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{{Selected tab|[[2. Introduction to force and gravity|Theory]]}}
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== '''Key Points''' ==

'''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'''

{| width="500px" cellspacing="10px"
| <math>F=\frac{Gm_{1}m_{2}}{{d}^{\ 2}}</math>

<math>G=6\textrm{.}67\times 10^{-11}\text{ kg}^{\text{-1}}\text{m}^{\text{3}}\text{s}^{\text{-2}}</math>
| valign="top"|[[Image:Gravitation.gif]]
|}

'''Gravitational force from an heavenly body'''
{| width="500px" cellspacing="10px"
| For a particle in the neighbourhood of a planet, moon or star the distance <math>d</math> is measured from the centre to the particle.

Thus
<math>d=R+h</math>, where <math>h</math> is distance to the surface.

| valign="top"|[[Image:fig2gif.gif]]
|}

'''Gravity on Earth'''

The force of gravity is often called the weight.

<math>\begin{align}
& F=mg \\
& g=9\textrm{.}8\text{ ms}^{\text{-2}} \\
\end{align}</math>

'''Data'''

Radius of Earth is
<math>\text{6}\textrm{.}\text{37}\times \text{1}0^{\text{6}}\text{ }</math>
metres

Mass of Earth is
<math>\text{5}\textrm{.}\text{98}\times \text{1}0^{\text{24}}\text{ }</math>
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 <math>mg</math>.

<math>\begin{align}
& mg=22000\times 9\textrm{.}8 \\
& =215600\text{ N}
\end{align}</math>

The diagram shows the lorry and its weight.

[[Image:truck.gif||center]]

Note that reaction forces also act upwards on each wheel.

<math>{{R}_{1}}+{{R}_{2}}+{{R}_{3}}+{{R}_{4}}=215600\ \text{N}</math>

'''[[Example 2.3]]'''

A box of mass 30 kg is at rest on a table.

a) Calculate the weight of the box.

b) State the magnitude of the upward force that the table exerts on the box.

'''Solution'''

a)

<math>\begin{align}
& W=30\times 9\textrm{.}8 \\
& =294\text{ N}
\end{align}</math>

b) An upward force of 294 N must act for the box to remain in equilibrium.

'''[[Example 2.4]]'''

A satellite, of mass 400 kg, is at a height of 12 km above the surface of the earth. Find the magnitude of the gravitational attraction on the satellite.

Data:
<math>G=6\textrm{.}67\times {{10}^{-11}}</math>
<math>\text{k}{{\text{g}}^{-\text{1}}}{{\text{m}}^{\text{3}}}{{\text{s}}^{-\text{2}}}</math>

Radius of earth <math>=6\textrm{.}37\times {{10}^{6}} \text{m} </math>

Mass of earth <math>=5\textrm{.}98\times {{10}^{24}} \text{kg}</math>

'''Solution'''

<math>\begin{align}
& \frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{\ {2}}}}=\frac{6\textrm{.}67\times {{10}^{-11}}\times 400\times 5\textrm{.}98\times {{10}^{24}}}{{{\left( 6\textrm{.}37\times {{10}^{6}}+12000 \right)}^{2}}} \\
& =3917\text{ N}
\end{align}</math>

'''[[Example 2.5]]'''

The sun has mass
<math>1\textrm{.}99\times {{10}^{30}} \text{kg}</math>
. The mean distance of the earth from the sun is approximately
<math>1\textrm{.}5\times {{10}^{11}} \text{m}</math>
.

(a) Calculate the force that the sun exerts on the earth.

(b) State the force that the earth exerts on the sun.

(c) Explain why this force varies.

'''Solution'''

(a)

<math>\begin{align}
& \frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{\ 2}}}=\frac{6\textrm{.}67\times {{10}^{-11}}\times 1\textrm{.}99\times {{10}^{30}}\times 5\textrm{.}98\times {{10}^{24}}}{{{\left( 1\textrm{.}5\times {{10}^{11}} \right)}^{2}}} \\
& =3\textrm{.}53\times {{10}^{22}}\text{ N}
\end{align}</math>

(b)
<math>3\textrm{.}53\times {{10}^{22}}\text{ N} </math>

(c) The distance between the earth and the sun varies.

2. Introduction to force and gravity - Versionshistorik

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