PAP Physics
Notes: Forces and the Laws of Motion
Goal: The students will gain knowledge and understanding of Newton’s laws of motion
and their universality and implications.
Objectives: Upon completion of this unit, the students should be able to:
1. Explain how force affects the motion of an object.
A force is usually a push or a pull upon an object resulting from the object’s
interaction with another object. Whenever there is an interaction between two
objects, there is a force acting on each of the objects. When the interaction ceases,
the two objects no longer experience a force. Forces only exist as a result of an
interaction.
Change of motion is caused by forces and only by forces. Net unbalanced forces
cause an object to start moving, stop moving, change direction, or change speed.
Unchanging motion, or uniform motion, requires no net force.
The SI unit of force is the Newton, named after Sir Isaac Newton (1642 – 1727),
whose work contributed much to the modern understanding of force and motion.
The Newton (N) is defined as the amount of force that, when acting on a 1-kg
mass, produces an acceleration of 1 m/s2. Therefore,
1 N = 1 kg x 1 m/s2
2.
Distinguish between contact forces and field forces.
Contact forces are types of forces in which the two interacting objects are physically
in contact with each other. Examples of contact forces include frictional forces,
applied forces, tensional forces, air resistance forces, and normal forces.
Field forces are types of forces in which the two interacting objects are not in
physical contact with each other, but are able to exert a push or a pull despite the
physical separation. Examples of field forces are gravitational forces, electric forces
and magnetic forces.
Whenever an object falls to Earth, it is accelerated by Earth’s gravity. Earth exerts a
force on the object, even when it is not in immediate physical contact with the
object. The sun and planets exert a gravitational pull on each other despite their
large separation.
Another example of a field force is the attraction or repulsion between electrical
charges. A balloon can be rubbed by fur and will attract little pieces of paper. The
paper is pulled by the balloon’s electric field. Magnetic poles can exert a pull on
each other even when separated by a distance of a few centimeters.
The theory of fields was developed as a tool to explain how objects could exert
forces on each other without touching. The concept of a field theory will be studied
later in this year.
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3. Interpret and construct free-body diagrams.
Because the effect of a force depends on its magnitude and direction, force is a
vector quantity. Diagrams that show force vectors as arrows are called force
diagrams.
A free-body diagram shows the object and the forces acting on it in the simplest
possible way. The object is represented by a dot, or a simple shape, and only the
forces that act directly ON the object are shown.
Descriptions of some of the commonly observed forces follow.
Applied force (Fa) – An applied force is a force which is applied to an object by
another object or by a person. If a person is pushing a desk across the room, then
there is an applied force acting on the desk. The applied force is the force exerted
on the desk by the person.
Gravitational Force, or Weight (Fg or FW) – The force of gravity is the force with
which the earth, moon, or other massive body attracts an object towards itself. By
definition, this is the weight of the object. All objects upon earth experience a force
of gravity which is directed downward towards the center of the earth.
Mass is the amount of matter in an object.
Weight is the gravitational force exerted by a large body. Fg = mg. The
acceleration of gravity (g) is 9.8 m/s2.
Inertial mass of an object is the ratio of the net force exerted on an object to its
acceleration. Gravitational mass can found by comparing the gravitational
force acting on an unknown with the gravitational force acting on a known object.
The inertial and gravitational mass of an object is the same value.
Friction Force (Ff) – The friction force is the force exerted by a surface as an
object moves across it or makes an effort to move across it. The friction force
opposes the motion of the object.
Air Resistance (Fair) – Air resistance is a special type of frictional force which acts
upon objects as they travel through the air. Like all frictional forces, the force of air
resistance always opposes the motion of the object. This force will frequently be
ignored due to its negligible magnitude. It is most noticeable for objects which travel
at high speeds or for objects with large surface areas.
Tensional Force (FT or T) – Tension is the force which is transmitted through a
string, rope, or wire when it is pulled tight by forces acting at each end. The
tensional force is directed along the wire and pulls equally on the objects on either
end of the wire.
Normal Force (FN) – The normal force is a force exerted by one object on another
object in a direction perpendicular to the surface of contact. For example, if a book
is resting upon a surface, then the surface is exerting an upward force upon the
book in order to support the weight of the book. The word normal is used because
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the direction of the contact force is perpendicular to the table surface, and one
meaning of the word normal is “perpendicular.”
Sample Problems
Draw free-body diagrams for each of the following:

A sky diver falls downward through the air at constant velocity (air resistance is
important).

