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Chapter 10 Lecture
physics
FOR SCIENTISTS AND ENGINEERS
a strategic approach
THIRD EDITION
randall d. knight
© 2013 Pearson Education, Inc.
Chapter 10 Preview
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Slide 10-5
Chapter 10 Preview
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Slide 10-6
Chapter 10 Preview
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Slide 10-7
Reading Question 10.3
Mechanical energy is
A. The energy due to internal moving parts.
B. The energy of motion.
C. The energy of position.
D. The sum of kinetic energy plus potential
energy.
E. The sum of kinetic, potential, thermal, and elastic
energy.
© 2013 Pearson Education, Inc.
Slide 10-13
Reading Question 10.3
Mechanical energy is
A. The energy due to internal moving parts.
B. The energy of motion.
C. The energy of position.
D. The sum of kinetic energy plus potential
energy.
E. The sum of kinetic, potential, thermal, and elastic
energy.
© 2013 Pearson Education, Inc.
Slide 10-14
Reading Question 10.5
A perfectly elastic collision is a collision
A. Between two springs.
B. That conserves thermal energy.
C. That conserves kinetic energy.
D. That conserves potential energy.
E. That conserves mechanical energy.
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Slide 10-17
Reading Question 10.5
A perfectly elastic collision is a collision
A. Between two springs.
B. That conserves thermal energy.
C. That conserves kinetic energy.
D. That conserves potential energy.
E. That conserves mechanical energy.
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Slide 10-18
The Basic Energy Model
 Within a system, energy can
be transformed from one
type to another.
 The total energy of the
system is not changed by
these transformations.
 This is the law of
conservation of energy.
 Energy can also be transferred
from one system to another.
 The mechanical transfer of energy to a system via
forces is called work.
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Slide 10-23
Kinetic Energy and Gravitational Potential
Energy
Define kinetic energy as an energy of motion:
Define gravitational potential energy as an
energy of position:
The sum K + Ug is not changed when an object is in
free fall. Its initial and final values are equal:
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Slide 10-25
Example 10.1 Launching a Pebble
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Slide 10-31
Example 10.1 Launching a Pebble
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Slide 10-32
Example 10.1 Launching a Pebble
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Slide 10-33
Energy Bar Charts
 A pebble is tossed up into the air.
 The simple bar charts below show how the sum of K + Ug
remains constant as the pebble rises and then falls.
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Slide 10-34
QuickCheck 10.4
Rank in order, from largest to
smallest, the gravitational
potential energies of the balls.
A. 1 > 2 = 4 > 3
B. 1 > 2 > 3 > 4
C. 3 > 2 > 4 > 1
D. 3 > 2 = 4 > 1
© 2013 Pearson Education, Inc.
Slide 10-38
QuickCheck 10.4
Rank in order, from largest to
smallest, the gravitational
potential energies of the balls.
A. 1 > 2 = 4 > 3
B. 1 > 2 > 3 > 4
C. 3 > 2 > 4 > 1
D. 3 > 2 = 4 > 1
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Slide 10-39
Gravitational Potential Energy on a Frictionless
Surface – Slide 1 of 4
 Figure (a) shows an object
of mass m sliding along a
frictionless surface.
 Figure (b) shows a magnified
segment of the surface that,
over some small distance, is
a straight line.
 Define an s-axis parallel to
the direction of motion
 Newton’s second law along
the axis is:
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Slide 10-45
QuickCheck 10.6
A small child slides down the four frictionless slides A–
D. Rank in order, from largest to smallest, her speeds at
the bottom.
A. vD > vA > vB > vC
B. vD > vA = vB > vC
C. vC > vA > vB > vD
D. vA = vB = vC = vD
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Slide 10-51
QuickCheck 10.6
A small child slides down the four frictionless slides A–
D. Rank in order, from largest to smallest, her speeds at
the bottom.
A. vD > vA > vB > vC
B. vD > vA = vB > vC
C. vC > vA > vB > vD
D. vA = vB = vC = vD
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Slide 10-52
Example 10.3 The Speed of a Sled
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Slide 10-53
Example 10.3 The Speed of a Sled
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Slide 10-54
Example 10.3 The Speed of a Sled
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Slide 10-55
Problem-Solving Strategy: Conservation
of Mechanical Energy
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Slide 10-56
QuickCheck 10.7
Three balls are thrown from
a cliff with the same speed
but at different angles.
Which ball has the greatest
speed just before it hits the
ground?
A.
Ball A.
B.
Ball B.
C.
Ball C.
D.
All balls have the same speed.
© 2013 Pearson Education, Inc.
Slide 10-57
QuickCheck 10.7
Three balls are thrown from
a cliff with the same speed
but at different angles.
