Energy

1
Energy

• Relate Work Energy
• Kinetic Energy
• Gravitational Potential Energy
• Elastic Potential Energy
• Law of Conservation of Energy

2
Throwing a ball

• Exert a constant force (F) on an object through a
  distance (d), you do an amount of work (W)
• Throwing the ball gains energy in the form of
  motion
• Kinetic energy (K)
• The kinetic energy after the work is done is
  equal to the sum of the initial kinetic energy
  plus the work done on the ball

3
Catching a ball

• Before you catch it the ball is moving
• By catching it, you exert a force on the ball
• In the opposite direction
• The final kinetic energy is zero
• The kinetic energy after the ball is stopped is
  equal to the sum of the initial kinetic energy
  plus the work done on the ball

4
Kinetic Energy

• K ½mv2
• A 875 kg car speeds up from 22 to 44 m/s while
  passing another car. What were its initial and
  final energies, and how much work was done on the
  car to increase its speed?
• m 875 kg K1 ?
• v1 22 m/s K2 ?
• v1 44 m/s W ?

5
Kinetic Energy Work

• K ½mv2
• K1 ½ (875 kg)(22 m/s)2
• 2.12 x 105 J
• K2 ½ (875 kg)(44 m/s)2
• 8.47 x 105 J
• W K2 K1
• (8.47 x 105 J - 2.12 x 105 J)
• 6.35 x 105 J

6
Stored Energy

• Boulders high on a hill
• Stored energy Potential Energy
• They begin to fall picking up speed
• Converting potential E to kinetic E
• Other examples of Potential Energy?
• Compressed spring
• Car, chemical energy from gasoline

7
Gravitational Potential Energy

• The energy stored in a system resulting from
  gravitational interaction between masses
• Ug mgh
• h is height

8
Reference level

• An arbitrary position selected to solve a problem

9
Gravitational Potential Energy

• You lift a 2.00 kg textbook from the floor to a
  shelf 2.10 m above the floor.
• What is the books gravitational potential energy
  relative to the floor?
• What is the gravitational potential relative to
  your head, assuming that youre 1.65 m tall?
• m 2 kg
• hshelf 2.10 m
• hhead 1.65 m
• g 9.80 m/s2

10
Gravitational Potential Energy

• Ug mgh
• h 2.10 m 0.00 m 2.10 m
• Ug (2.00 kg)(9.8 m/s2)(2.10 m)
• 41.2 J
• h 2.10 m 1.65 m 0.45 m
• Ug (2.00 kg)(9.8 m/s2)(0.45 m)
• 8.82 J

11
Elastic Potential Energy

• The potential energy stored in an object that is
  released as kinetic energy when the object
  undergoes a change in form or shape
• Found in
• Rubber bands, rubber ball, slingshot, trampoline,
  ect
• Bending of an object

12
Conversion of Energy

• Law of Conservation of Energy
• The energy in a closed, isolated system is
  constant
• Mechanical energy
• The sum of kinetic energy and gravitational
  potential energy in a given system
• E K Ug

13
Conversion of Energy

• Ball has a weight of 10 N, released above the
  ground at 2 m.
• Ug mgh
• Ug (10.0 N)(2.00 m)
• 20.0 J
• As the ball falls it loses kinetic energy
• At 1.00 m what is the potential energy
• Ug (10.0 N)(1.00 m)
• 10.0 J

14
Conversion of Energy

• E K Ug, so
• K E Ug
• K 20.0 J 10.0 J 10.0 J
• Conservation of Mechanical Energy
• Kbefore Ug before Kafter Ug after

15
Conversion of Energy

• Rolls down a ramp as opposed to being dropped??
• The path it takes does not matter
• Must the first hill of a roller coaster be the
  highest one?
• The total mechanical energy is equal to the
  coasters gravitational energy here

16
Conversion of Energy

• Pendulum
• As it is released, all energy is potential
• As it swings, it is converted to kinetic
• At equilibrium point, gravitational potential
  energy is zero
• kinetic energy is equal to the total mechanical
  energy in the system

17
Loss of Mechanical Energy

• Motion of a pendulum dies, bouncing ball comes to
  a rest, roller coaster hills become smaller
• Air resistance
• Frictional force
• Mechanical energy converted to Thermal energy

18
Conversion of Mechanical Energy

• A large chunk of ice with a mass of 15.0 kg falls
  from a roof 8.00 m above the ground.
• Find the kinetic energy of the ice when it
  reaches the ground.
• What is the speed of the ice when it reaches the
  ground?

19
Conversion of Mechanical Energy

• m 15.0 kg
• h 8.00 m
• g 9.80 m/s2
• K1 0
• Ug2 0
• Ug1 ?
• K2 ?
• v2 ?

• Ug1 mgh
• (15 kg)(9.8 m/s2)(8 m)
• 1.18 x 103 J
• K2 Ug1 1.18 x 103 J
• K2 ½ mv22
• v2 v 2K2 / m
• v2(1.18 x 103 J) / 15 kg
• 12.5 m/s

20
Collisions

• Elastic collisions
• Kind of collision in which the kinetic energy
  does not change
• Between hard, elastic objects
• Steel, glass, hard plastic, ect
• Inelastic collision
• Kind of collision in which kinetic energy
  decreases
• Between soft, sticky material
• Clay

21
Collision

• In an accident on a slippery road, a compact car
  with mass 575 kg, moving at 15.0 m/s, smashes
  into the rear end of a car with mass of 1575 kg
  moving at 5.00 m/s in the same direction.
• What is the final velocity if the wrecked cars
  lock together?
• How much kinetic energy was lost in the
  collision?
• What fraction of the energy was lost?

22
Collision

• Known
• mA 575 kg
• vA1 15.0 m/s
• mB 1575 kg
• vB1 5.00 m/s
• vA2 vB2 v2

• Unknown
• V2 ?
• K K2 K1 ?
• Fraction of ?K lost, ?K/K1 ?

23
Collision

• pA1 pB1 pA2 pB2
• mAvA1 mBvB1 (mA mB)v2
• v2 (mAvA1 mBvB1) / mA mB
• (575 kg)(15 m/s) (1575 kg)(5 m/s) / 575 kg
  1575 kg
• 7.67 m/s

24
Collision

• ?K K2 K1
• K2 ½ (mA mB)v22
• ½ (2150 kg)(7.67 m/s)2
• 6.33 x 104 J
• K1 ½mAvA12 ½mBvB12
• ½(575 kg)(15 m/s)2 ½(1575 kg)(5 m/s)2
• 8.44 x 104 J
• ?K (6.33 x 104 J) (8.44 x 104 J)
• -2.11 x 104 J

25
Collision

• Kinetic energy lost ?K/K1
• -2.11 x 104 J / 8.44 x 104 J
• -0.250
• 25 was lost

26
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