Forces and the Laws of Motion
Changes in motion
Force:
1. Is thought to be the push or pull on an object.
2. Represents the interaction of an object with its environment.
Force exerted on and object can:
1. Change the velocity of an object – a push from behind on a swing
Note: A change in velocity is acceleration.
2. Change the direction of an object – wind blows at the side of a boat
You can feel the force – change in velocity on your body – when:
1. Someone slams on the brakes of a car.
2. Someone steps HARD on the gas pedal of a car.
3. When you catch a ball, the force pushes back your arm.
The SI unit for force is the Newton, named for Sir Isaac Newton. A Newton is one
kilogram of mass accelerated through one meter in one second or 1kg  1m/s2.
Research the “Avoirdupois” system of units.
Contact Forces:
1. Contact forces result from the physical contact between two objects.
2. Easy to identify when analyzed.
Examples: football is caught; cars collide; “Q” ball contacts other balls on the pool
table
Field Forces:
1. No physical contact between two objects.
2. Difficult to identify and analyze
Examples: gravitational pull (directly proportional to the mass of the objects);
attraction or repulsion between electric charges (electric motors, static “cling”)
3. Used to study particle physics.
1
Force Diagrams – Force is a vector because its effect on an object:
1) Depends upon magnitude
2) Depends upon direction
Force Diagrams – Used to analyze all the forces affecting the motion of a single
object
1) Assume all forces act on a point at the center of an object.
2) Draw all forces as if they act on that point. Disregard where the force may be
applied to an object.
3) A free body diagram will show all the forces (vectors as arrows) acting on an
object.
Steps to draw a free-body diagram to analyze the forces acting on an object
1. Draw a simple shape of the object – realistically position the object in the
drawing
2. Draw and label vector arrow representing only external forces (all) acting on the
object.
Note: The arrow must accurately represent the direction and magnitude of the
force.
3. Do not draw any forces that the object under study may exert on other objects
Free-body diagrams revels much information about the physics of the object. Freebody diagrams can be used to find the net (total) external force acting on an object.
Use the rules for vector analysis.
2
Newton’s First Law
It is the nature of an object to maintain its state of motion. Some outside force
acting on the object will have an effect on the object and physicists like to study
and determine exactly what the effect is. Physicists, like all other scientists are
curious about the world around them.
Newton’s first law of motion states that an object at rest remains at rest and an
object in motion remains in motion unless an outside force acts upon the
object.
This tendency of an object to not accelerate is called inertia.
When the net external forces are zero, the acceleration is zero.
Acceleration of an object is determined by net external force.
Net external force – the vector sum of all the forces acting on an object
Look at the free body diagram below. There are several forces acting on the car. If
the sum of all the external forces is zero, the car will move at a constant velocity.
External force – a single force that acts on an object as a result
Fgravity – downward force of gravity on the car
Fnormal – upward force the road exerts on the car
Fengine – forward force of the road on the tires
Ffriction – friction between the road and car tires
Mass is a measurement of inertia:
1. The greater the mass of an object, then the greater the force is required to
accelerate it.
2. The smaller the mass of an object, then the smaller the force is required to
accelerate it.
3
Equilibrium – All forces acting on an object are balanced; the sum of all vector
forces is zero. The object does not experience acceleration or change in direction.
The following equations represent equilibrium of an object: Fx = 0 and Fy = 0.
A force required to bring an accelerating object into equilibrium must be equal to
and opposite to the force causing the acceleration.
Newton’s Second and Third Laws
Newton’s first law describes a state of equilibrium on an object. How is an object
described when an outside force acts on it? Newton’s second law describes the
relationship between the mass of an object, the unbalanced external forces, and
acceleration and/or change in direction of the object.
Newton’s Second Law of motion states that the acceleration of an object is
directly proportional to the net external force acting upon the object and
inversely proportional to the mass of the object.
