Transcript Chapter 7 - Newton`s Third Law

Chapter 7 Lecture
physics
FOR SCIENTISTS AND ENGINEERS
a strategic approach
THIRD EDITION
randall d. knight
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Chapter 7 Newton’s Third Law
Chapter Goal: To use Newton’s third law to understand
interacting objects.
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Chapter 7 Preview
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Chapter 7 Preview
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Chapter 7 Preview
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Chapter 7 Preview
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Chapter 7 Preview
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Chapter 7 Preview
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Chapter 7 Reading Quiz
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Reading Question 7.1
Two forces for which Newton’s Third Law
applies are called
A.
B.
C.
D.
E.
An action/reaction pair.
A couple.
An opposing pair.
A vector doublet.
Complementary components.
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Reading Question 7.1
Two forces for which Newton’s Third Law
applies are called
A.
B.
C.
D.
E.
An action/reaction pair.
A couple.
An opposing pair.
A vector doublet
Complementary components.
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Reading Question 7.2
What kind of diagram is this?
A.
B.
C.
D.
E.
Environment diagram.
Force diagram.
Free-body diagram.
Interaction diagram.
System diagram.
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Reading Question 7.2
What kind of diagram is this?
A.
B.
C.
D.
E.
Environment diagram.
Force diagram.
Free-body diagram.
Interaction diagram.
System diagram.
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Reading Question 7.3
The propulsion force on a car is due to
A.
B.
C.
D.
Static friction.
Kinetic friction.
The car engine.
Elastic energy.
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Reading Question 7.3
The propulsion force on a car is due to
A.
B.
C.
D.
Static friction.
Kinetic friction.
The car engine.
Elastic energy.
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Reading Question 7.4
Is the tension in rope 2 greater than, less
than, or equal to the tension in rope 1?
A. Greater than rope 2.
B. Less than rope 2.
C. Equal to rope 2.
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Reading Question 7.4
Is the tension in rope 2 greater than, less
than, or equal to the tension in rope 1?
A. Greater than rope 2.
B. Less than rope 2.
C. Equal to rope 2.
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Reading Question 7.5
An acceleration constraint says that in
some circumstances
A. The acceleration of an object has to be positive.
B. Two objects have to accelerate in the same
direction.
C. The magnitude of the accelerations of two
objects have to be equal.
D. An object is prevented from accelerating.
E. Acceleration constraints were not discussed in
this chapter.
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Reading Question 7.5
An acceleration constraint says that in
some circumstances
A. The acceleration of an object has to be positive.
B. Two objects have to accelerate in the same
direction.
C. The magnitude of the accelerations of two
objects have to be equal.
D. An object is prevented from accelerating.
E. Acceleration constraints were not discussed in
this chapter.
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Chapter 7 Content, Examples, and
QuickCheck Questions
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Interacting Objects
 When a hammer hits a
nail, it exerts a forward
force on the nail.
 At the same time, the
nail exerts a backward
force on the hammer.
 If you don’t believe it, imagine hitting the nail with a
glass hammer.
 It’s the force of the nail on the hammer that would
cause the glass to shatter!
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Interacting Objects
 When a bat hits a ball,
the ball exerts a force
on the bat.
 When you pull someone
with a rope in a tug-ofwar, that person pulls
back on you.
The bat and the ball are interacting with each other.
 When your chair pushes up on you (the normal force),
you push down on the chair.
 All forces come in pairs, called action/reaction pairs.
 These forces occur simultaneously, and we cannot say
which is the “action” and which is the “reaction.”
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Interacting Objects
 If object A exerts a force on object B, then object
B exerts a force on object A.
 The pair of forces, as shown, is called an
action/reaction pair.
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Interacting Objects
 Long-range forces, such as gravity, also come in pairs.
 If you release a ball, it falls because the earth’s gravity
exerts a downward force
.
 At the same time, the ball pulls upward on the earth with
a force
.
 The ocean tides are an indication of the long-range
gravitational interaction of the earth and moon.
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Objects, Systems, and the Environment
 Chapters 5 and 6
considered forces
acting on a single
object, modeled as
a particle.
 The figure shows a
diagram representing
single-particle dynamics.
 We can use Newton’s second law,
determine the particle’s acceleration.