A cable pulls a crate at constant speed across a horizontal surface (there is
friction).

A rope lifts a bucket upward at constant speed (ignore air resistance).

A rope lowers a bucket at constant speed (ignore air resistance).

A rocket blasts off and its vertical velocity increases with time (ignore air
resistance).

A skier accelerates down a slope (there is friction).
4. State Newton’s three laws of motion, and display an understanding of their
applications.
Newton’s first law of motion states: an object at rest remains at rest, and with
constant velocity (that is, constant speed in a straight line) unless the object
experiences a net external force.
The relationships between mass, force and acceleration are quantified in Newton’s
second law. Newton’s second law states: The acceleration of an object is directly
proportional to the net external force acting on the object and inversely proportional
to the object’s mass. In equation form, we can state Newton’s second law as:
accelerati on =
a=
net external force
mass
Fnet
or
m
a
F
m
Newton’s second law makes it possible, when the mass of an object is known to
determine what effect a given force will have on an object’s motion.
Newton’s third law states: If two objects interact, the magnitude of the force
exerted on object 1 by object 2 is equal to the magnitude of the force
simultaneously exerted on object 2 by object 1, and these two forces are opposite
in direction.
5. Define inertia and apply this concept to the solution of problems.
The tendency of an object not to accelerate is called inertia. Newton’s first law is
often referred to as the law of inertia because it states that in the absence of
forces, a body will preserve its state of motion. In other words, Newton’s first law
says that
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when the net external force on an object is zero,
its acceleration (and/or the change in its
velocity) is zero.
The inertia of a body is proportional to its mass. The greater the mass of a body,
the less the body accelerates under an applied force.
6.
Calculate the force required to bring an object into equilibrium.
Objects that are either at rest or moving with constant velocity are said to be in
equilibrium. Newton’s first law describes objects in equilibrium, whether they are at
rest or moving with constant velocity. Newton’s first law states one condition that
must be true for equilibrium: the net external force acting on a body in equilibrium
must be zero.
The net external force is the vector sum of all the forces acting on an object. An
external force is a single force that acts on an object as a result of the interaction
between the object and its environment.
7.
Demonstrate an understanding of the meaning of net external force and apply
Newton’s second law in problem situations.
When all the external forces acting on an object are known, the net external force
can be found using the methods for finding resultant vectors. That means an
object’s acceleration is determined by the combination of all the forces acting on it.
The net external force is equivalent to the one force that would produce the same
effect on the object as if the net external force were the only force acting on the
object.
When solving problems involving Newton’s second law, draw a free-body diagram
and determine the net force. Then apply Newton’s second law.
In solving problems, it is often easier to break the equation for Newton’s second law
into components. The sum of the forces acting in the x direction equals the mass
times the acceleration in the x direction (Fnet x = max), and the sum of the forces in
the y direction (Fnet y = may). If the net external force is zero, then a = 0, which
corresponds to the equilibrium situation where the velocity is either constant or
zero.
Sample Problem
§ A 750 kg dragster, starting from rest, is able to reach speeds of 50 m/s in 25 m.
What force must the dragster exert?
Sample Problem
A 75 kg rock climber is using a rope that can withstand a tension of 1000 N, what is
the maximum acceleration he can attain without the rope snapping?
Sample Problem
§ A 150 kg football player stands on a bathroom scale as he is rising in an
elevator, if the bathroom scale reads 1500 N, what is the acceleration of the
elevator?
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8. Isolate bodies in a system and use Newton’s Second Law to determine force, mass
or acceleration.
Newton’s Second Law applies to any complete system or to any part of a system of
objects. A system is a group of objects that are interrelated in some way. When
solving a problem, it is essential to decide clearly and definitely just which object or
system of objects is being considered. If all forces on a system are considered, the
total mass of the system must be used; if forces on only a part of a system are
considered, then the mass of only that part must be used.
Sample Problem
A 10.0-kg object is being pulled across a frictionless table by a 5.0-kg mass
hanging over the edge. What is the tension in the cord? What is the acceleration of
