Transcript of Layout of Chapter 6 6.1 Forces and Motion Contact v. Long Range Force Diagrams F = ma (2 nd Law)...
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- Layout of Chapter 6 6.1 Forces and Motion Contact v. Long Range
Force Diagrams F = ma (2 nd Law) Combining Forces Measurement 1 st
Law Inertia 6.2 Using Newtons Laws Mass and Weight Friction Force
Periodic Motion 6.3 Interaction Forces Identifying them Newtons 3
rd Law Fundamental Forces Ropes and Strings
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- FORCE AND MOTION 6.1
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- 4.1 The Concepts of Force and Mass A force is a push or a pull.
Contact forces arise from physical contact. Action-at-a-distance or
long- range forces do not require contact and include gravity and
electrical forces.
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- Mathematically, the net force is written as where the Greek
letter sigma denotes the vector sum.
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- Newtons Second Law When a net external force acts on an object
of mass m, the acceleration that results is directly proportional
to the net force and has a magnitude that is inversely proportional
to the mass. The direction of the acceleration is the same as the
direction of the net force.
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- MEASURE FORCE? IN A NEWTON, OF COURSE How do we
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- SI Unit for Force This combination of units is called a newton
(N).
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- DIAGRAM FORCE ON AN OBJECT How do we
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- Arrows are used to represent forces. The length of the arrow is
proportional to the magnitude of the force. 15 N 5 N
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- The net force on an object is the vector sum of all forces
acting on that object. The SI unit of force is the Newton (N).
Individual ForcesNet Force 10 N4 N 6 N
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- Individual Forces Net Force 3 N 4 N 5 N
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- What does unbalanced really mean? In pursuit of an answer,
consider a physics book at rest on a table top. There are two
forces acting upon the book. One force the Earth's gravitational
pull exerts a downward force. The second force the push of the
table on the book (sometimes referred to as a normal force) pushes
upward on the book.
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- Balancing Act Since these two forces are of equal magnitude and
in opposite directions, they balance each other. The book is said
to be at equilibrium. There is no unbalanced force acting upon the
book and thus the book maintains its state of motion. When all the
forces acting upon an object balance each other, the object will be
at equilibrium; it will not accelerate. (Note: diagrams such as the
one above are known as free-body diagrams and will be discussed in
detail in Lesson 2.)state of motionfree-body diagramsLesson 2
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- Another Pictorial Example
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- Object in motion
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- Balanced or Not? To determine if the forces acting upon an
object are balanced or unbalanced, an analysis must first be
conducted to determine which forces are acting upon the object and
in what direction. If two individual forces acting on an object are
of equal magnitude and opposite direction, then these forces are
said to be balanced. An object is said to be "acted upon by an
unbalanced force" only when there is an individual force acting on
the object which is not balanced by another force of equal
magnitude and in the opposite direction. Such analyses are
discussed in Lesson 2 of this unit and applied in Lesson 3.Lesson
2Lesson 3
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- Check your Understanding Copy this down for information used in
further examples. Luke Autbeloe drops a 5.0 kg box of shingles
(weight approximately 50.0 N) off the barn house roof into a
haystack below. Upon hitting the haystack, the box of shingles
encounters an upward restraining force of 50.0 N. Use this
description to answer the following questions.
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- Example 1 1. Which one of the following velocity-time graphs
best describes the motion of the shingles? Support your answer with
sound reasoning.
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- Answer 1 Graph B The shingles experience negative acceleration
until they hit the haystack. At that point the forces are balanced,
so velocity becomes constant
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- Example 2 2. Which one of the following ticker tapes best
describes the motion of the falling shingles from the time they are
dropped to the time they hit the ground? The arrows on the diagram
represent the point at which the shingles hit the haystack. Support
your answer with sound reasoning.
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- Answer to #2 Tape A is correct. It shows the negative
acceleration and constant velocity.
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- Example 3 (has many parts) 3. Several of Luke's friends were
watching the motion of the falling shingles. Being "physics types",
they began discussing the motion and made the following comments.
Indicate whether each of the comments is correct or incorrect.
Support your answers. A) A. Once the shingles hit the haystack, the
forces are balanced and the shingles will stop.
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- Correct or Incorrect? Incorrect. They stop accelerating but do
not stop moving.
