Topic 6: Fields and Forces 6.1 Gravitational force and field

Gravitational Force and Field Newton proposed that a force of attraction exists between any two masses. This force law applies to point masses not extended masses However the interaction between two spherical masses is the same as if the masses were concentrated at the centres of the spheres.

Newton´s Law of Universal Gravitation Newton proposed that “every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses, and inversely proportional to the square of their distance apart”

This can be written as F = G m1m2 r2 Where G is Newton´s constant of Universal Gravitation It has a value of 6.67 x 10-11 Nm2kg-2

Gravitational Field Strength A mass M creates a gravitational field in space around it. If a mass m is placed at some point in space around the mass M it will experience the existance of the field in the form of a gravitational force

We define the graviational field strength as the ratio of the force the mass m would experience to the mass, m That is the graviational field strength at a point, is the force exerted per unit mass on a particle of small mass placed at that point

The force experienced by a mass m placed a distance r from a mass M is F = G Mm r2 And so the gravitational field strength of the mass M is given by dividing both sides by m g = G M r2

The units of gravitational field strength are N kg-1 The gravitational field strength is a vector quantity whose direction is given by the direction of the force a mass would experience if placed at the point of interest

Field Strength at the Surface of a Planet If we replace the particle M with a sphere of mass M and radius R then relying on the fact that the sphere behaves as a point mass situated at its centre the field strength at the surface of the sphere will be given by g = G M R2

If the sphere is the Earth then we have g = G Me Re2 But the field strength is equal to the acceleration that is produced on the mass, hence we have that the acceleration of free fall at the surface of the Earth, g