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Gravitation

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Gravitation

AHL 8.2

- All objects exert a force on each other
- If either mass increases the force increases
- Double the mass doubles the force
- If the distance decreases the force increases
- Half the distance gives 4 times the force

- Gravitational field strength is the force per unit mass
- g = F/m
- On Earth g = 10Nkg-1
- How much force wil the Earth’s gravity exert on 3 kg
- 30N
- The force on 10kg on the moon is 17N. Calculate g on the moon
- g = F/m = 1.7 Nkg-1

- F = GMm/r2
- g = F/m = GM/r2
- Mass of Earth = 6x1024kg
- Radius of Earth = 6.4 x106m
- Calculate g on Earth
- g = GM/r2
- = 6.67x10-11 x 6x1024/ (6.4 x 106)2
- = 9.8 Nkg-1

Star

planet

g from star

g from planet

Total g = Vector sum

F

F

S

N

N

S

- These magnets have no energy when they are separated
- You do work when you push them together
- When they are close together potential energy is stored
- Let them go and the energy is released

PE

S

N

F

F

S

N

- The magnets have zero energy when they are apart.
- They slide together and have less energy (negative)
- A force must do work to pull them back to zero
- When objects attract each other they have negative potential energy

- PE

Amount of work needed to remove object

Zero energy

- Gravitational potential is always negative
- The potential at a point is the amount of energy needed to move 1 kg from infinity to that point
- V = -GM/r

Back to zero energy

Attracted by gravity

Negative PE

planet

A distant object has zero PE

Amount of work needed to remove 2 kg

Amount of work needed to remove 1kg

Zero energy

V = -GMm/r

The potential at a point is the energy needed to move 1 kg from infinity to that point

The potential energy of an object is the energy needed to move the object from infinity to that point

PE = mV = -GMm/r

Back to zero energy

Attracted by gravity

Negative PE

1 kg

2kg

planet

planet

- How fast must an object go so that it doesn’t come back?
- It must have enough KE to overcome the negative PE (-GMm/r) and get to zero energy
- 1/2mv2 = GMm/r
- V2 = 2GM/r
- V = (2GM/r)

Calculate the escape velocity of Earth

r= 6.4 x106m m =6 x 1024 kg

v = (2GM/r) = (2 x 6.67 x 10-11 x 6 x1024 / 6.4 x106)

= 11 000 ms-1 = 11kms-1