


Types of Forces
There are a number of forces that act in a wide variety
of cases and have been given specific names. Some of these, like
friction and the normal force, are so common that we’re hardly aware
of them as distinctive forces. It’s important that you understand
how and when these forces function, because questions on SAT II
Physics often make no mention of them explicitly, but expect you
to factor them into your calculations. Some of these forces will also
play an important role in the chapter on special problems in mechanics.
Weight
Although the words weight and mass are often interchangeable
in everyday language, these words refer to two different quantities
in physics. The mass of an object is a property of the object itself,
which reflects its resistance to being accelerated. The weight of
an object is a measure of the gravitational force being exerted
upon it, and so it varies depending on the gravitational force acting
on the object. Mass is a scalar quantity measured in kilograms, while
weight is a vector quantity measuring force, and is represented
in newtons. Although an object’s mass never changes, its weight
depends on the force of gravity in the object’s environment.
For example, a 10 kg mass has a different
weight on the moon than it does on Earth. According to Newton’s
Second Law, the weight of a 10 kg mass on Earth is
This force is directed toward the center of the Earth.
On the moon, the acceleration due to gravity is roughly onesixth
that on Earth. Therefore, the weight of a 10 kg mass
on the moon is only about 16.3 N toward the center
of the moon.
The Normal Force
The normal force always acts perpendicular
(or “normal”) to the surface of contact between two objects. The
normal force is a direct consequence of Newton’s Third Law. Consider
the example of a 10 kg box resting on the floor. The force of gravity
causes the box to push down upon the ground with a force, W,
equal to the box’s weight. Newton’s Third Law dictates that the
floor must apply an equal and opposite force, N =
–W, to the box. As a
result, the net force on the box is zero, and, as we would expect,
the box remains at rest. If there were no normal force pushing the
box upward, there would be a net force acting downward on the box,
and the box would accelerate downward
Be careful not to confuse the normal force vector N with
the abbreviation for newtons, N. It can be a bit confusing that
both are denoted by the same letter of the alphabet, but they are
two totally different entities.
Example

