1. Unit 3A: Gravitational Forces and Fields
Universal Law of Gravitation

2. Gravitational Force (revisited)
Gravity is a force of attraction between two masses of matter. It is a force that acts linearly between the centres of the two masses.
Cavendish and Newton derived the principles behind gravitational forces.
Cavendish used a torsion balance and found that the force varied directly with the product of the masses of the objects and inversely with the square of their separation distance.
Newton put these relationships together and found the proportionality constant which he labelled as G = 6.67 x Nm2/kg2.

3. Gravitational Force (revisited)
The Universal Law of Gravitation:

4. Gravitational Force (revisited)
What is the gravitational force between 2 electrons separated by 12.0 nm?
Fg = Gm1m2d-2
= 6.67E-11Nm2kg-2 (9.11E-31kg)2 (12.0E-9m)2
= 3.84E-55N [attractive]
(negligible!!)

5. Gravitational Force (revisited)
How does the gravitational force change on a body if moved 4 times as far away from an attracting body?
[1/16 x]
What if the distance was halved?
[4 x]

6. Gravitational Force (revisited)
A mass of lead has a 9.81 N gravitational force magnitude at the Earth’s surface. What is the force magnitude at km from the surface?
[9.79 N]

7. Gravitational Force (revisited)
A force of gravity of 100. N acts on an object km from the centre of the Earth. What’s the size of the force at km from the Earth’s surface?
[42.9 N]

8. Gravitational Force (revisited)
Find the net gravitational force on a 20.0 kg mass midway between a 10.0 kg mass and a 15.0 kg mass, each separated by 10.0 m.
An FBD is required
Fgnet = Fg10 + Fg15 as vectors
10.0 m
10.0 kg
20.0 kg
15.0 kg
20.0 kg
Fg15
Fg10

9. Gravitational Force (revisited)
Factoring out G, m2 and r2
[6.67E-11Nm2/kg2(20kg)/(10m)2]{(15kg-10kg)}
= 6.67 x N [E]