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- Part B B. Upon hitting the haystack, the shingles will
accelerate upwards because the haystack applies an upward
force.
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- Answer to B Incorrect The balanced forces on the shingles will
keep velocity constant.
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- Example C C. Upon hitting the haystack, the shingles will
bounce upwards due to the upward force.
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- Answer to C Incorrect Forces are balanced
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- Example 4 4. If the forces acting upon an object are balanced,
then the object A. must not be moving. B. must be moving with a
constant velocity. C. must not be accelerating. D. none of the
above.
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- Answer to #4 A is possible but is not necessarily true at all
times B an object with balanced forces cannot be accelerating C It
could be at rest and staying at rest or could be in motion with
constant velocity but not accelerating making C the correct
answer
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- A free-body-diagram is a diagram that represents the object and
the forces that act on it.
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- The net force in this case is: 275 N + 395 N 560 N = +110 N and
is directed along the + x axis of the coordinate system.
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- If the mass of the car is 1850 kg then, by Newtons second law,
the acceleration is
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- 4.4 The Vector Nature of Newtons Second Law
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- Forcex componenty component +17 N +(15 N) cos67 0 N +(15 N)
sin67 +23 N+14 N The net force on the raft can be calculated in the
following way:
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- An object continues in a state of rest or in a state of motion
at a constant speed along a straight line, unless compelled to
change that state by a net force. The net force is the vector sum
of all of the forces acting on an object. Newtons First Law
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- Ladder of Inertia
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- Inertia In Motion
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- NEWTONS 1 ST LAW, OTHER FORCES, AND MISCONCEPTIONS OF FORCE
Looking into
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- ForceSubDefinitionDirection FrictionFric or f The contact force
that acts to oppose sliding motion between two surfaces Parallel to
the surface and opposite the direction of sliding NormalNThe
contact force exerted by a surface on an object. Perpendicular to
and away from the surface SpringSpA restoring force, that is, the
push or pull a spring exerts on an object Opposite the displacement
of the object at the end of the spring TensionTThe pull exerted by
a string, rope, or cable when attached to a body and pulled taut
Away from the object and parallel to the string, rope, or cable at
the point of attachment ThrustthrustA general term for the forces
that move objects such as rockets, planes, cars, and people In the
same direction as the acceleration of the object barring any
resistive forces Weightgrav or g A long range force due to
gravitational attraction between two objects, generally Earth and
an object Straight down toward the center of the earth
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- Misconceptions about Forces WRONG 1.When a ball has been
thrown, the force of the hand that threw it remains on it. 2.A
force is needed to keep an object moving. 3.Inertia is a force.
4.Air does not exert a force 5.The quantity ma is a force. Right
1.No, it is a contact force; therefore, once the contact is broken,
the force is no longer exerted. 2.It will continue moving with no
change in velocity or direction. 3.Inertia is a property of matter.
4.Air exerts a huge, usually balanced force. 5.F = ma
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- 4.1 The Concepts of Force and Mass Mass is a measure of the
amount of stuff contained in an object. Weight is actually a force
and can be found by using Newtons 2 nd Law W = mg
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- Weightless and Apparent Weight Apparent Weight The force
exerted on the scale measuring your weight at any point If there is
additional force pushing down (i.e. you are in an elevator
accelerating upward), your apparent weight is greater than your
mass. If there is less force pushing down on the scale (i.e. the
elevator is now accelerating downward) then you have a weight less
than your mass. Weightless Specific circumstance of acceleration =
g Condition of free fall Your weight is zero but you are not
without mass
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- FRICTION Looking into
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- In nature there are two general types of forces, fundamental
and non-fundamental. Fundamental Forces 1. Gravitational force 2.
