Preview

1
Chapter 5
Section 1 Work
Preview

• Objectives
• Definition of Work

2
Objectives
Section 1 Work
Chapter 5

• Recognize the difference between the scientific
  and ordinary definitions of work.
• Define work by relating it to force and
  displacement.
• Identify where work is being performed in a
  variety of situations.
• Calculate the net work done when many forces are
  applied to an object.

3
Definition of Work
Chapter 5
Section 1 Work

• Work is done on an object when a force causes a
  displacement of the object.
• Work is done only when components of a force are
  parallel to a displacement.

4
Definition of Work
Chapter 5
Section 1 Work
5
Sign Conventions for Work
Chapter 5
Section 1 Work
Click below to watch the Visual Concept.
Visual Concept
6
Chapter 5
Section 2 Energy
Preview

• Objectives
• Kinetic Energy
• Sample Problem

7
Objectives
Section 2 Energy
Chapter 5

• Identify several forms of energy.
• Calculate kinetic energy for an object.
• Apply the workkinetic energy theorem to solve
  problems.
• Distinguish between kinetic and potential energy.
• Classify different types of potential energy.
• Calculate the potential energy associated with an
  objects position.

8
Kinetic Energy
Section 2 Energy
Chapter 5

• Kinetic Energy
• The energy of an object that is due to the
  objects motion is called kinetic energy.
• Kinetic energy depends on speed and mass.

9
Kinetic Energy
Chapter 5
Section 2 Energy
Click below to watch the Visual Concept.
Visual Concept
10
Kinetic Energy, continued
Section 2 Energy
Chapter 5

• Work-Kinetic Energy Theorem
• The net work done by all the forces acting on an
  object is equal to the change in the objects
  kinetic energy.
• The net work done on a body equals its change in
  kinetic energy.
• Wnet ?KE
• net work change in kinetic energy

11
Work-Kinetic Energy Theorem
Chapter 5
Section 2 Energy
Click below to watch the Visual Concept.
Visual Concept
12
Sample Problem
Section 2 Energy
Chapter 5

• Work-Kinetic Energy Theorem
• On a frozen pond, a person kicks a 10.0 kg sled,
  giving it an initial speed of 2.2 m/s. How far
  does the sled move if the coefficient of kinetic
  friction between the sled and the ice is 0.10?

13
Sample Problem, continued
Section 2 Energy
Chapter 5

• Work-Kinetic Energy Theorem
• 1. Define
• Given
• m 10.0 kg
• vi 2.2 m/s
• vf 0 m/s
• µk 0.10
• Unknown
• d ?

14
Sample Problem, continued
Section 2 Energy
Chapter 5

• Work-Kinetic Energy Theorem
• 2. Plan
• Choose an equation or situation This problem
  can be solved using the definition of work and
  the work-kinetic energy theorem.
• Wnet Fnetdcosq
• The net work done on the sled is provided by the
  force of kinetic friction.
• Wnet Fkdcosq µkmgdcosq

15
Sample Problem, continued
Section 2 Energy
Chapter 5

• Work-Kinetic Energy Theorem
• 2. Plan, continued
• The force of kinetic friction is in the
  direction opposite d, q 180. Because the sled
  comes to rest, the final kinetic energy is zero.
• Wnet ?KE KEf - KEi (1/2)mvi2
• Use the work-kinetic energy theorem, and solve
  for d.

16
Sample Problem, continued
Section 2 Energy
Chapter 5

• Work-Kinetic Energy Theorem
• 3. Calculate
• Substitute values into the equation

17
Sample Problem, continued
Section 2 Energy
Chapter 5

• Work-Kinetic Energy Theorem
• 4. Evaluate
• According to Newtons second law, the
  acceleration of the sled is about -1 m/s2 and the
  time it takes the sled to stop is about 2 s.
  Thus, the distance the sled traveled in the given
  amount of time should be less than the distance
  it would have traveled in the absence of
  friction.
• 2.5 m lt (2.2 m/s)(2 s) 4.4 m

18
Potential Energy
Section 2 Energy
Chapter 5

• Potential Energy is the energy associated with an
  object because of the position, shape, or
  condition of the object.
• Gravitational potential energy is the potential
  energy stored in the gravitational fields of
  interacting bodies.
• Gravitational potential energy depends on height
  from a zero level.
• PEg mgh
• gravitational PE mass ? free-fall acceleration
  ? height

19
Potential Energy
Chapter 5
Section 2 Energy
Click below to watch the Visual Concept.
Visual Concept
20
Potential Energy, continued
Section 2 Energy
Chapter 5

• Elastic potential energy is the energy available
  for use when a deformed elastic object returns to
  its original configuration.

• The symbol k is called the spring constant, a
  parameter that measures the springs resistance
  to being compressed or stretched.

21
Elastic Potential Energy
Chapter 5
Section 2 Energy
22
Spring Constant
Chapter 5
Section 2 Energy
Click below to watch the Visual Concept.
Visual Concept
23
Sample Problem
Section 2 Energy
Chapter 5

• Potential Energy
• A 70.0 kg stuntman is attached to a bungee cord
  with an unstretched length of 15.0 m. He jumps
  off a bridge spanning a river from a height of
  50.0 m. When he finally stops, the cord has a
  stretched length of 44.0 m. Treat the stuntman as
  a point mass, and disregard the weight of the
  bungee cord. Assuming the spring constant of the
  bungee cord is 71.8 N/m, what is the total
  potential energy relative to the water when the
  man stops falling?

