From Mechanics

Newton's First Law

A particle will move with a constant velocity or remain at rest if the resultant force on the particle is zero.

Equilibrium

If the resultant force on a particle is zero, then the forces acting on the particle are said to be in equilibrium.

The Universal Law of Gravitation

\displaystyle F=\frac{Gm_{1}m_{2}}{d^{2}}

\displaystyle G=6.67\times 10^{-11}\text{ kg}^{\text{-1}}\text{m}^{\text{3}}\text{s}^{\text{-2}}

Gravity on Earth

The force of gravity is often called the weight.

\displaystyle \begin{align} & F=mg \\ & g=9.8\text{ ms}^{\text{-2}} \\ \end{align}

Data

Radius of Earth is \displaystyle \text{6}.\text{37}\times \text{1}0^{\text{6}}\text{ } metres

Mass of Earth is \displaystyle \text{5}.\text{98}\times \text{1}0^{\text{24}}\text{ } kg

Example 2.1

Describe whether or not the forces acting on the following objects are in equilibrium:

(a) A passenger in a train that travels at a constant speed.

(b) A hot air balloon rising at a constant rate.

(c) A stone dropped into a very deep well full of water.

Solution

(a) Yes, if it is travelling in a straight line.

(b) Yes, if it is travelling in a straight line.

(c) Yes, if it reaches a terminal velocity, so that it is travelling in a straight line at a constant speed.

Example 2.2

Find the magnitude of the force of gravity (weight) acting on a lorry of mass 22 tonnes.

Solution

This is calculated using the fact that the weight is given by mg.

\displaystyle \begin{align} & mg=22000\times 9.8 \\ & =215600\text{ N} \end{align}

The diagram shows the lorry and its weight.

Note that reaction forces also act upwards on each wheel.

\displaystyle R_{1}+R_{2}+R_{3}+R_{4}=215600