Strong Nuclear force 3. Electroweak force
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- Examples of non-fundamental forces: friction tension in a rope
normal or support forces
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- FRICTION A force that opposes motion between two surfaces
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- Friction
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- Eliminating Friction
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- Static Friction The force that resists the initiation of
sliding motion between two surfaces that are in contact and at
rest
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- Kinetic Friction The force that opposes the movement of two
surfaces that are in contact and are sliding over each other
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- Ways to reduce harmful friction Lubricants (grease, oil, water)
Replace sliding friction with rolling friction Make the surface
smoother (sanding)
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- Ways to increase helpful friction Make surfaces rougher
Increase the force pushing the surfaces together
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- How cars move Cars wheels push against the road Road pushes
back Without friction between the tires and roadway, there would be
no net force and no movement
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- Air Drag and Terminal Velocity Air or fluids cause friction
that is dependent on speed As speed increases, so does the friction
An objects shape and density also affect the friction as well as
the nature of the fluid itself. Terminal velocity is reached when
the drag force equals the force of gravity
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- Dont try this at home! A common physics demonstration relies on
this principle that the more massive the object, the more it tends
to resist changes in its state of motion. The demonstration goes as
follows: several massive books are placed upon the physics
teacher's head. A wooden board is placed on top of the books and a
hammer is used to drive a nail into the board. Due to the large
mass of the books, the force of the hammer is sufficiently resisted
(inertia). This is demonstrated by the fact that the blow of the
hammer is not felt by the teacher. A common variation of this
demonstration involves smashing a brick over the teacher's hand
using a swift blow of the hammer. The massive brick resists the
force and the hand is not hurt at all. (CAUTION: Do not try these
demonstrations at home!)
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- For you to try 1. Imagine a place in the cosmos far from all
gravitational and frictional influences. Suppose an astronaut in
that place throws a rock. The rock will: a) gradually stop. b)
continue in motion in the same direction at constant speed.
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- Try this one: 2. An 2-kg object is moving horizontally with a
speed of 4 m/s. How much net force is required to keep the object
moving with the same speed and in the same direction?
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- And this one: 3. Mac and Tosh are arguing in the cafeteria. Mac
says that if he throws his jello with a greater speed it will have
a greater inertia. Tosh argues that inertia does not depend upon
speed, but rather upon mass. With whom do you agree? Why?
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- Example 4 4. If you were in a weightless environment in space,
would it require a force to set an object in motion?
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- Example 5 5. Mr. Wegley spends most Sunday afternoons at rest
on the sofa, watching pro football games and consuming large
quantities of food. What effect (if any) does this practice have
upon his inertia? Explain.
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- Example 6 6. Ben Tooclose is being chased through the woods by
a bull moose which he was attempting to photograph. The enormous
mass of the bull moose is extremely intimidating. Yet, if Ben makes
a zigzag pattern through the woods, he will be able to use the
large mass of the moose to his own advantage. Explain this in terms
of inertia and Newton's first law of motion.
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- Example 7 7. Two bricks are resting on the edge of a lab table.
Shirley Sheshort stands on her toes and spots the two bricks. She
acquires an intense desire to know which of the two bricks is more
massive. Since Shirley is vertically challenged, she is unable to
reach high enough and lift the bricks; she can, however, reach high
enough to give each brick a push. Discuss how the process of
pushing the bricks will allow Shirley to determine which of the two
bricks is more massive. What difference will Shirley observe and
how can this observation lead to the necessary conclusion?
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- Another Look at Inertia As you learned in the previous unit, an
object which is not changing its velocity is said to have an
acceleration of 0 m/s2. Thus, an alternate definition of inertia
would be:previous unit Inertia is the tendency of an object to
resist accelerations.
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- Example 1. Several physics teachers are taking some time off to
play a little putt-putt golf. The 15th hole at the Hole-In-One
Putt-Putt Golf Course has a large metal rim which putters must use
to guide their ball towards the hole. Mr. Schmidgall guides his
golf ball around the metal rim. When the ball leaves the rim, which
path (1, 2, or 3) will the golf ball follow?
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- Answer 2 because it will go in an inertial direction which is a
straight path
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- Pictorial Review
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- Pictorial Representation
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- Example 1 An applied force of 50 N is used to accelerate an
object to the right across a frictional surface. The object
encounters 10 N of friction. Use the diagram to determine the
normal force, the net force, the mass, and the acceleration of the
object. (Neglect air resistance.)
