F = G Mm

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Calculation of g • F = GMm/r 2 • g = F/m = GM/r 2 • Mass of Earth = 6x10 24 kg • Radius of Earth = 6.4 x10 6 m • Calculate g on Earth • g = GM/r 2 • = 6.67x10 -11 x 6x10 24 / (6.4 x 10 6 ) 2 • = 9.8 Nkg -1

Transcript of F = G Mm

Page 1: F = G Mm

Calculation of g

• 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

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g is a vector

Star

planet

g from planet

g from star

Total g = Vector sum

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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

N SS NF F

PE

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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

S NS N

- PE

FF

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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

planet A distant object has zero PE

Attracted by gravity

Negative PE

Amount of work needed to remove object

Zero energy

Back to zero energy

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Gravitational Potential Energy

planet

1 kg

Attracted by gravity

Negative PE

Amount of work needed to remove 1kg

Zero energy

Back to zero energy

2kg

Amount of work needed to remove 2 kg

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

V = -GMm/r

Page 7: F = G Mm

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)

planet

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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