#### Force

A force is an interaction between objects that tends to produce acceleration of the objects.

A force is a vector, with both a magnitude and a direction.

The MKS unit of force is the newton (N). 1 N = 1 kg m / s2.

Acceleration occurs when there is a net force on an object; no acceleration occurs when the net force (the sum of all the forces) is zero. An acceleration produces a change in velocity (magnitude and/or direction), so an unbalanced force will change the velocity of an object.

Isaac Newton (1642-1727) studied forces and noticed three things in particular about them. These are important enough that we call them Newton's laws of motion.

#### Newton's First Law

• Aristotle (384-322 BC) thought that objects were naturally at rest.
• Galileo (1564-1642) realized that the Greeks weren't accounting for forces such as friction.
• Newton summarized Galileo's thoughts in the following statement:

Newton's first law: an object at rest tends to remain at rest, and an object in motion tends to remain in motion with a constant velocity (constant speed and direction of motion), unless it is acted on by a nonzero net force.

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

The tendency of an object to maintain its state of motion is known as inertia. Mass is a good measure of inertia; light objects are easy to move, but heavy objects are much harder to move, and it is much harder to change their motion once they start moving.

Do Newton's laws apply all the time? As long as we're in a stationary reference frame, or even moving at constant velocity, Newton's law are valid. Such reference frames are called inertial reference frames.

Newton's Laws are not enough to account for motion observed from non-inertial (accelerating) reference frames.

#### Newton's Second Law

What is the acceleration produced by applying a force to an object? Newton's second law states that the acceleration of an object is proportional to the net force and inversely proportional to the mass of the object.

Newton's Second Law: ΣF = m a

#### Newton's Third Law

A force is an interaction between objects, and forces exist in equal-and-opposite pairs. These statements are summarized by:

Newton's third law: when one object exerts a force on a second object, the second object exerts an equal-and-opposite force on the first object.

"equal-and-opposite" is short for "equal in magnitude but opposite in direction".

Although the forces between two objects are equal-and-opposite, the effect of the forces may or may not be similar - it depends on the relative masses of the objects.

If we drop a 100 g (0.1 kg) ball, it experiences a downward acceleration of 9.8 m/s2, and a force of about 1 N, because it is attracted towards the Earth. The ball exerts an equal-and-opposite force on the Earth, so why doesn't the Earth accelerate upwards towards the ball?

It does, but the mass of the Earth is so large (6.0 x 1024 kg) that the acceleration is much too small (about 1.67 x 10-25 m/s2) for us to notice.

When objects have similar mass, the equal-and-opposite pairs of forces are much easier to see.

#### Force of Gravity

Whenever two objects are touching, they usually exert forces on each other. The force of gravity, on the other hand, is an example of a force that exists between objects without them having to be in contact.

Objects with mass exert forces on each other via the force of gravity. This force is proportional to the mass of the two interacting objects, and is inversely proportional to the square of the distance between them.
Newton's Universal Law of Gravitation: Fg =
 - G m M r2

The factors G, M, and r are the same for all masses at the surface of the Earth. We roll those factors together into the constant g, which we call the acceleration due to gravity.
g =
 G M r2
=
 6.67 x 10-11 N m2/kg2 * 5.98 x 1024 kg (6.37 x 106 m)2
= 9.8 m/s2

At the Earth's surface the gravitational force exerted on an object of mass m by the Earth has a magnitude mg and is directed down.

#### Tension

Whenever we use a string or rope to exert a force on an object, we're creating tension in the rope that transmits the force we exert at one end of the rope to the object at the other end. This force is usually labeled T.

We usually assume that the rope has no mass, and does not stretch. When we exert a certain force on our massless unstretchable rope, the rope exerts that same force on the object. Tension makes the rope feel like it's being pulled apart.

One rule to remember - you can't push with a rope. The tension force always goes along a string or rope away from the object attached to it.

#### The Normal Force

Objects in contact generally exert forces on one another. A book rests on a table: the book exerts a downward force on the table, and the table exerts an equal-and-opposite force up on the book. We call this the normal force - "normal" is the technical physics word for perpendicular. The normal force is perpendicular to the interface where the book meets the table.

The normal force is one component of the contact force between objects, the other component being the frictional force. The normal force is usually symbolized by N.

When the normal force is the only thing counteracting the force of gravity, the normal force is equal in magnitude to the force of gravity. This is not always true - always be careful to calculate the normal force by applying Newton's second law.

Objects lose contact with one another when the normal force goes to zero.

The normal force is the force that would be measured by a scale placed between the objects in contact.

Your "apparent weight" (how heavy you feel) is directly related to the normal force you are experiencing.