# Weight

## Calculating Weight

Weight is a measure of the pull of gravity on the mass of an object. Weight is, therefore, an example of a force. In common with all forces, weight is a vector quantity and is measured in the SI unit of newtons (N).

Recall that mass is a base quantity and is measured in Kilograms (kg). Mass is the amount of material that makes up an object.

To calculate the weight of an objected, the mass of the object (kg) is multiplied by the pull of gravity on that objects.

Therefore: _Weight =mass x gravity _or _ w =mg _

Here on Earth, the pull of gravity is constant at 10 N per kg.

Worked Example:

What is the weight of a person with a mass of 55 kg?

*Weight = mass x gravity*

*Weight = 55 x 10*

*Weight = 550 N*

On the moon, the pull of gravity is much smaller, due to the smaller size of the moon compared to the Earth.

Gravity = 1.62 N per kg (moon).

The same 55 kg person on the moon would have a lower weight. There would be less pull of gravity on the same mass.

*w = mg*

*w =55 x* 1.62

*w = _89.1 _N*

Notice that the person’s mass has not changed, only the effect of gravity (weight) has changed.

Question:

An astronaut has a mass of 90 kg, so on Earth, they have a weight of 900 N. They travel to Mars and measure their weight, it is 334 N.

What is the gravitational pull on Mars?

*w = mg therefore g = w /m*

*g= 334 / 90*

*g = 3.71 N per kg*

## Measuring Weight

**A Newton Meter**

A mass suspended on the lower hook will pull the spring inside and move the indicator along the scale.

The scale is calibrated to newtons.

We can use a newton meter to measure the weight of an object, in newtons.

A balance, whether digital or analogue can be used to help determine the weight of an object. The measurement from a balance will be in kg (the mass of the object). As gravity on Earth, is 10 N per kg, the measurement from the balance is multiplied by 10 to give the weight in newtons.

Examples of digital and analogue scales

The words mass and weight get used interchangeably, and incorrectly in everyday use. Do not make this mistake in science exams, they are very different.

Mass - the amount of material (Kilograms)

Weight - pull of gravity (newtons) - a type of force.

## Gravitational Field Strength

The magnitude of the pull of gravity is known as the Gravitational Field Strength.

Gravity is actually a very weak force. It pulls all objects together, however, it is so weak that at least one of the objects has to have a very large mass for the effects of gravity to be noticed.

Example: You are an object, you have a gravitational field, but it is really small. The computer you are reading this on is an object, it too has a gravitational field, but it is even smaller. The two gravitational fields are too small to make either you or the computer move towards each other. (Remember gravity is always a pulling force).

The Earth is very large (Mass =5.98 x 10^{24} kg), so its gravitational field is large enough to pull other objects towards it; such as when we drop something.

The gravitational field strength depends on two main factors.

**•** The masses of the two objects

**•** The distance between the two objects.

The larger the two masses the higher the field strength.

The further apart they are the lower the field strength.

**How does this affect the weight of an object?**

The same object on Earth has a higher weight than it does on the moon because the moon is smaller and has a lower mass than the Earth.

The further away from the Earth’s surface an object is the lower its weight becomes.

Even in a plane at 10,000m (about 30,000 feet the average cruising height of a passenger plane), you weight a few newtons less than you did at the airport.