Newton’s second law can also be directly describe with the following formula:
F = ma
F = vector sum of all external forces
m = mass of the object
a = acceleration of the object
The formula can also be rearranged to determine the acceleration of an object when
the object mass is known and the sum of the forces is known.
a=
F
m
4
Again, look at the free body diagram below. What is different from the prior
figure? Are the forces balanced or unbalance? What is the car doing?
Fgravity – downward force of gravity on the car
Fnormal – upward force the road exerts on the car
Fengine – forward force of the road on the tires
Ffriction – friction between the road and car tires
If all the external forces are balance (zero), then the acceleration is zero and the
object reverts to Newton’s first law of motion or a state of equilibrium.
What happens when the unstoppable force meets the immovable object??????
Newton’s Third Law of motion simply states that for every action, there is an
opposite and equal reaction.
Forces always occur in pairs, even if they are opposite and equal. When two
objects interact, each will exert a force on the other object. This coexistence of
forces is called the action-reaction pair. One object will have the action force, a
car. The other force will have the reaction force, a barrier. What happens when the
car encounters the barrier?
The term reaction has the implication of a delayed action or a response. Not so in
physics. In physics the reaction force occurs at exactly the same moment as the
action force. Because the forces are different on objects acting on each other, the
action-reaction pairs do not result in equilibrium.
5
Everyday Forces
What is the difference between weight and force? Both have the same units, the
Newton. Force is a mass that is accelerated through a distance; F = ma. Weight is
the magnitude of the force of gravity acting on an object; Fg = mg.
What is the difference of weight and mass? Mass is the amount of matter in an
object. The mass of an object will not change if you travel from Earth to outer
space or to the moon. The weight will change since weight is the response of mass
to gravity. An object that free-falls to the surface of the Earth is acted upon by the
force of gravity; Fg. On Earth g = 9.81 m/s2.
Normal Force – the force exerted by one object on another object in a direction
perpendicular to the surface of contact. Normal Force may not always be opposite
the force of gravity.
Example: An object will not fall to the center of the Earth because the surface of
the Earth is pushing up with an equal force. This is the normal force, Fn. On the
Earth’s Fn will be equal to Fg.
The Force of Friction
p. 142
Frictions:
Static friction (Fs) – resistive force that opposes the relative motion of two
contacting surfaces that are at rest with respect to one another
The maximum value of static friction (Fs,max) is equal to the maximum external
force that can be applied (-Fapplied) to an object before the object begins to move.
Kinetic friction – Fk – resistive force that opposes the relative motion of two
contacting surfaces that are moving past one another
The frictional forces acting between surfaces at rest with respect to each other are
called forces of static friction. The maximum force of static friction will be the
same as the smallest force necessary to start motion. Once motion is started, the
frictional forces acting between the surfaces usually decrease so that a smaller
force is necessary to maintain uniform motion. The forces acting between surfaces
in relative motion are called forces of kinetic friction.1
1. David Halliday and Robert Resnick. Physics for Students of Science and
Engineering. Edition I and II combined. New York: John Wiley & Sons, Inc, 1965.
96
6
Once the Fs has been over come and the object is now moving, the net force is the
difference between the applied force and the force of kinetic friction. (F-Fk). Fk is
most always less than Fs.
Frictional forces depend on the surfaces in contact. The normal force of an object
on different types of surfaces but the static friction can have large amounts of
variance on different surfaces. The friction on a particular surface is coefficient of
friction. The coefficient of friction is expressed as a quantity and represented by
the Greek symbol . This quantity has no units and thus is a ratio between the
force of kinetic friction to the normal force. The ration is solved with the following
formula:
k =
Fk
Fn
The coefficient of static friction is solved with the following formula:
s =
Fs ,max
Fn
Fluid Friction – air is a fluid and offers resistance to the objects motion. The force
of the air resistance (FR) is opposite to the movement of the object and at high
velocities, the magnitude of FR is roughly proportional to the square of the car’s
speed.
7