84C - Forces

In physics, a force is any influence that causes an object to undergo a certain change, either in its motion, direction, or geometrical construction. It is measured with the SI unit of newtons and represented by the symbol F. In other words, a force is that which can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform.

Force can also be described by intuitive concepts such as a push or pull. A force has both magnitude and direction, making it a vector quantity.

In solving problems involving forces there are four principles that must always be observed:

  1. The net force acting on an object is the vector sum of all forces acting on the object,

  2. Objects remain stationary or move at a constant velocity unless a net force acts on them (Newton's first law),

  3. The net force on any object is the product of its mass and velocity, F = ma (Newton's second law), and

  4. For every action force there is an equal and opposite reaction force (Newton's third law).

84C1 - Net Force

Here you will learn to:

Represent forces using symbols, units and vectors,

Predict how forces change the motion of objects,

Determine the net (unbalanced) force acting on an object, and

Draw free body force diagrams.


When we say that there is a force on an object we mean that there is a push or a pull on the object. Some outside agent is placing this push or pull on the object. Forces change the velocity of objects or cause them to deform or change shape. In the metric system, forces are measured in units of newtons (N).

Forces are vectors. That is, they are quantities that have both magnitude and direction. Like all vectors, forces can be symbolised with arrows where the arrowhead indicates direction and the length of the arrow indicates the magnitude.

Net Force

More than one force can act on an object at once. For example, two people could pull on a rope at the same time in opposite directions. One person could pull toward the left and the other could pull toward the right. In

this case the two forces would act against each other. If the force toward the left was greater than the force toward the right, then the prevailing force would be toward the left. The strength of this prevailing force would be the difference between the strengths of the two separate forces. This prevailing force is called the net force.

Diagrams showing how the sum of all forces acting
on an object gives the net force.

Basically, the word net means total. For example, if one person pulled on the rope with a force of 20 N toward the right and the other person pulled with a force of 18 N toward the left, then the net force would be 2 N in size and directed toward the right (Fnet = 20 + [-2] = 18 N). This object will move as if it had a single force of 2 N moving toward the right and this is called the net force. Whenever there is a net force on an object we say that the forces are unbalanced.

If the two people pulling on the rope each pull with the same force of 20 N in opposite directions, the two forces would exactly cancel each other out. The net force on the rope in this case would be 0 N. If there is no net force, then we say that the forces are balanced.

The examples above refer to forces acting in one dimension and the net force is calculated by adding together all of the forces acting on the object. The same principles can be applied to forces acting in two or even three dimensions. When several forces act in two dimensions on any object, the net force is still the sum of all of the forces acting on the object, but a vector addition is needed to calculate the net force.

In summary, the sum of all forces acting on an object gives the net force acting on the object.

Free-Body Force Diagrams

Free-body force diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. The size of the arrow in a free-body diagram indicates of the magnitude of the force. The direction of the arrow reveals the direction in which the force acts. Each force arrow in the diagram is labelled to indicate the type of force. It is customary in a free-body force diagram to represent the object by a box and to draw the force arrow from the centre of the box outward in the direction in which the force is acting. One example of a free-body diagram is shown on the right. The diagram shows all four forces acting on the car that is moving at a constant velocity such that the net force in the horizontal and vertical directions is zero.

A free body force diagram for a car moving along a freeway at a constant velocity
where the net force in the horizontal and vertical directions is zero.

Objects do not always have four forces acting upon them. There will be cases in which the number of forces depicted by a free-body force diagram will be one, two, or three. There is no hard and fast rule about the number of forces which must be drawn in a free-body force diagram. The only rule for drawing free-body force diagrams is to depict all the forces which exist for that object in the given situation. Thus, to construct free-body diagrams, it is extremely important to know the types of forces. If given a description of a physical situation, begin by using your understanding of the force types to identify which forces are present. Then determine the direction in which each force is acting. Finally, draw a box and add arrows for each existing force in the appropriate direction and label each force arrow according to its type.

Stuff to Do

TutorialTutorial 84C1 - Net Force
TutorialTutorial 84C1 - Net Force - Answers
MovieBozeman Science - Free Body Diagrams
MovieKahn Academy - Balanced and Unbalanced Forces


84C2 - Newton's Law of Motion

In this section you will learn to:

Define and apply Newton's First Law,

Define and apply Newton's First Law,

Define and apply Newton's First Law, and

Distinguish betwee mass and weight.

Newton's First Law

This law is also called the Law of Inertia or Galileo's Principle.

An object at rest will remain at rest or continue at a constant velocity unless acted on by a net (unbalanced ) force.

