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# Gravitation - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Gravitation' - hedley-boone

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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

planet

g is a vector

g from star

g from planet

Total g = Vector sum

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

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

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

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

• 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