does
  it rise?

19
Answer

• PEs1 ½ kx2
• ½ x 309 x 1.32
• 261 Joules
• KE2 PEs1
• KE2 261 Joules

20
Answer cont

• KE2 ½ mv2
• 261 J ½ x 0.3 x v2
• v 42 m/s

21
Answer cont

• Now all energy is converted to gravitational
  potential energy
• PEg 261 J
• 261 J mgh
• 261 0.3 x 9.8 h
• h 89 meters

22
Power

• Power is the rate of doing work
• It is measured in Watts.
• P Work/time

23
Collisions

• Elastic collision kinetic energy is conserved.
  Collisions between hard objects such as billiard
  balls
• Inelastic collision kinetic energy is converted
  to thermal energy or sound. Collision is not
  reversible. (cars, guard rails)
• Super-elastic collision explosion. For
  example, spring potential energy is converted to
  kinetic energy

24
(No Transcript)
25
Prob 61 p. 270 A railroad car with a mass of
5.0 x 105 kg collides with a stationary railroad
car of equal mass. After the collision, the two
cars lock together and move off at 4.0 m/s.

• Do you think the collision is elastic or
  inelastic?
• A. Before the collision, the first railroad car
  was moving at 8.0 m/s. What was its momentum?
• B. What was the total momentum of the two cars
  after the collision?
• Why is momentum conserved?
• C. What were the kinetic energies of the two cars
  before and after the collision?
• D. Account for the loss of kinetic energy.