Which ball has the greatest
speed just before it hits the
ground?
A.
Ball A.
B.
Ball B.
C.
Ball C.
D.
All balls have the same speed.
© 2013 Pearson Education, Inc.
Slide 10-58
QuickCheck 10.8
A hockey puck sliding on smooth ice at 4 m/s comes to a
1-m-high hill. Will it make it to the top of the hill?
A.
Yes.
B.
No.
C.
Can’t answer without knowing the mass of the puck.
D.
Can’t say without knowing the angle of the hill.
© 2013 Pearson Education, Inc.
Slide 10-59
QuickCheck 10.8
A hockey puck sliding on smooth ice at 4 m/s comes to a
1-m-high hill. Will it make it to the top of the hill?
A.
Yes.
B.
No.
C.
Can’t answer without knowing the mass of the puck.
D.
Can’t say without knowing the angle of the hill.
© 2013 Pearson Education, Inc.
Slide 10-60
Restoring Forces and Hooke’s Law
 The figure shows how a
hanging mass stretches
a spring of equilibrium
length L0 to a new
length L.
 The mass hangs in static
equilibrium, so the upward
spring force balances the
downward gravity force.
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Slide 10-61
Restoring Forces and Hooke’s Law
 The figure shows measured
data for the restoring force
of a real spring.
 s is the displacement
from equilibrium.
 The data fall along the
straight line:
 The proportionality constant k is called the spring
constant.
 The units of k are N/m.
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Slide 10-62
Hooke’s Law
 One end of a spring is
attached to a fixed wall.
 (Fsp)s is the force produced
by the free end of the spring.
 s = s – se is the
displacement from
equilibrium.
 The negative sign is the
mathematical indication of
a restoring force.
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Slide 10-63
QuickCheck 10.9
The restoring force of three
springs is measured as they are
stretched. Which spring has the
largest spring constant?
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Slide 10-64
QuickCheck 10.9
The restoring force of three
springs is measured as they are
stretched. Which spring has the
largest spring constant?
Steepest slope.
Takes lots of force for
a small displacement.
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Slide 10-65
Example 10.5 Pull Until It Slips
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Slide 10-66
Example 10.5 Pull Until It Slips
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Slide 10-67
Example 10.5 Pull Until It Slips
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Slide 10-70
Example 10.5 Pull Until It Slips
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Slide 10-71
Elastic Potential Energy
 The figure shows a beforeand-after situation in which
a spring launches a ball.
 Integrating the net force
from the spring, as given by
Hooke’s Law, shows that:
 Here K = ½ mv2 is the kinetic
energy.
 We define a new quantity:
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Slide 10-74
QuickCheck 10.10
A spring-loaded gun shoots a plastic ball with a launch
speed of 2.0 m/s. If the spring is compressed twice as
far, the ball’s launch speed will be
A.
B.
C.
D.
E.
1.0 m/s.
2.0 m/s.
2.8 m/s
4.0 m/s.
16.0 m/s.
© 2013 Pearson Education, Inc.
Slide 10-76
QuickCheck 10.10
A spring-loaded gun shoots a plastic ball with a launch
speed of 2.0 m/s. If the spring is compressed twice as
far, the ball’s launch speed will be
A.
B.
C.
D.
E.
1.0 m/s.
2.0 m/s.
2.8 m/s
4.0 m/s.
16.0 m/s.
© 2013 Pearson Education, Inc.
Conservation of energy:
Double x double v
Slide 10-77
QuickCheck 10.11
A spring-loaded gun shoots a plastic ball with a launch
speed of 2.0 m/s. If the spring is replaced with a new
spring having twice the spring constant (but still
compressed the same distance), the ball’s launch
speed will be
A.
B.
C.
D.
E.
1.0 m/s.
2.0 m/s.
2.8 m/s.
4.0 m/s.
16.0 m/s.
© 2013 Pearson Education, Inc.
Slide 10-78
QuickCheck 10.11
A spring-loaded gun shoots a plastic ball with a launch
speed of 2.0 m/s. If the spring is replaced with a new
spring having twice the spring constant (but still
compressed the same distance), the ball’s launch
speed will be
A.
B.
C.
D.
E.
1.0 m/s.
2.0 m/s.
2.8 m/s.
4.0 m/s.
16.0 m/s.
© 2013 Pearson Education, Inc.
Conservation of energy:
Double k  increase
v by square root of 2
Slide 10-79
Example 10.6 A Spring-Launched Plastic Ball
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Slide 10-80
Example 10.6 A Spring-Launched Plastic Ball
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Slide 10-83
Energy Diagrams
 Shown is a more general
energy diagram.
