Page 286 - Physics Coursebook 2015 (A level)

Cambridge International A Level Physics
274
The gravitational field strength at a point is the gravitational force exerted per unit mass on a small object placed at that point.
the force. This can be seen from the diagram of the field lines in Figure 18.6. If the distance is doubled, the lines are spread out over four times the surface area, so their concentration is reduced to one-quarter. This is called an inverse square law – you may have come across a similar law for radiation such as light or γ-rays spreading out uniformly from a point source.
M
F
r
F
Figure 18.7 A person and the Earth exert equal and opposite attractive forces on each other.
Gravitational field strength g
We can describe how strong or weak a gravitational field is by stating its gravitational field strength. We are used to this idea for objects on or near the Earth’s surface. The gravitational field strength is the familiar quantity g. Its value is approximately 9.81 m s−2. The weight of a body of mass m is mg.
To make the meaning of g clearer, we should write it as 9.81 N kg−1. That is, each 1 kg of mass experiences a gravitational force of 9.81 N.
The gravitational field strength g at any point in a gravitational field is defined as follows:
This can be written as an equation:
g = mF
where F is the gravitational force on the object and m is the mass of the object. Gravitational field strength has units of N kg−1. This is equivalent to m s−2.
We can use the definition above to determine the gravitational field strength for a point (or spherical) mass. The force between two point masses is given by:
F = GMm r2
The gravitational field strength g due to the mass M at a distance of r from its centre is thus:
g = F = GM m m r2m
or
g = GM r2
r
r
Figure 18.6 Field lines are spread out over a greater surface area at greater distances, so the strength of the field is weaker.
We measure distances from the centre of mass of one body to the centre of mass of the other (Figure 18.7). We treat each body as if its mass were concentrated at one point. The two bodies attract each other with equal and opposite forces, as required by Newton’s third law of motion. The Earth pulls on you with a force (your weight) directed towards the centre of the Earth; you attract the Earth with an equal force, directed away from its centre and towards you. Your pull on an object as massive as the Earth has little effect on it. The Sun’s pull on the Earth, however, has a very significant effect.
QUESTIONS
1 Calculate the gravitational force of attraction between:
a two objects separated by a distance of 1.0 cm and each having a mass of 100 g
b two asteroids separated by a distance of 4.0 × 109 m and each having a mass of 5.0 × 1010 kg
c a satellite of mass 1.4 × 104 kg orbiting the Earth at a distance of 6800 km from the Earth’s centre. (The mass of the Earth is 6.0 × 1024 kg.)
2 Estimate the gravitational force of attraction between two people sitting side by side on a park bench. How does this force compare with the gravitational force exerted on each of them by the Earth, i.e. their weight?