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Gravitation

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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  1. Gravitation AHL 8.2

  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

  3. 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

  4. 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

  5. Star planet g is a vector g from star g from planet Total g = Vector sum

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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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