1. Can you give your ‘Internal resistance’ practical to Mr Porter?
Do now!
Can you give your ‘Internal resistance’ practical to Mr Porter?

2. This is pretty much the same with qs replaced by ms and k by G!
Today’s lesson
Gravitational force and fields
This is pretty much the same with qs replaced by ms and k by G!

3. Gravitational Force and Field
We already know that;

4. Gravitational Force and Field
We already know that;
Masses attract each other

5. Gravitational Force and Field
We will know that;
2. Mass/energy is conserved
(E = mc2)

6. Gravitational Force and Field
The force between masses was formulated (discovered?) by Isaac Newton in 1687

7. Gravitational Force and Field
Newton found that the force between two masses is proportional to the product of the two masses
F α m1 x m2
and inversely proportional to the square of the distance (r) between the masses
F α 1/r2

8. Newton’s law of universal gravitation
It follows that
F α m1m2 r2
or F = Gm1m2

9. Newton’s law of universal gravitation
F = Gm1m2 r2
The constant G is known as “Big G” and is equal to x Nm2kg-2

10. Newton’s law of universal gravitation
F = Gm1m2 r2
For large objects like the earth, r is the distance to the centre of mass

11. Calculations using Newton’s law
What is the force of attraction between Jan and Bartosz?
2 m
63kg ?
70kg ?

12. Calculations using Newton’s law
F = Gm1m2 = x x 63 x 70 = 7.3 x 10-8 N
r2 22
2 m
63kg ?
70kg ?

13. Force of gravity due to earth on Jan?
F = Gm1m2 = x x 63 x 6 x 1024 = N (= mg)
r2 (6400 x 103)2
Jan’s weight
63kg ?
R = 6400 km, m = 6 x 1024 kg

14. Force of gravity due to earth on Pascal?
F = Gm1m2 = x x 63 x 6 x 1024 = N (= mg)
r2 (6400 x 103)2
In other words, for any planet;
g = Gmp
rp2

15. Gravitational field
An area or region where a mass feels a gravitational force is called a gravitational field.
The gravitational field strength at any point in space is defined as the force per unit mass (on a small test mass) at that point.
g = F/m (in N.kg-1)

16. Gravitational field around a point mass
If we have two masses m1 and m2 distance r apart
F = Gm1m2/r2
Looking at the force on m1 due to m2, F = gm1
F = Gm1m2/r2 = gm1
g (field due to m2) = Gm2/r2 m1 m2

17. Gravitational field around a point mass
I told you, for any planet;
g = Gmp
rp2
Don’t forget that for a non point mass, r is the distance to the centre of mass
If we have two masses m1 and m2 distance r apart
F = Gm1m2/r2
Looking at the force on m1 due to m2, F = gm1
F = Gm1m2/r2 = gm1
g (field due to m2) = Gm2/r2 m1 m2

18. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field here due to both masses? m1 m2

19. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field here due to both masses?
Field due to m1 m1 m2

20. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field due to m2
Field due to m1 m1 m2

21. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field due to m2
Field due to m1
Resultant Field m1 m2

22. Gravitational field patterns
A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines.

23. Gravitational field patterns
A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines.
The closer the lines are together, the stronger the force felt.
Note, gravity is ALWAYS attractive
This is an example of a radial field

24. Field around a uniform spherical mass

25. Field close to the earth’s surface
Uniform

27. Let’s try some questions
Page 130 Qs 1, 2, 3, 8.