The total force pushing the box toward the ground is W + F.
From Newton’s Third Law, the normal force exerted on the box by
the floor has the same magnitude as W + F but
is directed upward. Therefore, the net force on the box is zero
and the box remains at rest.
Friction
Newton’s First Law tells us that objects in motion stay
in motion unless a force is acting upon them, but experience tells
us that when we slide coins across a table, or push boxes along
the floor, they slow down and come to a stop. This is not evidence
that Newton was wrong; rather, it shows that there is a force acting
upon the coin or the box to slow its motion. This is the force of friction,
which is at work in every medium but a vacuum, and is the bugbear
of students pushing boxes across the sticky floors of dorm rooms
everywhere.
Roughly speaking, frictional forces are caused by the
roughness of the materials in contact, deformations in the materials,
and molecular attraction between materials. You needn’t worry too
much over the causes of friction, though: SAT II Physics isn’t going
to test you on them. The most important thing to remember about
frictional forces is that they are always parallel to the plane
of contact between two surfaces, and opposite to the direction that
the object is being pushed or pulled.
There are two main types of friction: static friction and kinetic
friction. Kinetic friction is the force between two surfaces
moving relative to one another, whereas static friction is the force
between two surfaces that are not moving relative to one another.
Static Friction
Imagine, once more, that you are pushing a box along a
floor. When the box is at rest, it takes some effort to get it to
start moving at all. That’s because the force of static friction
is resisting your push and holding the box in place.
In the diagram above, the weight and the normal force
are represented as W and N respectively,
and the force applied to the box is denoted by . The force of static friction is represented
by , where . The net force on the
box is zero, and so the box does not move. This is what happens
when you are pushing on the box, but not hard enough to make it
budge.
Static friction is only at work when the net force on
an object is zero, and hence when . If there is a net force on the object,
then that object will be in motion, and kinetic rather than static
friction will oppose its motion.
Kinetic Friction
The force of static friction will only oppose a push up
to a point. Once you exert a strong enough force, the box will begin
to move. However, you still have to keep pushing with a strong,
steady force to keep it moving along, and the box will quickly slide
to a stop if you quit pushing. That’s because the force of kinetic
friction is pushing in the opposite direction of the motion of the
box, trying to bring it to rest.
Though the force of kinetic friction will always act in
the opposite direction of the force of the push, it need not be
equal in magnitude to the force of the push. In the diagram above, the
magnitude of is less than the magnitude of . That means that the box has a net force
in the direction of the push, and the box accelerates forward. The
box is moving at velocity v in
the diagram, and will speed up if the same force is steadily applied
to it. If were equal to , the net force acting on the box would
be zero, and the box would move at a steady velocity of v,
since Newton’s First Law tells us that an object in motion will
remain in motion if there is no net force acting on it. If the magnitude
of were less than the magnitude of , the net force would be acting against
the motion, and the box would slow down until it came to a rest.
The Coefficients of Friction
The amount of force needed to overcome the force of static
friction on an object, and the magnitude of the force of kinetic
friction on an object, are both proportional to the normal force
acting on the object in question. We can express this proportionality
mathematically as follows:
where is the coefficient
of kinetic friction, is the coefficient
of static friction, and N is the
magnitude of the normal force. The coefficients of kinetic and static
friction are constants of proportionality that vary from object
to object.
Note that the equation for static friction is for the maximum value
of the static friction. This is because the force of static friction
is never greater than the force pushing on an object. If a box has
a mass of 10 kg and = 0.5, then:
If you push this box with a force less than 49 newtons,
the box will not move, and consequently the net force on the box
must be zero. If an applied force is less than , then = –.
Three Reminders
Whenever you need to calculate a frictional force on SAT
II Physics, you will be told the value of , which will fall between 0 and 1. Three
things are worth noting about frictional forces:
 The smaller µ is, the more slippery the surface. For instance, ice will have much lower coefficients of friction than Velcro. In cases where , the force of friction is zero, which is the case on ideal frictionless surfaces.
 The coefficient of kinetic friction is smaller than the coefficient of static friction. That means it takes more force to start a stationary object moving than to keep it in motion. The reverse would be illogical: imagine if you could push on an object with a force greater than the maximum force of static friction but less than the force of kinetic friction. That would mean you could push it hard enough to get it to start moving, but as soon as it starts moving, the force of kinetic friction would push it backward.
 Frictional forces are directly proportional to the normal force. That’s why it’s harder to slide a heavy object along the floor than a light one. A light coin can slide several meters across a table because the kinetic friction, proportional to the normal force, is quite small.
Example

In order to solve this problem, we have to determine whether
the horizontal component of is of greater magnitude
than the maximum force of static friction.
We can break the vector into horizontal
and vertical components. The vertical component will push the box
harder into the floor, increasing the normal force, while the horizontal
component will push against the force of static friction. First,
let’s calculate the vertical component of the force so that we can
determine the normal force, N,
of the box:
If we add this force to the weight of the box, we find
that the normal force is 15 + 5.0 = 20 N. Thus, the
maximum force of static friction is:
The force pushing the box forward is the horizontal component
of , which is:
As we can see, this force is just slightly greater than
the maximum force of static friction opposing the push, so the box
will slide forward.
Tension
Consider a box being pulled by a rope. The person pulling
one end of the rope is not in contact with the box, yet we know
from experience that the box will move in the direction that the
rope is pulled. This occurs because the force the person exerts
on the rope is transmitted to the box.
The force exerted on the box from the rope is called the tension force,
and comes into play whenever a force is transmitted across a rope
or a cable. The freebody diagram below shows us a box being pulled
by a rope, where W is
the weight of the box, N is the normal force, T is
the tension force, and is the frictional force.
In cases like the diagram above, it’s very easy to deal
with the force of tension by treating the situation just as if there
were somebody behind the box pushing on it. We’ll find the force
of tension coming up quite a bit in the chapter on special problems
in mechanics, particularly when we deal with pulleys.