An object may be acted on by many forces and maintain a constant velocity so long as the vector sum of these forces is zero. For example, a rock resting upon the Earth keeps a constant velocity (in this case, zero) because the downward force of its weight balances out the upward force (called the normal force) that the Earth exerts upwardly on the rock. Only unbalanced forces cause acceleration or a change in the velocity or an object. If you push someone, he or she will accelerate in the direction of the unbalanced force that you have provided (called the applied force). Likewise if you roll a ball along the floor, the unbalanced force of friction will decelerate the ball from some positive velocity to rest.

Before Galileo, people agreed with Aristotle that a body's natural state was at rest, and that movement needed a cause. This is understandable, since in everyday experience, moving objects eventually stop because of friction (except for celestial objects, which were deemed perfect). Moving from Aristotle's "A body's natural state is at rest" to Galileo's discovery was one of the most profound and important discoveries in physics.

There are no true examples of the law, as friction is usually present, and even in space gravity acts upon an object, but it serves as a basic principle for Newton's mathematical model from which the motions of bodies from elementary causes could be derived: forces.

Another way to put it is, "An object in motion tends to stay in motion and an object at rest tends to stay at rest until a net force acts upon it".

Newton's Second Law

Newton's second law as originally stated in terms of momentum is

An applied force is equal to the rate of change of momentum of an object.

The physical meaning of this equation is that objects interact by exchanging momentum, and they do this via a force. You will learn more about this in the next section on momentum.

For our purposes now, when the mass, m, of the object is constant, the relation p = mv gives another useful form of the second law, F = ma.

For example, if a bowstring exerts a constant force of 100 N on an arrow having a mass of 0.10 kg, then the arrow's acceleration will be 100 ms-2 until it leaves the bow (after which the arrow will stop speeding up).

In these equations, F is the net force, i.e., the sum of all the forces acting on the object. When the forces on the object all act in the same dimension, they can be added as positive and negative numbers, depending on their direction. When they do not all act along the same line, the total must be found by vector addition.

The quantity m, or mass, is a characteristic of the object. The greater the total force acting on an object, the greater the change in its acceleration will be. This equation, therefore, indirectly defines the concept of mass. In the equation, F = ma, a is directly measurable but F is not. The second law only has meaning if we are able to assert, in advance, the value of F. Rules for calculating force include Newton's law of universal gravitation, Coulomb's law, and other principles.

Said simply, an object needs a net force if it is to accelerate. The larger the force the larger the acceleration. The larger the mass the smaller the acceleration. The size of the acceleration is directly proportional to the force and inversely proportional to the mass.

Newton's Third Law

Newton's third law in action.

Newton's third law says

All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.

As shown in the diagram on the right, the skaters' forces on each other are equal in magnitude, and opposite in direction. Although the forces are equal, the accelerations are not: the skater with less mass will have a greater acceleration due to Newton's second law. If a basketball hits the ground, the basketball's force on the Earth is the same as Earth's force on the basketball. However, due to the ball's much smaller mass, Newton's second law predicts that its acceleration will be much greater.

Not only do planets accelerate toward stars; but, stars accelerate toward planets. The two forces in Newton's third law are of the same type, e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing against the road.

Mass and Weight

Weight is often used as a synonym for mass but in Physics, weight is actually a force. For instance, when we buy or sell goods "by weight", we are in principle interested in the amount of goods exchanged, not how hard it presses down on the table. Similarly, in measurements of body weight we are interested in the amount of tissue (fat, muscle, etc.) present. In most circumstances, this ambiguity is not a problem because the weight of an object is directly proportional to its mass. Newton's Second Law tells us that F = ma and for objects in the Earth's gravitational field, a is the acceleration due to gravity which is 9.8 ms-2. Weight it the force of gravity measured in newtons and mass is the amount of matter in something and is measured in kilograms.

In the physics we are usually more careful about the distinction between weight and mass. For instance, a body will have a smaller weight if it is located on the Moon than if it is on the Earth, since the gravitational field of the Moon is weaker; its mass, on the other hand, does not depend on position.

The weight force that we sense is actually the normal force exerted by the surface we stand on, which prevents us from being pulled to the centre of the Earth and not, the weight itself. This normal force that we call apparent weight is equal and opposite to our weight, is the one that is measured by a weighing scale. Because they are equal and opposite, the magnitude is the same. The scales are designed to divide the reaction force (weight) by 9.8 to give us a reading of mass.

Stuff to Do

TutorialTutorial 84C2 - Forces
TutorialTutorial 84C2 - Forces - Answers
MovieBozeman Science - Newton's Three Laws of Motion
MovieKahn Academy - Newton's First Law
MovieKahn Academy - Newton's Second Law
MovieKahn Academy - Normal Force in an Elevator
MovieKahn Academy - Newton's Third Law
Investigation 84C3 - Newton's Second Law