Forces and Newton

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Chapter 4

• Forces and Newtons Laws of Motion

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4.1 The Concepts of Force and Mass
A force is a push or a pull.
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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4.3 Newtons Second Law of Motion
SI Unit for Force
This unit of force is called a newton (N).
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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. SI Unit of Mass
kilogram (kg)
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4.2 Newtons First Law of Motion
Newtons First Law (Law of Inertia)
An object continues in a state of rest or in a
state of motion at a constant Speed unless
changed by a net force
The net force is the SUM of all of the forces
acting on an object.
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4.2 Newtons First Law of Motion
The net force on an object is the sum of all
forces acting on that object.
Individual Forces
Net Force
10 N
4 N
6 N
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4.2 Newtons First Law of Motion
Individual Forces
Net Force
5 N
3 N
4 N
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4.3 Newtons Second Law of Motion
Mathematically, the net force is written as
where the Greek letter sigma denotes the vector
sum.
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4.3 Newtons Second Law of Motion
Newtons Second Law
When a net 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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4.4 The Vector Nature of Newtons Second Law
The direction of force and acceleration
vectors can be taken into account by using x and
y components.
is equivalent to
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4.4 The Vector Nature of Newtons Second Law
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4.4 The Vector Nature of Newtons Second Law
The net force on the raft can be calculated in
the following way
Force x component y component
17 N (15 N) cos67 0 N (15 N) sin67
23 N 14 N
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4.4 The Vector Nature of Newtons Second Law
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4.5 Newtons Third Law of Motion
Newtons Third Law of Motion
Whenever one body exerts a force on a second
body, the second body exerts an oppositely
directed force of equal magnitude on the first
body.
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4.5 Newtons Third Law of Motion
Suppose that the magnitude of the force is 36 N.
If the mass of the spacecraft is 11,000 kg and
the mass of the astronaut is 92 kg, what are the
accelerations?
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4.5 Newtons Third Law of Motion
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4.7 The Gravitational Force
Newtons Law of Universal Gravitation
Every particle in the universe exerts an
attractive force on every other particle.
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4.7 The Gravitational Force
For two particles that have masses m1 and m2 and
are separated by a distance r, the force has a
magnitude given by
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4.7 The Gravitational Force
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4.7 The Gravitational Force
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4.7 The Gravitational Force
Definition of Weight The weight of an object on
or above the earth is the gravitational force
that the earth exerts on the object. The weight
always acts downwards, toward the center of the
earth. SI Unit of Weight newton (N)
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4.8 The Normal Force
Definition of the Normal Force
The normal force is the force that a
surface exerts on an object with which it is in
contact It is ALWAYS perpendicular to the
surface.
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4.8 The Normal Force
A hand pushes down on a block with a force of 11
N. The block weighs 15N. What is the magnitude
of the normal force?
A rope is now used to lift the block with a force
of 11 N. What is the magnitude of the normal
force?
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4.8 The Normal Force
Apparent Weight
The apparent weight of an object is the reading
of the scale. It is equal to the normal force
the man exerts on the scale.
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4.8 The Normal Force
true weight
apparent weight
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4.9 Static and Kinetic Frictional Forces
When an object is in contact with a surface there
is a force acting on that object. The component
of this force that is parallel to the surface is
called the frictional force.
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4.9 Static and Kinetic Frictional Forces
When the two surfaces are not sliding across one
another the friction is called static friction.
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4.9 Static and Kinetic Frictional Forces
Note that the magnitude of the frictional force
does not depend on the contact area of the
surfaces.
What does it depend on???
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4.9 Static and Kinetic Frictional Forces
Static friction opposes the impending relative
motion between two objects. Kinetic friction
opposes the relative sliding motion motions
that actually does occur.
is called the coefficient of kinetic friction.
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4.9 Static and Kinetic Frictional Forces
Page 104
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4.9 Static and Kinetic Frictional Forces
The sled comes to a halt because the kinetic
frictional force opposes its motion and causes
the sled to slow down.
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4.9 Static and Kinetic Frictional Forces
Suppose the coefficient of kinetic friction is
0.05 and the total mass is 40kg. What is the
kinetic frictional force?
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4.3 Newtons Second Law of Motion
A free-body-diagram is a diagram that represents
the object and the forces that act on it.
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4.3 Free Body Diagrams
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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4.6 Types of Forces An Overview

• Examples of different forces
• Friction force
• Tension force
• Normal force
• Weight (Force due to gravity)
• Gravitational Force
• Magnetic Force
• Electric Force

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4.10 The Tension Force
Cables and ropes transmit forces through tension.
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• This diagram shows four forces acting upon an
  object. There arent always four forces, For
  example, there could be one or more forces.

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Problem 1

• A book is at rest on a table top. Diagram the
  forces acting on the book.

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Problem 1

• In this diagram, there are normal and
  gravitational forces on the book.

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Problem 2

• An egg is free-falling from a nest in a tree.
  Neglect air resistance. Draw a free-body diagram
  showing the forces involved.

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• Gravity is the only force acting on the egg as it
  falls.

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Problem 3

• A rightward force is applied to a book in order
  to move it across a desk. Consider frictional
  forces. Neglect air resistance. Construct a
  free-body diagram. Lets see what this one looks
  like.

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• Note the applied force arrow pointing to the
  right. Notice how friction force points in the
  opposite direction. Finally, there is still
  gravity and normal forces involved.

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Problem 4

• A block is at rest on an incline and stays in
  place because of static friction. Draw a
  free-body diagram

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• A skier is standing motionless on a horizontal
  tow rope, which is about to pull her forward.
  The skiers mass is 59kg and the coefficient of
  static friction between the skis and the snow is
  0.14. Draw a free body diagram. What is the
  magnitude of the maximum force that the tow rope
  can apply to the skier without causing her to
  move.

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Objects in Equilibrium

• Objects that are either at rest or moving with
  constant velocity are said to be in equilibrium
• This means that the net force acting on the
  object is zero
• Equivalent to the set of component equations
  given by

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4.11 Equilibrium Application of Newtons Laws of
Motion

• Reasoning Strategy
• Draw a free-body diagram.
• Choose a set of x, y axes for each object and
  resolve all forces
• in the free-body diagram into components that
  point along these
• axes.

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4.11 Equilibrium Application of Newtons Laws of
Motion
What is the Tension in Rope 1 and 2? The engine
has a weight of 3150 N
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4.11 Equilibrium Application of Newtons Laws of
Motion
Force x component y component

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4.11 Equilibrium Application of Newtons Laws of
Motion
The first equation gives
Substitution into the second gives
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4.11 Equilibrium Application of Newtons Laws of
Motion
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4.12 Nonequilibrium Application of Newtons Laws
of Motion
When an object is accelerating, it is not in
equilibrium.
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4.12 Nonequilibrium Application of Newtons Laws
of Motion
The mass of the supertanker is 1.5 x 108 kg.
There is a drive force with magnitude 75000 N
and an opposing force of 40000 N. The tanker
moves with an acceleration of 2.0 x 10-3 m/s2.
Solve for the Tension in each of the ropes.
The acceleration is along the x axis so
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4.12 Nonequilibrium Application of Newtons Laws
of Motion
Force x component y component

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4.12 Nonequilibrium Application of Newtons Laws
of Motion
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4.12 Nonequilibrium Application of Newtons Laws
of Motion