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, to
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Objects, Systems, and the Environment
 In this chapter we extend
the particle model to
include two or more
objects that interact.
 The figure shows three
objects interacting via
action/reaction pairs
of forces.
 The forces can be given labels, such as
.
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and
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Objects, Systems, and the Environment
 For example, set:
• Object A = the hammer
• Object B = the nail
• Object C = the earth
 The earth interacts with
both the hammer and the
nail via gravity.
 Practically, the earth remains at rest while the hammer
and the nail move.
 Define the system as those objects whose motion we
want to analyze.
 Define the environment as objects external to the
system.
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Objects, Systems, and the Environment
 The figure shows a new
kind of diagram, an
interaction diagram.
 The objects of the
system are in a box.
 Interactions are
represented by lines
connecting the objects.
 Interactions with objects in the environment are
called external forces.
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Tactics: Analyzing Interacting Objects
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Tactics: Analyzing Interacting Objects
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Tactics: Analyzing Interacting Objects
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Example 7.1 Pushing a Crate
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Example 7.1 Pushing a Crate
VISUALIZE
1. The person and crate are obvious objects, with a pushing force
connecting them.
2. There are normal and friction contact forces between the person
and crate and the surface. Also there is the long-range force of
gravity between the person and crate and the entire earth.
3. The person and crate are the System; these are the objects
whose motion we wish to analyze.
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Example 7.1 Pushing a Crate
4. Below are the free-body diagrams of the person and the crate.
For each, three forces are external forces. Subscripts label
which object each force acts on. There is one internal interaction,
labeled as an action/reaction pair.
ASSESS The completed free-body diagrams above could now be
the basis for a quantitative analysis.
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Propulsion
 If you try to walk across a
frictionless floor, your foot
slips and slides backward.
 In order to walk, your foot must
stick to the floor as you straighten
your leg, moving your body forward.
 The force that prevents slipping is
static friction.
 The static friction force points in the
forward direction.
 It is static friction that propels
you forward!
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What force causes this sprinter
to accelerate?
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Examples of Propulsion
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Newton’s Third Law
 Every force occurs as one member of an action/reaction
pair of forces.
 The two members of an action/reaction pair act on
two different objects.
 The two members of an action/reaction pair are equal
in magnitude, but opposite in direction:
 A catchy phrase, which is less precise, is:
“For every action there is an equal but opposite reaction.”
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Reasoning with Newton’s Third Law
 When you release a ball, it
falls down.
 The action/reaction forces of
the ball and the earth are
equal in magnitude.
 The acceleration of the ball is
 The acceleration of the earth is
 If the ball has a mass of 1 kg, the earth accelerates
upward at 2  10−24 m/s2.
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QuickCheck 7.1
A mosquito runs head-on into a truck. Splat! Which is true
during the collision?
A.
B.
C.
D.
E.
The mosquito exerts more force on the truck than the truck
exerts on the mosquito.
The truck exerts more force on the mosquito than the
mosquito exerts on the truck.
The mosquito exerts the same force on the truck as the
truck exerts on the mosquito.
The truck exerts a force on the mosquito but the mosquito
does not exert a force on the truck.
The mosquito exerts a force on the truck but the truck does
not exert a force on the mosquito.
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QuickCheck 7.1
A mosquito runs head-on into a truck. Splat! Which is true
during the collision?
A.
B.
C.
D.
E.
The mosquito exerts more force on the truck than the truck
exerts on the mosquito.
The truck exerts more force on the mosquito than the
mosquito exerts on the truck.
The mosquito exerts the same force on the truck as the
truck exerts on the mosquito.
The truck exerts a force on the mosquito but the mosquito
does not exert a force on the truck.
The mosquito exerts a force on the truck but the truck does
not exert a force on the mosquito.
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QuickCheck 7.2
A mosquito runs head-on into a truck. Which is true during
the collision?
A.
B.
C.
D.
E.
The magnitude of the mosquito’s acceleration is larger
than that of the truck.
The magnitude of the truck’s acceleration is larger than that
of the mosquito.
The magnitude of the mosquito’s acceleration is the same as
that of the truck.
The truck accelerates but the mosquito does not.
The mosquito accelerates but the truck does not.
