Transcript Chapter 4x - HCC Learning Web

Chapter 4 The Laws of Motion
Ying Yi PhD
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Outline
 Force
 Newton’s Three Law
 Force example 1: Gravitational force
 Force example 2: Friction
 Application of Newton’s Laws
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Sir Isaac Newton
 1642 – 1727
 Formulated basic
concepts and laws of
mechanics
 Universal Gravitation
 Calculus
 Light and optics
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Classical Mechanics
 Describes the relationship between the motion of
objects in our everyday world and the forces
acting on them
 Conditions when Classical Mechanics does not
apply
 Very tiny objects (< atomic sizes)
 Objects moving near the speed of light
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Contact and Field Forces
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Fundamental Forces
 Types
 Strong nuclear force
 Electromagnetic force
 Weak nuclear force
 Gravity
 Characteristics
 All field forces
 Listed in order of decreasing strength
 Only gravity and electromagnetic in mechanics
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Newton’s First Law
 An object moves with a velocity that is constant in
magnitude and direction, unless acted on by a
nonzero net force
 Note that: The net force is defined as the vector sum
of all the external forces exerted on the object
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External and Internal Forces
 External force
 Any force that results from the interaction between the
object and its environment
 Internal forces
 Forces that originate within the object itself
 They cannot change the object’s velocity
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Inertia
 Is the tendency of an object to continue in its original
motion
 In the absence of a force
 Thought experiment




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Hit a golf ball
Hit a bowling ball with the same force
The golf ball will travel farther
Both resist changes in their motion
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Newton’s Second Law
 The acceleration of an object is directly proportional
to the net force acting on it and inversely proportional
to its mass.
 Can also be applied three-dimensionally
F
x
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 max ; Fy  may ; Fz  maz ;
Units of Force
 SI unit of force is a Newton (N)
kg m
1N  1 2
s
 US Customary unit of force is a pound (lb)
 1 N = 0.225 lb
 See table 4.1
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Some Notes About Forces
 Forces cause changes in motion
 Motion can occur in the absence of forces
 All the forces acting on an object are added as
vectors to find the net force acting on the object
 ma is not a force itself
 Newton’s Second Law is a vector equation
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Example 4.2 Horses Pulling a Barge
Two horses are pulling a barge with mass 2.00×103Kg
along a canal, as shown in Figure 4.7. The cable
connected to the first horse makes an angle of Ɵ1=30.0°
with respect to the direction of the canal, while the
cable connected to the second horse makes an angle of
Ɵ2=-45.0°. Find the initial acceleration of the barge,
starting at rest, if each horse exerts a force of
magnitude 6.00×102N on the barge. Ignore forces of
resistance on the barge.
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Newton’s Third Law
 If object 1 and object 2 interact, the force exerted by
object 1 on object 2 is equal in magnitude but opposite
in direction to the force exerted by object 2 on object
1.

F12  F21
 Equivalent to saying a single isolated force cannot exist
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Newton’s Third Law cont.
 F12 may be called the
action force and F21 the
reaction force
 Actually, either force can be
the action or the reaction
force
 The action and reaction
forces act on different
objects
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Some Action-Reaction Pairs

n and n '
 n is the normal force, the force
the table exerts on the TV
 is always perpendicular to the
nsurface
 is the reaction – the TV on the
ntable
'

n  n '
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More Action-Reaction pairs
'
F
and
F

g
g
F is the force the Earth
g
exerts on the object
F ' is the force the object
g
exerts on the earth

