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: F = - G m M / r²

The factors G M / r² 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. Thus, 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. mg is the weight of an object.

Mass and weight are often used interchangeably, but they are quite different. Your mass is the same everywhere. Your weight depends on the force you are experiencing.

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.

Many forces do come from objects being in contact with each other. 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 just one component of the contact force between objects, the other component being the frictional force. The normal force is usually symbolized by N .

In many cases the normal force is simply equal to the weight of an object, but that's only when the normal force is the only thing counteracting the weight. That is not always true, and one should always be careful to calculate any force by applying Newton's second law.

The normal force is the force that would be measured by a scale placed between the objects in contact. Consider the normal force on you when you're in an elevator, for instance. Stand on a typical bathroom scale.

• N = mg if the elevator is at rest or is moving at constant velocity
• N = mg + ma if the elevator has an upward acceleration
• N = mg - ma if the elevator has a downward acceleration

The normal force is equal to your apparent weight. For instance, on a roller coaster you feel very light at the top of loops, but heavier than usual at the bottom. The normal force applied by the seat on you is less than mg at the top and larger than mg at the bottom.