## Effects of a force

A force is a push or a pull. A force can be detected by its effects.

Effects of a force:

- It can accelerate an object, as described by Newton’s laws of motion.
- It can change an object’s shape or size, as described by Hooke’s law.
- It can produce a turning effect, as described by the law of moments.

### The newton

The newton (N) is the unit of force, and *one newton is defined as the force which gives a mass of 1 kg an acceleration of 1 m/s ^{2}*. In other words, 1 N = 1 kg m/s

^{2}.

### Weight

**Weight** is the **force** of gravity acting on an object. It is the force that pulls everything towards the earth and causes unsupported objects to fall to the ground with an acceleration of *g*.

The weight of a body is measured using a spring balance marked in newtons (also known as a forcemeter).

The weight of the object stretches the spring in the balance, and the greater the weight, the more the spring stretches. On the Earth’s surface, the weight of a body of mass 1 kg is approximately 9.81N.

Gravity is a non-contact force, i.e. no contact is needed between the earth and the object that is to be pulled by gravity. Non-contact forces are also called action-at-a-distance forces. Other examples of such forces are:

- magnetic force
- electric force

## Hooke’s law

Robert Hooke discovered that **the extension of a spring is proportional to the stretching force provided the spring is not permanently deformed**. This is now known as Hooke’s law. What this means that if we double the stretching force the extension doubles and if we treble the stretching force the extension trebles, and so on.

Since extension is proportional to the stretching force, Hooke’s law can be expressed mathematically (using the proportionality sign, ∝) as:

Force ∝ extension

Or

F ∝ e

*When removing the proportionality sign we replace it with an equal sign and a constant to get:*

F = ke

Whereby *k* is the **spring constant** or **force constant** of the spring.

This formula is true only if the **elastic limit** or **limit of
proportionality** of the spring is not exceeded. The region before the elastic limit is exceed is the region before permanent deformation of the spring sets in, ie the spring returns to its original length when the stretching force is removed.