Energy

1
Chapter 5

• Energy

Conceptual questions 4,5,9,11,14,15 Quick
quizzes 1,2,3 Problems 8,28,45,63
2
Forms of Energy

• mechanical
• chemical
• electromagnetic
• nuclear

3
Work

• Provides a link between force and energy
• The work, W, done by a constant force on an
  object is defined as the product of the component
  of the force along the direction of displacement
  and the magnitude of the displacement

4
Work, cont.

• F cos ? is the component of the force in the
  direction of the displacement
• ? x is the displacement

UNITS

• SI
• Newton meter Joule
• N m J
• US Customary
• foot pound ft lb

5
When Work is Zero

• Displacement is horizontal
• Force is vertical
• cos 90 0

6
Work Can Be Positive or Negative

• Work is positive when lifting the box
• Work would be negative if lowering the box

7
More About Work

• Scalar quantity
• The work done by a force is zero when the force
  is perpendicular to the displacement
• cos 90 0
• If there are multiple forces acting on an object,
  the total work done is the algebraic sum of the
  amount of work done by each force
• Work can be positive or negative
• Positive if the force and the displacement are in
  the same direction
• Negative if the force and the displacement are in
  the opposite direction

8
Quick quiz 5-1

• Figure 5.4 shows four situations in which a
  force is exerted on an object. In all four
  cases, the force has the same magnitude, and the
  displacement of the object is to the right of the
  same magnitude. Rank the situations in order of
  the work done by the force on the object, from
  most positive to most negative.

9
Problem 5-8
A block of mass 2.50 kg is pushed 2.20 m along a
frictionless horizontal table by a constant 16.0
N force directed 25.0 below the horizontal.
Determine the work done by (a) the applied force,
(b) the normal force exerted by the table, (c)
the force of gravity, and (d) the net force on
the block.
10
Kinetic Energy

• Energy associated with the motion of an object
• Scalar quantity with the same units as work
• Work is related to kinetic energy

11
Conceptual question
4a. Can the kinetic energy of a system be
negative?
12
Work-Kinetic Energy Theorem

• When work is done by a net force on an object and
  the only change in the object is its speed, the
  work done is equal to the change in the objects
  kinetic energy
• Speed will increase if work is positive
• Speed will decrease if work is negative

13
Work and Kinetic Energy

• An objects kinetic energy can also be thought of
  as the amount of work the moving object could do
  in coming to rest
• The moving hammer has kinetic energy and can do
  work on the nail

14
Conceptual question
14. The driver of a car slams on her brakes to
avoid colliding with a deer. What happens to the
cars kinetic energy as it comes to rest?
15
Potential Energy

• Potential energy is associated with the position
  of the object within some system
• Potential energy is a property of the system, not
  the object
• A system is a collection of objects or particles
  interacting via forces or processes that are
  internal to the system

16
Work and Gravitational Potential Energy

• Gravitational Potential Energy is the energy
  associated with the relative position of an
  object in space near the Earths surface
• PE mgy
• Units of Potential Energy are the same as those
  of Work and Kinetic Energy

17
Conceptual questions

• 4b. Can the gravitational potential energy be
  negative?
• You are reshelving books in a library. You lift
  a book from the floor to the top of the shelf.
  The kinetic energy of the book on the floor is
  zero and the kinetic energy of the book on the
  shelf is zero, so there is no change in the
  kinetic energy. Yet you did some work in lifting
  the book. Is the work-kinetic energy theorem
  violated?

18
Reference Levels for Gravitational Potential
Energy

• A location where the gravitational potential
  energy is zero must be chosen for each problem
• The choice is arbitrary since the change in the
  potential energy is the important quantity
• Choose a convenient location for the zero
  reference height
• often the Earths surface
• may be some other point suggested by the problem

19
Conservative Forces

• A force is conservative if the work it does on an
  object moving between two points is independent
  of the path the objects take between the points
• The work depends only upon the initial and final
  positions of the object

20
More About Conservative Forces

• Examples of conservative forces include
• Gravity (Fmg or FGm1m2/r2)
• Spring force (F-kx)
• Electromagnetic forces (we will define them
  later, in the second semester)
• In general

21
Nonconservative Forces

• A force is nonconservative if the work it does on
  an object depends on the path taken by the object
  between its final and starting points.
• Examples of nonconservative forces
• kinetic friction, air drag, propulsive forces

22
Friction Depends on the Path

• The blue path is shorter than the red path
• The work required is less on the blue path than
  on the red path
• Friction depends on the path and so is a
  nonconservative force

23
Friction as a Nonconservative Force

• The friction force is transformed from the
  kinetic energy of the object into a type of
  energy associated with temperature (internal
  energy)
• the objects are warmer than they were before the
  movement
• Internal Energy is the term used for the energy
  associated with an objects temperature

24
Conservation of Mechanical Energy

• Conservation in general
• To say a physical quantity is conserved is to say
  that the numerical value of the quantity remains
  constant
• Conservation of Energy, the total mechanical
  energy remains constant
• In any isolated system of objects that interact
  only through conservative forces, the total
  mechanical energy of the system remains constant.