24
Sample Problem, continued
Section 2 Energy
Chapter 5

• Potential Energy
• 1. Define
• Givenm 70.0 kg
• k 71.8 N/m
• g 9.81 m/s2
• h 50.0 m 44.0 m 6.0 m
• x 44.0 m 15.0 m 29.0 m
• PE 0 J at river level
• Unknown PEtot ?

25
Sample Problem, continued
Section 2 Energy
Chapter 5

• Potential Energy
• 2. Plan
• Choose an equation or situation The zero level
  for gravitational potential energy is chosen to
  be at the surface of the water. The total
  potential energy is the sum of the gravitational
  and elastic potential energy.

26
Sample Problem, continued
Section 2 Energy
Chapter 5

• Potential Energy
• 3. Calculate
• Substitute the values into the equations and
  solve

27
Sample Problem, continued
Section 2 Energy
Chapter 5

• Potential Energy
• 4. Evaluate
• One way to evaluate the answer is to make an
  order-of-magnitude estimate. The gravitational
  potential energy is on the order of 102 kg ? 10
  m/s2 ? 10 m 104 J. The elastic potential energy
  is on the order of 1 ? 102 N/m ? 102 m2 104 J.
  Thus, the total potential energy should be on the
  order of 2 ? 104 J. This number is close to the
  actual answer.

28
Section 3 Conservation of Energy
Chapter 5
Preview

• Objectives
• Conserved Quantities
• Mechanical Energy
• Sample Problem

29
Objectives
Section 3 Conservation of Energy
Chapter 5

• Identify situations in which conservation of
  mechanical energy is valid.
• Recognize the forms that conserved energy can
  take.
• Solve problems using conservation of mechanical
  energy.

30
Conserved Quantities
Section 3 Conservation of Energy
Chapter 5

• When we say that something is conserved, we mean
  that it remains constant.

31
Mechanical Energy
Section 3 Conservation of Energy
Chapter 5

• Mechanical energy is the sum of kinetic energy
  and all forms of potential energy associated with
  an object or group of objects.
• ME KE ?PE
• Mechanical energy is often conserved.
• MEi MEf
• initial mechanical energy final mechanical
  energy (in the absence of friction)

32
Conservation of Mechanical Energy
Section 3 Conservation of Energy
Chapter 5
Click below to watch the Visual Concept.
Visual Concept
33
Sample Problem
Section 3 Conservation of Energy
Chapter 5

• Conservation of Mechanical Energy
• Starting from rest, a child zooms down a
  frictionless slide from an initial height of 3.00
  m. What is her speed at the bottom of the slide?
  Assume she has a mass of 25.0 kg.

34
Sample Problem, continued
Section 3 Conservation of Energy
Chapter 5

• Conservation of Mechanical Energy
• 1. Define
• Given
• h hi 3.00 m
• m 25.0 kg
• vi 0.0 m/s
• hf 0 m
• Unknown
• vf ?

35
Sample Problem, continued
Section 3 Conservation of Energy
Chapter 5

• Conservation of Mechanical Energy
• 2. Plan
• Choose an equation or situation The slide is
  frictionless, so mechanical energy is conserved.
  Kinetic energy and gravitational potential energy
  are the only forms of energy present.

36
Sample Problem, continued
Section 3 Conservation of Energy
Chapter 5

• Conservation of Mechanical Energy
• 2. Plan, continued
• The zero level chosen for gravitational
  potential energy is the bottom of the slide.
  Because the child ends at the zero level, the
  final gravitational potential energy is zero.
• PEg,f 0

37
Sample Problem, continued
Section 3 Conservation of Energy
Chapter 5

• Conservation of Mechanical Energy
• 2. Plan, continued
• The initial gravitational potential energy at
  the top of the slide is
• PEg,i mghi mgh
• Because the child starts at rest, the initial
  kinetic energy at the top is zero.
• KEi 0
• Therefore, the final kinetic energy is as
  follows

38
Sample Problem, continued
Section 3 Conservation of Energy
Chapter 5

• Conservation of Mechanical Energy
• 3. Calculate
• Substitute values into the equations
• PEg,i (25.0 kg)(9.81 m/s2)(3.00 m) 736 J
• KEf (1/2)(25.0 kg)vf2
• Now use the calculated quantities to evaluate
  the final velocity.
• MEi MEf
• PEi KEi PEf KEf
• 736 J 0 J 0 J (0.500)(25.0 kg)vf2
• vf 7.67 m/s

39
Sample Problem, continued
Section 3 Conservation of Energy
Chapter 5

• Conservation of Mechanical Energy
• 4. Evaluate
• The expression for the square of the final speed
  can be written as follows

Notice that the masses cancel, so the final speed
does not depend on the mass of the child. This
result makes sense because the acceleration of an
object due to gravity does not depend on the mass
of the object.
40
Mechanical Energy, continued
Section 3 Conservation of Energy
Chapter 5

• Mechanical Energy is not conserved in the
  presence of friction.
• As a sanding block slides on a piece of wood,
  energy (in the form of heat) is dissipated into
  the block and surface.

41
Chapter 5
Section 4 Power
Preview

• Objectives
• Rate of Energy Transfer

42
Objectives
Section 4 Power
Chapter 5

• Relate the concepts of energy, time, and power.
• Calculate power in two different ways.
• Explain the effect of machines on work and power.

43
Rate of Energy Transfer
Section 4 Power
Chapter 5

• Power is a quantity that measures the rate at
  which work is done or energy is transformed.
• P W/?t
• power work time interval
• An alternate equation for power in terms of force
  and speed is
• P Fv
• power force ? speed

44
Power
Chapter 5
Section 4 Power
Click below to watch the Visual Concept.
Visual Concept