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- Answer 1 Since there is no VERTICAL acceleration, there is no
net vertical force so F norm = F grav = 80 N The mass can be
calculated using F = mg or 80 N = m (10 m/s 2 ) = 8 kg F net is the
sum of all forces F norm F grav = 0 N 50 N right 10 N Left = 40 N
right F net = m a 40 N = (8 kg) a a = 5 m/s 2
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- Example 2 An applied force of 20 N is used to accelerate an
object to the right across a frictional surface. The object
encounters 10 N of friction. Use the diagram to determine the
normal force, the net force, the coefficient of friction () between
the object and the surface, the mass, and the acceleration of the
object. (Neglect air resistance.)
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- Answer 2 Again, no vertical acceleration so F grav = F norm =
100 N Mass can be found by W = mg or F = mg 100 N = m (10 m/s 2 ) =
10 kg = F fric / F norm = 10 N /100 N = 0. 1 F net is the sum of
all forces 100 N up 100 N down = 0 N 20 N right 10 N left = 10 N
right F net = m x a (10 N) = 10 kg x a a = 1 m/s 2
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- Example 3 A 5-kg object is sliding to the right and
encountering a friction force which slows it down. The coefficient
of friction () between the object and the surface is 0.1. Determine
the force of gravity, the normal force, the force of friction, the
net force, and the acceleration. (Neglect air resistance.)
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- Answer 3 Since there is no vertical acceleration, there is no
vertical force, so F grav = F norm = 50 N F fric = F norm F fric =
0.1 (50 N) = 5 N F net is the sum of all unbalanced forces. 50 N up
50 N down = 0 N 5 N left is unbalanced = 5 N left F net = m x a 5N
= 5 kg x a A = 1 m/s 2
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- Word of Caution Avoid forcing a problem into the form of a
previously solved problem. Problems in physics will seldom look the
same. Instead of solving problems by rote or by mimicry, utilize
your conceptual understanding of Newton's laws to work towards the
solution. Use your understanding of weight and mass to find the m
or the F grav in a problem. Use your conceptual understanding of
net force (vector sum of all the forces) to find the value of F net
or the value of an individual force. Do not divorce the solving of
physics problems from your understanding of physics concepts. If
you are unable to solve physics problems like the ones above, it is
unlikely that you are having a math difficulty; rather it is more
likely that you are having a physics difficulty.
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- PERIODIC MOTION Looking at
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- Simple Harmonic Motion If the force that restores the object to
its equilibrium position is directly proportional to the
displacement of the object, the motion is called simple harmonic
motion Period = time needed to repeat one complete cycle of motion
(T) Amplitude = maximum distance the object moves from
equilibrium
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- The pendulum A pendulum is an example of simple harmonic motion
T = 2 x x ( 1/g)
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- Resonance Small forces applied at regular intervals to a
vibrating or oscillating object resulting in a greater amplitude
The time interval between applications of force is equal to the
period of the oscillation. Examples: rocking a car to get out of
snow bank or rhythmically jumping on a trampoline or pushing a
swing to get higher
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- Recap A force is a push or a pull upon an object which results
from its interaction with another object. Forces result from
interactions! As discussed in the last lesson, some forces result
from contact interactions (normal, frictional, tensional, and
applied forces are examples of contact forces) and other forces
result from action-at-a-distance interactions (gravitational,
electrical, and magnetic forces are examples of
action-at-a-distance forces).
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- Moving on According to Newton, whenever objects A and B
interact with each other, they exert forces upon each other. When
you sit in your chair, your body exerts a downward force on the
chair and the chair exerts an upward force on your body. There are
two forces resulting from this interaction a force on the chair and
a force on your body. These two forces are called action and
reaction forces and are the subject of Newton's third law of
motion. Formally stated, Newton's third law is: "For every action,
there is an equal and opposite reaction."
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- But what does it mean? The statement means that in every
interaction, there is a pair of forces acting on the two
interacting objects. The size of the force on the first object
equals the size of the force on the second object. The direction of
the force on the first object is opposite to the direction of the
force on the second object. Forces always come in pairs equal and
opposite action-reaction force pairs.
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- Implications A variety of action-reaction force pairs are
evident in nature. Consider the propulsion of a fish through the
water. A fish uses its fins to push water backwards. But a push on
the water will only serve to accelerate the water. In turn, the
water reacts by pushing the fish forwards, propelling the fish
through the water. The size of the force on the water equals the
size of the force on the fish; the direction of the force on the
water (backwards) is opposite to the direction of the force on the
fish (forwards). For every action, there is an equal (in size) and
opposite (in direction) reaction force. Action-reaction force pairs
make it possible for fishes to swim.
