# 1.03 Mass and Gravity

## Gravity

Gravity is the name we give to an attractive force that acts between two objects due to their mass. It is important to point out from the outset that even Isacc Newton who discovered the force of gravity did not claim to know what gravity was or how it actually produced attraction between objects. Newton's work was concerned with explaining the way in which gravity acts rather than how and why it does so.

The Equation for calculating the gravitational force between two objects is

F = Gm1m2/d2
Where

• F = force measured in Newtons (N)
• G = gravitational constant
• m1 = mass of object 1
• m2 = mass of object 2
• d = distance between each object""s centre of gravity (see next section)

The gravitational constant "G" is a value that has been determined experimentally. (You will come across many other physical constants in your study of physics).

## Centre of Gravity and particle model

When it actually came to calculating gravitational forces between real objects, this posed a major problem even for Newton, simply because of the complexity involved. Imagine say, working out the gravitational force between the Earth and the Moon. Both are extremely large extended objects which are made of "countless" tiny particles. To calculate the overall gravitational force then first for each particle in the Earth we would need to calculate the gravitational force between it and every particle in the Moon. Then we would need to add all of these forces together taking into account their directions!

To solve this problem Newton developed a new branch of mathematics called calculus. Calculus was able to show that for any object there is a point called the centre of gravity. In some calculations involving forces we can treat the object as if all of it's mass were located at the centre of gravity (ie as if it were a single particle!). This simplified the calculation of the gravitational force between the Earth and the Moon to a single calculation for just two particles! The use of the particle model (based on the centre of gravity) is used extensively in mechanics to simplify the analysis of forces acting on objects. When studying motion in the following sections you will treat many objects as if they were particles.

## Determining the centre of gravity

We can determine the centre of gravity of an object by a simple procedure

• suspend the object from a point about which it can freely rotate
• use a plumb line to mark a vertical line from the point at which it is suspended
• repeat this choosing a second point to suspend the object from
• where the two lines cross marks the centre of gravity Note
(unbeknown to Newton, a German mathematician called Leibnitz independently developed the same branch of mathematics before Newton had published his work. They are now both accredited with the development of calculus).

Summary

• An attractive force called the gravitational force exist between objects due to their mass
• The force between two particles can be calculated using F = Gm1m2/d2
• In some situations we can treat an extended object as a particle by using its centre of gravity. This greatly simplifies calculations involving forces