 The particle is released
from rest at position x1.
 Since K at x1 is zero,
the total energy TE = U
at that point.
 The particle speeds up
from x1 to x2.
 Then it slows down from x2 to x3.
 The particle reaches maximum speed as it passes x4.
 When the particle reaches x5, it turns around and
reverses the motion.
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Slide 10-89
Equilibrium Positions: Stable
 Consider a particle
with the total energy
E2 shown in the figure.
 The particle can be
at rest at x2, but it
cannot move away
from x2: This is
static equilibrium.
 If you disturb the particle,
giving it a total energy slightly
larger than E2, it will oscillate very close to x2.
 An equilibrium for which small disturbances cause small
oscillations is called a point of stable equilibrium.
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Slide 10-90
QuickCheck 10.12
A particle with the potential
energy shown is moving
to the right. It has 1.0 J of
kinetic energy at x = 1.0 m.
In the region 1.0 m < x < 2.0 m,
the particle is
A.
Speeding up.
B.
Slowing down.
C.
Moving at constant speed.
D.
I have no idea.
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Slide 10-99
QuickCheck 10.12
A particle with the potential
energy shown is moving
to the right. It has 1.0 J of
kinetic energy at x = 1.0 m.
In the region 1.0 m < x < 2.0 m,
the particle is
A.
Speeding up.
B.
Slowing down.
C.
Moving at constant speed.
D.
I have no idea.
© 2013 Pearson Education, Inc.
Slide 10-100
QuickCheck 10.13
A particle with the potential
energy shown is moving to
the right. It has 1.0 J of kinetic
energy at x = 1.0 m. Where
is the particle’s turning point?
A.
1.0 m.
B.
2.0 m.
C.
5.0 m.
D.
6.0 m.
E.
It doesn’t have a turning point.
© 2013 Pearson Education, Inc.
Slide 10-101
QuickCheck 10.13
A particle with the potential
energy shown is moving to
the right. It has 1.0 J of kinetic
energy at x = 1.0 m. Where
is the particle’s turning point?
A.
1.0 m.
B.
2.0 m.
C.
5.0 m.
D.
6.0 m.
E.
It doesn’t have a turning point.
© 2013 Pearson Education, Inc.
Slide 10-102
Elastic Collisions
 During an inelastic collision of two objects, some of the
mechanical energy is dissipated inside the objects as
thermal energy.
 A collision in which mechanical energy is conserved is
called a perfectly elastic collision.
 Collisions between
two very hard objects,
such as two billiard
balls or two steel balls,
come close to being
perfectly elastic.
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Slide 10-106
Using Reference Frames: Quick Example
A 200 g ball moves to the right at 2.0 m/s. It has a
head-on, perfectly elastic collision with a 100 g ball that
is moving toward it at 3.0 m/s. What are the final
velocities of both balls?
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Slide 10-113
Using Reference Frames: Quick Example
 Figure (a) shows the situation just before the collision
in the lab frame L.
 Figure (b) shows the situation just before the collision
in the frame M that is moving along with ball 2.
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Slide 10-114
Using Reference Frames: Quick Example
 We can use Equations 10.42 to find the post-collision
velocities in the moving frame M:
 Transforming back to the lab frame L:
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Slide 10-115
Chapter 11 Preview
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Slide 11-3
Chapter 11 Preview
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Slide 11-3
Chapter 11 Preview
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Slide 11-8
Work and Kinetic Energy
 Consider a force acting on
a particle which moves
along the s-axis.
 The force component Fs
causes the particle to
speed up or slow down,
transferring energy to or
from the particle.
 The force does work on the particle:
 The units of work are N m, where 1 N m = 1 kg m2/s2 = 1 J.
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Slide 11-26
An Analogy with the Impulse-Momentum Theorem
 The impulse-momentum
theorem is:
 The work-kinetic energy
theorem is:
 Impulse and work are both
the area under a force graph,
but it’s very important to know
what the horizontal axis is!
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Slide 11-28
QuickCheck 11.3
A crane lowers a girder into place at constant speed.
Consider the work Wg done by gravity and the work
WT done by the tension in the cable. Which is true?
A.
Wg > 0 and WT > 0
B.
Wg > 0 and WT < 0
C.
Wg < 0 and WT > 0
D.
Wg < 0 and WT < 0
E.
Wg = 0 and WT = 0
© 2013 Pearson Education, Inc.
Slide 11-34
QuickCheck 11.3
A crane lowers a girder into place at constant speed.
Consider the work Wg done by gravity and the work
WT done by the tension in the cable. Which is true?
A.
Wg > 0 and WT > 0
B.
Wg > 0 and WT < 0
C.