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- What makes birds fly? Consider the flying motion of birds. A
bird flies by use of its wings. The wings of a bird push air
downwards. In turn, the air reacts by pushing the bird upwards. The
size of the force on the air equals the size of the force on the
bird; the direction of the force on the air (downwards) is opposite
to the direction of the force on the bird (upwards). For every
action, there is an equal (in size) and opposite (in direction)
reaction. Action-reaction force pairs make it possible for birds to
fly.
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- Motion in everyday Consider the motion of your automobile on
your way to school. An automobile is equipped with wheels that spin
backwards. As the wheels spin backwards, they push the road
backwards. In turn, the road reacts by pushing the wheels forward.
The size of the force on the road equals the size of the force on
the wheels (or automobile); the direction of the force on the road
(backwards) is opposite to the direction of the force on the wheels
(forwards). For every action, there is an equal (in size) and
opposite (in direction) reaction. Action- reaction force pairs make
it possible for automobiles to move.
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- Example 1 1. While driving, Anna Litical observed a bug
striking the windshield of her car. Obviously, a case of Newton's
third law of motion. The bug hit the windshield and the windshield
hit the bug. Which of the two forces is greater: the force on the
bug or the force on the windshield?
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- Answer 1 For every action there is an EQUAL reaction. The fact
that the bug splatters only means that with its smaller mass, it is
less able to withstand the larger acceleration resulting from the
interaction. The forces are EQUAL in size.
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- Example 2 2. Rockets are unable to accelerate in space
because... A) there is no air in space for the rockets to push off
of. B) there is no gravity is in space. C) there is no air
resistance in space. D)... nonsense! Rockets do accelerate in
space.
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- Answer 2 It is a common misconception that rockets do not
accelerate in space. Rockets do accelerate in space. Rockets are
able to accelerate due to the fact that they burn fuel and push the
exhaust in a direction opposite to the direction they wish to
accelerate Answer is D
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- Example 3 3. A gun recoils when it is fired. The recoil is the
result of action-reaction force pairs. As the gases from the
gunpowder explosion expand, the gun pushes the bullet forwards and
the bullet pushes the gun backwards. The acceleration of the
recoiling gun is... a) greater than the acceleration of the bullet.
b) smaller than the acceleration of the bullet. c) the same size as
the acceleration of the bullet
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- Answer 3 The force on the gun equals the force on the bullet.
However, acceleration depends on both force and mass. The bullet
has a great acceleration due to the fact that it has a smaller
mass. Remember acceleration and mass are inversely proportional.
The correct answer is B
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- Example 4 4. In the top picture, a physics student is pulling
upon a rope which is attached to a wall. In the bottom picture, the
physics student is pulling upon a rope which is held by the
Strongman. In each case, the force scale reads 500 Newtons. The
physics student is pulling a) with more force when the rope is
attached to the wall. b) with more force when the rope is attached
to the Strongman. c) the same force in each case.
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- Answer 4 The rope transmits the force from the physics student
to the wall (or Strongman) and vice versa. Since the force of the
student pulling on the wall and the wall pulling on the student are
action-reaction force pairs, they must have equal magnitudes.
Inanimate objects such as walls can have push and pull. The correct
answer is C. The student is pulling with 500 N in both cases.
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- Force Pairs According to Newton's third law, for every action
force there is an equal (in size) and opposite (in direction)
reaction force. Forces always come in pairs known as
"action-reaction force pairs." Identifying and describing
action-reaction force pairs is a simple matter of identifying the
two interacting objects and making two statements describing who is
pushing on whom and in which direction. For example, consider the
interaction between a baseball bat and a baseball.Newton's third
law
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- Label the diagram Which is action and reaction pairs? The
baseball forces the bat to the right (an action); the bat forces
the ball to the left (the reaction). Note that the nouns in the
sentence describing the action force switch places when describing
the reaction force.
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- Athlete pushes bar upward Bar pushes athlete downward.
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- Bowling ball pushes pin rightwards. Pin pushes bowling ball
leftward.
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- Compressed air pushes balloon wall outwards. Balloon wall
pushes compressed air inward.