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# F = G Mm

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### F = G Mm

1. 1. Calculation of g <ul><li>F = GMm/r 2 </li></ul><ul><li>g = F/m = GM/r 2 </li></ul><ul><li>Mass of Earth = 6x10 24 kg </li></ul><ul><li>Radius of Earth = 6.4 x10 6 m </li></ul><ul><li>Calculate g on Earth </li></ul><ul><li>g = GM/r 2 </li></ul><ul><li>= 6.67x10 -11 x 6x10 24 / (6.4 x 10 6 ) 2 </li></ul><ul><li>= 9.8 Nkg -1 </li></ul>
2. 2. g is a vector g from planet g from star Total g = Vector sum Star planet
3. 3. Gravitational PE <ul><li>These magnets have no energy when they are separated </li></ul><ul><li>You do work when you push them together </li></ul><ul><li>When they are close together potential energy is stored </li></ul><ul><li>Let them go and the energy is released </li></ul>PE N S S N F F
4. 4. Gravitational PE <ul><li>The magnets have zero energy when they are apart. </li></ul><ul><li>They slide together and have less energy (negative) </li></ul><ul><li>A force must do work to pull them back to zero </li></ul><ul><li>When objects attract each other they have negative potential energy </li></ul>- PE S N S N F F
5. 5. Gravitational Potential <ul><li>Gravitational potential is always negative </li></ul><ul><li>The potential at a point is the amount of energy needed to move 1 kg from infinity to that point </li></ul><ul><li>V = -GM/r </li></ul>planet A distant object has zero PE Attracted by gravity Negative PE Back to zero energy Amount of work needed to remove object Zero energy
6. 6. Gravitational Potential Energy planet 1 kg Attracted by gravity Negative PE Back to zero energy 2kg 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 Amount of work needed to remove 1kg Zero energy Amount of work needed to remove 2 kg
7. 7. Escape velocity <ul><li>How fast must an object go so that it doesn’t come back? </li></ul><ul><li>It must have enough KE to overcome the negative PE (-GMm/r) and get to zero energy </li></ul><ul><li>1/2mv 2 = GMm/r </li></ul><ul><li>V 2 = 2GM/r </li></ul><ul><li>V =  (2GM/r) </li></ul>Calculate the escape velocity of Earth r= 6.4 x10 6 m m =6 x 10 24 kg v =  (2GM/r) =  (2 x 6.67 x 10 -11 x 6 x10 24 / 6.4 x10 6 ) = 11 000 ms -1 = 11kms -1 planet