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QuickCheck 7.2
A mosquito runs head-on into a truck. Which is true during
the collision?
A.
B.
C.
D.
E.
The magnitude of the mosquito’s acceleration is larger
than that of the truck.
The magnitude of the truck’s acceleration is larger than that
of the mosquito.
The magnitude of the mosquito’s acceleration is the same as
that of the truck.
The truck accelerates but the mosquito does not.
The mosquito accelerates but the truck does not.
Newton’s second law:
Don’t confuse cause and effect! The same force can have very different effects.
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Example 7.3 The Forces on Accelerating Boxes
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Example 7.3 The Forces on Accelerating Boxes
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Example 7.3 The Forces on Accelerating Boxes
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Acceleration Constraints
 If two objects A and B move together, their
accelerations are constrained to be equal: aA = aB.
 This equation is called an acceleration constraint.
 Consider a car being towed by a truck.
 In this case, the acceleration
constraint is aCx = aTx = ax .
 Because the accelerations
of both objects are equal,
we can drop the subscripts
C and T and call both of
them ax .
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Acceleration Constraints
 Sometimes the
acceleration of A and B
may have different signs.
 Consider the blocks A
and B in the figure.
 The string constrains
the two objects to
accelerate together.
 But, as A moves to the right in the +x direction, B
moves down in the −y direction.
 In this case, the acceleration constraint is aAx = −aBy .
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Problem-Solving Strategy: Interacting-Objects
Problems
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Problem-Solving Strategy: Interacting-Objects
Problems
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QuickCheck 7.3
What, if anything, is wrong with these
free-body diagrams for a truck towing a
car at steady speed? The truck is heavier
than the car and the rope is massless.
A.
B.
C.
D.
E.
Nothing is wrong.
One or more forces have the wrong length.
One of more forces have the wrong direction.
One or more action/reaction pairs are wrong.
Both B and D.
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QuickCheck 7.3
What, if anything, is wrong with these
free-body diagrams for a truck towing a
car at steady speed? The truck is heavier
than the car and the rope is massless.
A.
B.
C.
D.
E.
Nothing is wrong.
One or more forces have the wrong length.
One of more forces have the wrong direction.
One or more action/reaction pairs are wrong.
Both B and D.
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QuickCheck 7.4
A car is parked at rest on a horizontal road. The
upward force of the road on the car (the normal force)
is the same size as the downward pull of gravity
A.
B.
C.
D.
Because they are an action/reaction pair.
Because of Newton’s first law.
Both A and B.
Neither A nor B. Some other reason.
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QuickCheck 7.4
A car is parked at rest on a horizontal road. The
upward force of the road on the car (the normal force)
is the same size as the downward pull of gravity
A.
B.
C.
D.
Because they are an action/reaction pair.
Because of Newton’s first law.
Both A and B.
Neither A nor B. Some other reason.
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Tension Revisited
 Figure (a) shows a heavy
safe hanging from a rope.
 The combined pulling force of
billions of stretched molecular
springs is called tension.
 Tension pulls equally in both
directions.
 Figure (b) is a very thin cross
section through the rope.
 This small piece is in
equilibrium, so it must be
pulled equally from both sides.
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Example 7.5 Pulling a Rope
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Example 7.5 Pulling a Rope
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Example 7.5 Pulling a Rope
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Example 7.5 Pulling a Rope
The rope’s tension is the same in both situations.
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The Massless String Approximation
 Often in problems the mass of the string or rope is
much less than the masses of the objects that it
connects.
 In such cases, we can adopt the following massless
string approximation:
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The Massless String Approximation
 Two blocks are connected by a
massless string, as block B is
pulled to the right.
 Forces
and
act as if they are an
action/reaction pair:
 All a massless string does is transmit a force from A to B
without changing the magnitude of that force.
 For problems in this book, you can assume that any
strings or ropes are massless unless it explicitly
states otherwise.
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QuickCheck 7.5
Boxes A and B are being pulled to the right on a
frictionless surface. Box A has a larger mass than B.
How do the two tension forces compare?
A.
B.
C.
D.
T1 > T2
T1 = T2
T1 < T2
Not enough information to tell.
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QuickCheck 7.5
Boxes A and B are being pulled to the right on a
frictionless surface. Box A has a larger mass than B.
