Gravitation
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Gravitation. AHL 8.2. F = GMm/r 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.

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Gravitation

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Gravitation

Gravitation

AHL 8.2


F gmm r 2

F = GMm/r2

  • 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

Gravitational field strength

  • 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


G gm r 2

g = GM/r2

  • 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


G is a vector

Star

planet

g is a vector

g from star

g from planet

Total g = Vector sum


Gravitational pe

F

F

S

N

N

S

Gravitational PE

  • 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


Gravitational pe1

S

N

F

F

S

N

Gravitational PE

  • 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


Gravitational potential

Amount of work needed to remove object

Zero energy

Gravitational Potential

  • 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


Gravitational potential energy

Amount of work needed to remove 2 kg

Amount of work needed to remove 1kg

Zero energy

Gravitational Potential 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


Escape velocity

planet

Escape velocity

  • 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


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