the system? How far does the object move after 5.0 s?
Sample Problem
A 5.0-kg mass and a 10.0-kg mass are hanging over a frictionless pulley. What is
the tension in the cord? What is the acceleration of the system? How long does it
take for the masses to move 10.0 m?
Sample Problem
Repeat the above problem for masses of 5.0 kg and 20.0 kg. What are the
differences in the acceleration and the time?
9.
Identify action-reaction pairs.
An alternate statement of Newton’s third law is that for every action there is an
equal and opposite reaction. When two objects interact with one another, the forces
they mutually exert on each other are called an action-reaction pair. The force that
object 1 exerts on object 2 is sometimes called the action force, while the force that
object 2 exerts on object 1 is called the reaction force. The action force is equal in
magnitude and opposite in direction to the reaction force.
10. Explain why action-reaction pairs do not result in equilibrium.
The most important thing to remember about action-reaction pairs is that each
force acts on a different object. Because they act on different objects, actionreaction pairs do not result in equilibrium.
11. Recognize that friction is a force which resists the relative movement of two bodies
that are in contact.
Friction is a resistive force that acts in a direction opposite to the direction of the
relative motion of two contacting surfaces. Static friction is the resistive force that
opposes the relative motion of two contacting surfaces that are at rest with respect
to one another. As long as the object does not move, the force of static friction is
always equal to and opposite in direction to the component of the applied force that
is parallel to the surface (Fs = -Fapplied). As the applied force increases, the force of
static friction also increases; if the applied force decreases, the force of static
friction also decreases. When the applied force is as great as it can be without
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causing the object to move, the force of static friction reaches its maximum value,
Fs, max.
When the applied force on the object exceeds F s, max, the object begins to move
with an acceleration. There is still a frictional force acting on the jug as it moves, but
that force is less than Fs, max. The retarding frictional force on an object in motion is
called the force of kinetic friction. The net external force acting on the object is
equal to the difference between the applied force and the force of kinetic friction
(Fapp - Fk).
Frictional forces arise from complex interactions at the microscopic level between
contacting surfaces. Most surfaces, even those that seem very smooth to the
touch, are actually quite rough at the microscopic level. When two surfaces are
stationary with respect to each other, the surfaces stick together somewhat at the
contact points. This adhesion is caused by electrostatic forces between the
molecules of the two surfaces. Because of adhesion, the force required to cause a
stationary object to begin moving is usually greater than the force necessary to
keep it moving at constant speed.
The force of friction is proportional to the magnitude of the normal force exerted on
an object by a surface. In addition to the normal force, the force of friction also
depends on the composition and qualities of the surfaces in contact. The quantity
that expresses the dependence of frictional forces on the particular surfaces in
contact is called the coefficient of friction. The coefficient of friction is
represented by the symbol µ, the lowercase Greek letter mu.
12. Apply their knowledge of friction to the solution of problems.
The coefficient of friction is defined as the ration between the force of friction and
the normal force between two surfaces. The coefficient of kinetic friction is the
ratio of the force of kinetic friction to the normal force.
μk =
Fk
Fn
The coefficient of static friction is the ratio of the maximum value of the force of
static friction to the normal force.
μs =
Fs ,max
Fn
If the value of  and the normal force on the object are known, then the magnitude
of the force of friction can be calculated directly.
F f = μFn
Because kinetic friction is less than or equal to the maximum static friction, the
coefficient of kinetic friction is always less than or equal to the coefficient of static
friction.
Sample Problem
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A 10 kg box is slide across the floor at a constant speed by a rope held at an angle
of 35o when a force of 25 N is applied, what is the coefficient of friction?
Sample Problem
A 20 kg box is accelerated at 1 m/s2 across the floor where the coefficient of friction
is 0.35. What horizontal force must be applied to accomplish this?
Sample Problem
A 100 kg trunk is slid at a constant speed up a 10o incline by a 200 N force. What
is the coefficient of sliding friction?
References:
Holt Physics, pages 123 – 157.
Physics Tutorial: http://www.physicsclassroom.com/Class/newtlaws/newtltoc.html
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