25
Conservation of Energy, cont.

• Total mechanical energy is the sum of the kinetic
  and potential energies in the system
• For the system with only kinetic and
  gravitational energies
• mgyi 1/2mvi2 mgyf 1/2mvf2

26
Quick quiz 5.2

• Three identical balls are thrown from the top of
  a building, all with the same initial speed. The
  first ball is thrown horizontally, the second at
  some angle above the horizontal, and the third at
  some angle below the horizontal as in Figure
  5.15. Neglecting air resistance, rank the speeds
  of the balls as they reach the ground.

27
Problem Solving with Conservation of Energy

• Define the system
• Select the location of zero gravitational
  potential energy
• Do not change this location while solving the
  problem
• Determine whether or not nonconservative forces
  are present
• If only conservative forces are present, apply
  conservation of energy and solve for the unknown

28
Problem 5-28
28. A 0.400-kg bead slides on a curved wire,
starting from rest at point A in Figure P5.28. If
the wire is frictionless, find the speed of the
bead (a) at B and (b) at C.
C
B
A
B
29
Potential Energy Stored in a Spring

• Involves the spring constant (or force constant),
  k
• Hookes Law gives the force
• F - k x
• F is the restoring force
• F is in the opposite direction of x
• k depends on how the spring was formed, the
  material it is made from, thickness of the wire,
  etc.

30
Potential Energy in a Spring

• Elastic Potential Energy
• related to the work required to compress a spring
  from its equilibrium position to some final,
  arbitrary, position x

31
Conservation of Energy including a Spring

• The PE of the spring is added to both sides of
  the conservation of energy equation

32
Nonconservative Forces with Energy Considerations

• When nonconservative forces are present, the
  total mechanical energy of the system is not
  constant
• The work done by all nonconservative forces
  acting on parts of a system equals the change in
  the mechanical energy of the system

33
Nonconservative Forces and Energy

• The energy is transformed into heat or another
  form not yet accounted for
• Friction is an example of a nonconservative
  force that will transform energy into heat

34
Transferring Energy

• By Work
• By applying a force
• Produces a displacement of the system

35
Transferring Energy

• Heat
• The process of transferring heat by collisions
  between molecules

36
Transferring Energy

• Electrical transmission
• transfer by means of electrical current

37
Transferring Energy

• Electromagnetic radiation
• any form of electromagnetic waves
• Light, microwaves, radio waves

38
Quick quiz 5-3

• Bob, of mass m, drops from a tree limb at the
  same time that Esther, also of mass m, begins her
  descent down a frictionless slide. The slide is
  in the shape of a quadrant of a circle. If they
  both start at the same height above the ground,
  which of the following is true about their
  kinetic energies as they reach the ground?
•  
• (a)  The kinetic energy of Bob is greater than
  that of Esther.
• (b)  The kinetic energy of Esther is greater than
  that of Bob.
• (c)   They have the same kinetic energy.
• (d) The answer depends on the shape of the
  slide.

39
Problem 5-45
A skier starts from rest at the top of a hill
that is inclined at 10.5 with the horizontal.
The hillside is 200 m long, and the coefficient
of friction between snow and skis is 0.075 0. At
the bottom of the hill, the snow is level and the
coefficient of friction is unchanged. How far
does the skier glide along the horizontal portion
of the snow before coming to rest?
40
Power

• Often also interested in the rate at which the
  energy transfer takes place
• Power is defined as this rate of energy transfer
• SI units are Watts (W)

41
Power, cont.

• US Customary units are generally hp
• need a conversion factor
• Can define units of work or energy in terms of
  units of power
• kilowatt hours (kWh) are often used in electric
  bills

42
Conceptual questions
5. Roads going up mountains are constructed with
switchbacks with the road weaving back and forth,
such that there is only a little rise on any
portion of the roadway. Does this require any
less work to be done by an automobile climbing
the mountain, compared to driving on a roadway
that is straight up the slope? Why are the
switchbacks used? 9. An old car accelerates from
0 to v in 10 seconds. A newer car accelerates
from 0 to 2v in the same time interval. What is
the ratio of powers expended by the two cars?
Consider the energy coming from the engine to
appear only as kinetic energy of the cars.
43
Center of Mass

• The point in the body at which all the mass may
  be considered to be concentrated
• When using mechanical energy, the change in
  potential energy is related to the change in
  height of the center of mass

44
Work Done by Varying Forces

• The work done by a variable force acting on an
  object that undergoes a displacement is equal to
  the area under the graph of F versus x

45
Conceptual questions
11. When a punter kicks a football, is he doing
any work on the ball while the toe of his foot is
in contact with it? Is he doing any work on the
ball after it loses contact with his toe? Are
any forces doing work on the ball while it is in
flight?
46
Spring Example

• Spring is slowly stretched from 0 to xmax
• Fapplied -Frestoring kx
• W ½kx²

47
Problem 5-63
Two objects are connected by a light string
passing over a light, frictionless pulley as in
Figure P5.63. The 5.00-kg object is released from
rest at a point 4.00 m above the floor. (a)
Determine the speed of each object when the two
pass each other. (b) Determine the speed of each
object at the moment the 5.00-kg object hits the
floor. (c) How much higher does the 3.00-kg
object travel after the 5.00-kg object hits the
floor?