Wg < 0 and WT > 0
D.
Wg < 0 and WT < 0
E.
Wg = 0 and WT = 0
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The downward force of gravity is in the
direction of motion  positive work.
The upward tension is in the direction
opposite the motion  negative work.
Slide 11-35
QuickCheck 11.4
Robert pushes the box to the
left at constant speed. In doing
so, Robert does ______ work
on the box.
A.
positive
B.
negative
C.
zero
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Slide 11-39
QuickCheck 11.4
Robert pushes the box to the
left at constant speed. In doing
so, Robert does ______ work
on the box.
A.
positive
B.
negative
C.
zero
Force is in the direction of displacement  positive work
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Slide 11-40
QuickCheck 11.6
Which force below does the most work? All three
displacements are the same.
A.
B.
C.
D.
The 10 N force.
The 8 N force
The 6 N force.
They all do the same work.
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sin60 = 0.87
cos60 = 0.50
Slide 11-47
QuickCheck 11.6
Which force below does the most work? All three
displacements are the same.
A.
B.
C.
D.
The 10 N force.
The 8 N force
The 6 N force.
They all do the same work.
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sin60 = 0.87
cos60 = 0.50
Slide 11-48
QuickCheck 11.7
A light plastic cart and a heavy
steel cart are both pushed with
the same force for a distance
of 1.0 m, starting from rest.
After the force is removed, the
kinetic energy of the light
plastic cart is ________ that of
the heavy steel cart.
A.
B.
C.
D.
greater than
equal to
less than
Can’t say. It depends on how big the force is.
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Slide 11-49
QuickCheck 11.7
A light plastic cart and a heavy
steel cart are both pushed with
the same force for a distance
of 1.0 m, starting from rest.
After the force is removed, the
kinetic energy of the light
plastic cart is ________ that of
the heavy steel cart.
A.
B.
C.
D.
greater than
Same force, same distance  same work done
equal to
Same work  change of kinetic energy
less than
Can’t say. It depends on how big the force is.
© 2013 Pearson Education, Inc.
Slide 11-50
QuickCheck 11.8
A car on a level road turns a
quarter circle ccw. You learned
in Chapter 8 that static friction
causes the centripetal
acceleration. The work done
by static friction is _____.
A.
positive
B.
negative
C.
zero
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Slide 11-52
QuickCheck 11.8
A car on a level road turns a
quarter circle ccw. You learned
in Chapter 8 that static friction
causes the centripetal
acceleration. The work done
by static friction is _____.
A.
positive
B.
negative
C.
zero
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Slide 11-53
Example 11.6 Using Work to Find the Speed
of a Car
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Slide 11-63
Example 11.6 Using Work to Find the Speed
of a Car
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Slide 11-64
Example 11.6 Using Work to Find the Speed
of a Car
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Slide 11-65
Example 11.8 Using Work and Potential Energy
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Slide 11-70
Example 11.8 Using Work and Potential Energy
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Slide 11-71
Finding Force from Potential Energy
 In the limit s  0, we
find that the force at
position s is:
 The force on the object is the negative of the
derivative of the potential energy with respect to
position.
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Slide 11-74
Finding Force from Potential Energy
 Figure (a) shows the
potential-energy diagram
for an object at height y.
 The force on the object
is (FG)y = mg.
 Figure (b) shows the
corresponding F-versus-y
graph.
 At each point, the value
of F is equal to the
negative of the slope
of the U-versus-y graph.
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Slide 11-75
QuickCheck 11.9
A particle moves along the
x-axis with the potential
energy shown. At x = 4 m,
the x-component of the
force on the particle is
A.
–4 N.
B.
–2 N.
C.
0 N.
D.
2 N.
E.
4N
© 2013 Pearson Education, Inc.
Slide 11-77
QuickCheck 11.9
A particle moves along the
x-axis with the potential
energy shown. At x = 4 m,
the x-component of the
force on the particle is
A.
–4 N.
B.
–2 N.
C.
0 N.
D.
2 N.
E.
4 N.
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Slide 11-78
Power
 The rate at which energy is transferred or transformed
is called the power P.
 The SI unit of power is the
watt, which is defined as:
Highly trained athletes have a tremendous
power output.
1 watt = 1 W = 1 J/s
 The English unit of power
is the horsepower, hp.
1 hp = 746 W
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Slide 11-98
Example 11.13 Choosing a Motor
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Slide 11-99
Example 11.13 Choosing a Motor
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Slide 11-100
Example 11.14 Power Output of a Motor
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Slide 11-105
Example 11.14 Power Output of a Motor
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Slide 11-106
Important Concepts
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Slide 11-112
Important Concepts
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Slide 11-113