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Fg  Fg'
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Forces Acting on an Object
 Newton’s Law uses the
forces acting on an
object
n and Fg are acting on
the object
 n ' and Fg' are acting
on other objects
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Example 4.5 Action-reaction
A man of mass M=75.0 kg and woman of mass m=55.0
kg stand facing each other on an ice rink, both wearing
ice skates. The woman pushes the man with a horizontal
force of F=85.0 N in the positive x-direction. Assume
the ice is frictionless. (a)What is the man’s acceleration?
(b) What is the reaction force acting on the woman? (c)
Calculate the woman’s acceleration.
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Gravitational Force
 Mutual force of attraction between any two objects
 Expressed by Newton’s Law of Universal
Gravitation:
 Every particle in the Universe attracts every other
particle with a force that is directly proportional to the
square of the distance between them
m1 m2
Fg  G 2
r
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Weight
 The magnitude of the gravitational force acting on an
object of mass m near the Earth’s surface is called the
weight w of the object
 w = m g is a special case of Newton’s Second Law
 g is the acceleration due to gravity
 g can also be found from the Law of Universal
Gravitation
 Weight is not an inherent property of an object
 Mass is an inherent property
 Weight depends upon location
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Example 4.3 Forces of Distant Worlds
(a) Find the gravitational force exerted by the Sun on a
70.0 kg man located at the Earth’s equator at noon,
when the man is closest to the Sun. (b) Calculate the
gravitational force of the Sun on the man at midnight,
when he is farthest from the Sun. (c) Calculate the
difference in the acceleration due to the Sun between
noon and midnight. (For values, see Table 7.3, page 223)
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Application of Newton’s Laws
A Crate being pulled to
the right on a frictionless
surface.
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Assumptions about crate
 Objects behave as particles
 Can ignore rotational motion (for now)
 Masses of strings or ropes are negligible
 Interested only in the forces acting on the object
 Can neglect reaction forces
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Assumptions about Ropes
 Ignore any frictional effects of the rope
 Ignore the mass of the rope
 The magnitude of the force exerted along the rope is
called the tension
 The tension is the same at all points in the rope
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Free Body Diagram of Crate
 Must identify all the forces acting on the object of
interest
 Choose an appropriate coordinate system
 If the free body diagram is incorrect, the solution will
likely be incorrect
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Free Body Diagram of Crate
 The force
is the tension
acting on the box
 The tension is the same at all
points along the rope
 n and Fg are the forces
exerted by the earth and the
ground
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Apply Newton’s second Law to Crate
max  T
ma y  n  mg  0
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Solving Newton’s Second Law Problems
 Read the problem at least once
 Draw a picture of the system
 Identify the object of primary interest
 Indicate forces with arrows
 Label each force
 Use labels that bring to mind the physical quantity involved
 Draw a free body diagram
 If additional objects are involved, draw separate free body diagrams
for each object
 Choose a convenient coordinate system for each object
 Apply Newton’s Second Law
 The x- and y-components should be taken from the vector equation
and written separately
 Solve for the unknown(s)
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Example 4.8: Moving a crate
The combined weight of the crate and dolly is
3.00×102N. If the man pulls on the rope with a
constant force of 20.0N, what is the acceleration of the
system(crate and dolly), and how far will it move in
2.00s? Assume the system starts from rest and that
there are no friction forces opposing the motion?
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Group problem: Running car
(a) A car of mass m is on an icy driveway inclined at an
angle Ɵ=20.0°, as in Figure. Determine the acceleration
of the car, assuming the incline is frictionless. (b) If the
length of the drive way is 25.0 m and the car starts
from rest at the top, how long does it take to travel to
the bottom? (c) What is the car’s speed at the bottom?
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Equilibrium
 An object either at rest or moving with a constant
velocity is said to be in equilibrium
 The net force acting on the object is zero (since the
acceleration is zero)
F  0
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Equilibrium cont.
 Easier to work with the equation in terms of its
components:
F
x
 0 and
F
y
0
 This could be extended to three dimensions
 A zero net force does not mean the object is not
moving, but that it is not accelerating
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Example 4.6 A Traffic light at rest
A traffic light weighting 1.00×102N hangs from a
vertical cable tied to two other cables that are fastened
to a support as in Figure 4.14a. The upper cables make
angles of 37.0° and 53.0° with the horizontal. Find the
tension in each of the three cables.
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Multiple Objects – Example
 When you have more than one object, the problem-
solving strategy is applied to each object
 Draw free body diagrams for each object
 Apply Newton’s Laws to each object
 Solve the equations
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Example 4.11: Atwood’s Machine
Two objects of mass m1 and m2, with m2>m1, are
connected by a light, inextensible cord and hung over a
frictionless pulley, as in Figure 4.20a. Both cord and
pulley have negligible mass. Find the magnitude of the
acceleration of the system and the tension in the cord.
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Forces of Friction
 When an object is in motion on a surface or through a
viscous medium, there will be a resistance to the
motion
 This is due to the interactions between the object and its
environment
 This is resistance is called friction
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Static Friction, ƒs
 Static friction acts to keep
the object from moving
 If F increases, so does ƒs
 If F decreases, so does ƒs
 ƒs  µs n
 Use = sign for impending
motion only
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Kinetic Friction, ƒk
 The force of kinetic
friction acts when the
object is in motion
 ƒk = µ k n
 Variations of the
coefficient with speed
will be ignored
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Some Coefficients of Friction
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Example 4.12 A Block on a Ramp
Suppose a block with a mass of 2.50 kg is resting on a
ramp. If the coefficient of static friction between the
block and ramp is 0.350, what maximum angle can the
ramp make with the horizontal before the block starts to
slip down?
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The system approach
 The objects are rigidly connected.
 When two objects are considered a system, external
force of one objects becomes internal force of the
system.
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Example 4.15 Two Blocks and a cord
A block of mass m=5.00 kg rides on top of a second
block of mass M=10.0 kg. A person attaches a string to
the bottom block and pulls the system horizontally
across a frictionless surface, as in Figure 4.26a. Friction
between the two blocks keeps the 5.00 kg block from
slipping off. If the coefficient of static friction is 0.350,
(a) what maximum force can be exerted by the string on
the 10.0 kg block without causing the 5.00 kg block to
slip? (b) Use the system approach to calculate the
acceleration.
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Group Problem: Two Blocks
Suppose instead the string is attached to the top block
in Example 4.15. Find the maximum force that can be
exerted by the string on the block without causing the
top block to slip.
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