How do the two tension forces compare?
A.
B.
C.
D.
T1 > T2
T1 = T2
T1 < T2
Not enough information to tell.
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Example 7.6 Comparing Two Tensions
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Example 7.6 Comparing Two Tensions
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Example 7.6 Comparing Two Tensions
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Example 7.6 Comparing Two Tensions
T1 > T2
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QuickCheck 7.6
Boxes A and B are sliding to the right on a frictionless surface.
Hand H is slowing them. Box A has a larger mass than B.
Considering only the horizontal forces:
A.
FB on H = FH on B = FA on B = FB on A
B.
FB on H = FH on B > FA on B = FB on A
C.
FB on H = FH on B < FA on B = FB on A
D.
FH on B = FH on A > FA on B
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QuickCheck 7.6
Boxes A and B are sliding to the right on a frictionless surface.
Hand H is slowing them. Box A has a larger mass than B.
Considering only the horizontal forces:
A.
FB on H = FH on B = FA on B = FB on A
B.
FB on H = FH on B > FA on B = FB on A
C.
FB on H = FH on B < FA on B = FB on A
D.
FH on B = FH on A > FA on B
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Pulleys
 Block B drags block A across a frictionless table as it
falls.
 The string and the pulley are both massless.
 There is no friction where the pulley turns on its axle.
 Therefore, TA on S = TB on S.
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Pulleys
 Since TA on B = TB on A, we can draw the simplified freebody diagram on the right, below.
 Forces
and
act as if they are in an
action/reaction pair, even though they are not
opposite in direction because the tension force gets
“turned” by the pulley.
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QuickCheck 7.7
All three 50-kg blocks are at rest.
The tension in rope 2 is
A.
greater than the tension in rope 1.
B.
equal to the tension in rope 1.
C.
less than the tension in rope 1.
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QuickCheck 7.7
All three 50-kg blocks are at
rest. The tension in rope 2 is
A.
greater than the tension in rope 1.
B.
equal to the tension in rope 1.
C.
less than the tension in rope 1.
Each block is in static equilibrium, with
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.
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QuickCheck 7.8
The two masses are at rest. The pulleys are frictionless.
The scale is in kg. The scale reads
A.
B.
C.
0 kg.
5 kg.
10 kg.
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QuickCheck 7.8
The two masses are at rest. The pulleys are frictionless.
The scale is in kg. The scale reads
A.
B.
C.
0 kg.
5 kg.
10 kg.
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QuickCheck 7.9
The acceleration constraint
here is
A. aAy = aBy.
B. –aAy = –aBy.
C. aAy = –aBy.
D. aBy = –aAy.
E. Either C or D.
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QuickCheck 7.9
The acceleration constraint
here is
A.
B.
C.
D.
E.
aAy = aBy.
–aAy = –aBy.
aAy = –aBy.
aBy = –aAy.
Either C or D.
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Either says that the
acceleration
vectors point in
opposite directions.
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Tactics: Working With Ropes and Pulleys
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QuickCheck 7.10
The top block is accelerated across a frictionless table
by the falling mass m. The string is massless, and the
pulley is both massless and frictionless. The tension in
the string is
A. T < mg.
B. T = mg.
C. T > mg.
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QuickCheck 7.10
The top block is accelerated across a frictionless table
by the falling mass m. The string is massless, and the
pulley is both massless and frictionless. The tension in
the string is
A. T < mg.
B. T = mg.
C. T > mg
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Tension has to be
less than mg for
the block to have
a downward
acceleration.
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QuickCheck 7.11
Block A is accelerated across a frictionless table. The string is
massless, and the pulley is both massless and frictionless.
Which is true?
A. Block A accelerates faster in case a than in case b.
B. Block A has the same acceleration in case a and case b.
C. Block A accelerates slower in case a than in case b.
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QuickCheck 7.11
Block A is accelerated across a frictionless table. The string is
massless, and the pulley is both massless and frictionless.
Which is true?
A. Block A accelerates faster in case a than in case b.
B. Block A has the same acceleration in case a and case b.
C. Block A accelerates slower in case a than in case b.
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Chapter 7 Summary Slides
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General Principles
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General Principles
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Important Concepts
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Important Concepts
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