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.
Contact forces arise from physical contact .
Action-at-a-distance forces do not require
contact and include gravity and electrical forces.
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4.1 The Concepts of Force and Mass
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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4.1 The Concepts of Force and Mass
Mass is a measure of the amount of stuff
contained in an object.
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4.2 Newtons First Law of Motion
Newtons First Law
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.
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4.2 Newtons First Law of Motion
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 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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4.2 Newtons First Law of Motion
Inertia is the natural tendency of an object to
remain at rest in motion at a constant speed
along a straight line. The mass of an object is
a quantitative measure of inertia. SI Unit of
Mass kilogram (kg)
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4.2 Newtons First Law of Motion
An inertial reference frame is one in which
Newtons law of inertia is valid. All
accelerating reference frames are noninertial.
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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 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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4.3 Newtons Second Law of Motion
SI Unit for Force
This combination of units is called a newton (N).
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4.3 Newtons Second Law of Motion
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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 Newtons Second Law of Motion
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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4.3 Newtons Second Law of Motion
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
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
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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Example

• 3.  In the amusement park ride known as Magic
  Mountain Superman, powerful magnets accelerate a
  car and its riders from rest to 45 m/s (about 100
  mi/h) in a time of 7.0 s. The mass of the car and
  riders is . Find the average net force exerted on
  the car and riders by the magnets.

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Example

• 6.  Interactive LearningWare 4.1 at
  www.wiley.com/college/cutnell reviews the
  approach taken in problems such as this one. A
  1580-kg car is traveling with a speed of 15.0
  m/s. What is the magnitude of the horizontal net
  force that is required to bring the car to a halt
  in a distance of 50.0 m?

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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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4.6 Types of Forces An Overview
In nature there are two general types of
forces, fundamental and nonfundamental.
Fundamental Forces 1. Gravitational force 2.
Strong Nuclear force 3. Electroweak force
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4.6 Types of Forces An Overview
Examples of nonfundamental forces friction tens
ion in a rope normal or support forces
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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. A
particle is a piece of matter, small enough in
size to be regarded as a mathematical
point. The force that each exerts on the other
is directed along the line joining the particles.
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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. On or above another astronomical body,
the weight is the gravitational force exerted on
the object by that body. SI Unit of Weight
newton (N)
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Example

• 18.  On earth, two parts of a space probe weigh
  11 000 N and 3400 N. These parts are separated by
  a center-to-center distance of 12 m and may be
  treated as uniform spherical objects. Find the
  magnitude of the gravitational force that each
  part exerts on the other out in space, far from
  any other objects.

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4.7 The Gravitational Force
Relation Between Mass and Weight
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4.7 The Gravitational Force
On the earths surface
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Example

• 26.  A space traveler weighs 540 N on earth. What
  will the traveler weigh on another planet whose
  radius is three times that of earth and whose
  mass is twice that of earth?

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4.8 The Normal Force
Definition of the Normal Force
The normal force is one component of the force
that a surface exerts on an object with which it
is in contact namely, the component that is
perpendicular to the surface.
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4.8 The Normal Force
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Example

• 34.  A 35-kg crate rests on a horizontal floor,
  and a 65-kg person is standing on the crate.
  Determine the magnitude of the normal force that
  (a) the floor exerts on the crate and (b) the
  crate exerts on the person.

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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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Example

• 36.  A 95.0-kg person stands on a scale in an
  elevator. What is the apparent weight when the
  elevator is (a) accelerating upward with an
  acceleration of 1.80 m/s2, (b) moving upward at a
  constant speed, and (c) accelerating downward
  with an acceleration of 1.30 m/s2?

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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
The magnitude of the static frictional force can
have any value from zero up to a maximum value.
is called the coefficient of 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.
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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
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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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Example

• 39.  ssm A 60.0-kg crate rests on a level floor
  at a shipping dock. The coefficients of static
  and kinetic friction are 0.760 and 0.410,
  respectively. What horizontal pushing force is
  required to (a) just start the crate moving and
  (b) slide the crate across the dock at a constant
  speed?

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4.10 The Tension Force
Cables and ropes transmit forces through tension.
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4.10 The Tension Force
A massless rope will transmit tension
undiminished from one end to the other. If the
rope passes around a massless, frictionless
pulley, the tension will be transmitted to the
other end of the rope undiminished.
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4.11 Equilibrium Application of Newtons Laws of
Motion
Definition of Equilibrium An object is in
equilibrium when it has zero acceleration.
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4.11 Equilibrium Application of Newtons Laws of
Motion

• Reasoning Strategy
• Select an object(s) to which the equations of
  equilibrium are
• to be applied.
• Draw a free-body diagram for each object chosen
  above.
• Include only forces acting on the object, not
  forces the object
• exerts on its environment.
• 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.
• Apply the equations and solve for the unknown
  quantities.

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4.11 Equilibrium Application of Newtons Laws of
Motion
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4.11 Equilibrium Application of Newtons Laws of
Motion
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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 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