Work and Energy

1
Work and Energy

• Chapter 6

2
Expectations

• After Chapter 6, students will
• understand and apply the definition of work.
• solve problems involving kinetic and potential
  energy.
• use the work-energy theorem to analyze physical
  situations.
• distinguish between conservative and
  nonconservative forces.

3
Expectations

• After Chapter 6, students will
• perform calculations involving work, time, and
  power.
• understand and apply the principle of
  conservation of energy.
• be able to graphically represent the work done by
  a non-constant force.

4
The Work Done by a Force

• The woman in the picture exerts a force F on her
  suitcase, while it is displaced through a
  distance s. The force makes an angle q with the
  displacement vector.

5
The Work Done by a Force

• The work done by the woman is
• Work is a scalar quantity. Dimensions
  forcelength
• SI units Nm joule (J)

6
History/Biography Break

• James Prescott Joule
• December 24, 1818
• October 11, 1889
• English physicist, son of a wealthy brewer, born
  near Manchester. He was the first scientist to
  propose a kinetic theory of heat.

7
The Work Done by a Force

• Notice that the component of the force vector
  parallel to the displacement vector is F cos q.
  We could say that the work is done entirely by
  the force parallel to the displacement.

8
The Work Done by a Force

• Recalling the definition of the scalar product of
  two vectors, we could also write a vector
  equation

9
The Work Done by a Force

• Work can be either positive or negative.
• In both (b) and (c), the man is doing work.
• (b) q 0
• (c) q 180

10
A Force Accelerates an Object

• Lets look at what happens when a net force F
  acts on an object whose mass is m, starting from
  rest over a distance s.

11
A Force Accelerates an Object

• The object accelerates according to Newtons
  second law

12
A Force Accelerates an Object

• Applying the fourth kinematic equation

13
Kinetic Energy

• A closer look at that result
• We call the quantity kinetic energy.
  
• In the equation we derived, it is equal to the
  work (Fs) done by the accelerating force.
• Kinetic energy, like work, has the dimensions of
  forcelength and SI units of joules.

14
The Work-Energy Theorem

• The equation we derived is one form of the
  work-energy theorem. It states that the work
  done by a net force on an object is equal to the
  change in the objects kinetic energy. More
  generally,
• If the work is positive, the kinetic energy
  increases. Negative work decreases the kinetic
  energy.

15
The Work-Energy Theorem

• A hand raises a book from height h0 to height hf,
  at
• constant velocity.
• Work done by the hand force, F
• Work done by the gravitational force

16
The Work-Energy Theorem

• Total (net) force exerted
• on the book zero.
• Total (net) work done
• on the book zero.
• Change in books kinetic energy
• zero.

17
The Work-Energy Theorem

• Now, we let the book fall freely
• from rest at height hf to height h0.
• Net force on the book mg.
• Work done by the gravitational
• force

18
The Work-Energy Theorem

• Calculate the books final kinetic
• energy kinematically
• The book gained a kinetic energy equal
• to the work done by the gravitational force
• (per the work-energy theorem).

19
Gravitational Potential Energy

• The quantity
• is both work done on the
• book and kinetic energy gained by
• it. We call this the gravitational
• potential energy of the book.

20
Work and the Gravitational Force

• The total work done by the
• gravitational force does not
• depend on the path the book takes.
• The work done by the gravitational
• force is path-independent. It
• depends only on the relative
• heights of the starting and
• ending points.

21
Work and the Gravitational Force

• Over a closed path (starting and ending points
  the same), the total work done by the
  gravitational force is zero.

22
Forces and Work

• Compare with the frictional force. The longer
  the path, the more work the frictional force
  does. This is true even if the starting and
  ending points are the same. Think about dragging
  a sled around a race course.
• The work done by
• the frictional force
• is path-dependent.

23
Conservative Forces

• The gravitational force is an example of a
  conservative force
• The work it does is path-independent.
• A form of potential energy is associated with it
  (gravitational potential energy).
• Other examples of conservative forces
• The spring force
• The electrical force

24
Nonconservative Forces

• The frictional force is an example of a
  nonconservative force
• The work it does is path-dependent.
• No form of potential energy is associated with
  it.
• Other examples of nonconservative forces
• normal forces
• tension forces
• viscous forces

25
Total Mechanical Energy

• A man lifts weights upward at a constant
  velocity.
• He does positive work on the weights.
• The gravitational force does equal negative work.
• The net work done on
• the weights is zero.
• But

26
Conservation of Mechanical Energy

• The gravitational potential energy of the weights
• increases
• The work done by the nonconservative normal force
  of
• the mans hands on
• the bar changed the
• total mechanical
• energy of the weights

27
Conservation of Mechanical Energy

• Work done on an object by nonconservative forces
• changes its total mechanical energy.
• If no (net) work is done by nonconservative
  forces, the
• total mechanical
• energy remains
• constant (is conserved)

28
Conservation of Mechanical Energy

• This equation is another form of the work-energy
  theorem.
• Note that it does not require both kinetic and
  potential energy to remain constant only their
  sum. Work done by a conservative force often
  increases one while decreasing the other.
  Example a freely-falling object.

29
Conservation of Every Kind of Energy

• Energy is neither created nor destroyed.
• Work done by conservative forces conserves total
  mechanical energy. Energy may be interchanged
  between kinetic and potential forms.
• Work done by nonconservative forces still
  conserves total energy. It often converts
  mechanical energy into other forms notably,
  heat, light, or noise.

30
Power

• Power is defined as the
• time rate of doing work.
• Since power may not
• be constant in time, we
• define average power
• SI units J/s watt (W)

31
James Watt

• 1736 1819
• Scottish engineer
• Invented the first efficient
• steam engine, having a
• separate condenser for the
• used steam.

32
Graphical Analysis of Work

• Plot force vs. position (for a constant force)

33
Graphical Analysis of Work

• Plot force vs. position (for a variable force)