Gravity and weight calculations

In a nutshell

Gravity is the universal force of attraction between all masses. It arises from gravitational fields, which surround all matter. The force due to gravity is called weight.

Equations

Variable definitions

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Gravity

Gravity is the attractive force that pulls matter together. Gravity is present because of the gravitational fields that surround all matter. The more massive the object, the greater the strength of its gravitational field. 

Gravity is actually a relatively weak force. Even though all objects have a gravitational field,  it is only noticeable with very large masses (such as planets).

Example

Earth has got a gravitational field. It acts to pull everything less massive than it towards it.

Curiosity: The gravitational field of the Moon is what causes tides to generate in the Earth's oceans.

Gravitational fields

A gravitational field is the region of space surrounding a body in which another body experiences a force of gravitational attraction. The symbol $$g$$​ is referred to as the gravitational field strength. It is can also be referred to as the acceleration due to gravity. This is essentially the magnitude of the acceleration an object will have when falling towards the surface of the massive object, such as the Earth (neglecting air resistance).

The value of the gravitational field strength $$g$$​, near the surface of the Earth, is around $$10\ N/kg$$​. The value of $$g$$​ is different on other planets, because their overall mass is of differing values. 

Example

The gravitational field strength $$g$$​ near the surface of the Moon is around $$1.6\ N/kg$$​. This is because the overall mass of the Moon is around five times smaller than the mass of the Earth.

Weight

The force acting on an object when its in a gravitational field is called the weight, or gravitational force. The unit for weight is Newtons ($$N$$​). The formula used to calculate weight is as follows:

​$$weight = \space mass \times gravitational \space field \space strength$$​​

​$$W = m \times g$$

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Mass

Mass is a measure of the amount of matter in a substance or object. It is not the same as weight. An object of a fixed mass will have this same mass at any location in the universe. 

However, the gravitational field strength can vary depending on where you are in the universe, and which planet you are on. So even though an object's mass is always fixed, its weight can vary.

In order to simplify calculations, mass is usually considered to act from a single point in the object. This point is referred to as the centre of mass.

Example

An adult cow has a mass of $$1100\ kg$$​. What is the weight, in Newtons, of the cow on Earth ($$g = 10\ N/kg$$​)?

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First, write down the quantities needed and make sure they are in the correct form:

$$m = 1100 \space kg \newline g = 10 \space N/kg$$

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Next, write down the equation you need to use:

​​$$W = m \times g$$

Then, substitute the values into the equation:

$$W = 1100 \times 10$$​​

Don't forget to include your units:

$$11\,000 \space N$$​​

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The cow has a weight of $$\underline{11 000\ N}$$​ on Earth.