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Gravitational Potential Energy

Gravitational Potential Energy. When you have previously considered gravitational potential energy, you would have used the equation:. ∆G.P.E = mg∆h. Consider a monkey climbing 2 metres up a tree.

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Gravitational Potential Energy

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  1. Gravitational Potential Energy When you have previously considered gravitational potential energy, you would have used the equation: ∆G.P.E = mg∆h Consider a monkey climbing 2 metres up a tree If that same monkey were to climb to 4 metres high in the next tree its change in potential energy would be double. If we were to make the monkey go 50km up towards the edge of space, would this equation still be valid?

  2. Field lines • We use the idea of field lines to represent both the magnitude and direction of any gravitational field. • The field lines show the direction in which a small test mass would move if placed into the field. • The higher the density of field lines, the stronger the field. • Over small distances (?) the Earths gravitational field can considered to be uniform, that is the field lines are parallel and equal distance apart

  3. The strength of the Earth’s gravitational field decreases as you get further from the centre. • This is shown by the density of field lines reducing (i.e. they become further apart). Radial field • At large distances the equation ∆G.P.E = mg∆h no longer holds. This is because the gravitational field strength changes (g < 9.8Nkg-1)

  4. Gravitational Force Gravity is a force that acts between any two objects that have mass. What factors affect the size of the gravitational force between any two masses? • The mass of the 1st object (m1) • The mass of the 2nd object (m2) • The distance between the two objects (r) G is the constant of proportionality (6.67 × 10-11m3kg-1s-2) The minus sign indicates that the force is attractive.

  5. G =6.67 × 10-11m3kg-1s-2 Calculate the size of the attractive force between the Earth (5.97×1024 kg) and the moon (7.35× 1022 kg). The moon is on average 384,000km away from the Earth. Estimate the size of the attractive force between these two women sitting on a park bench. We can consider that the entire mass of an object is found at its centre of gravity.

  6. 9.79Nkg-1 9.76Nkg-1 8.78Nkg-1 • The Gravitational field strength at any point is the force per unit mass exerted on a mass placed at that point [g= F/m] (1) Calculate the gravitational field strength on the surface of the Earth given that it has a radius of 6378km and a mass of 5.97×1024 kg. G =6.67 × 10-11m3kg-1s-2 (2) What will be the gravitational field strength due to the Earth • on top of mount Everest (8848m)? • at the height of the international space station (354km)?

  7. What will happen to the G.P.E of the spacecraft as it journeys through the solar system? For now we will consider it to have 0J of G.P.E on the surface of the Earth. Potential energy of spacecraft Jupiter Saturn 0 OuterSpace Mars Earth

  8. By convention we take the potential energy of an object to be 0J when it is an infinite distance from all other masses, this also avoids the problems of positive and negative potential energies. OuterSpace Earth Mars Jupiter Saturn Potential energy of spacecraft 0

  9. Calculate the change in potential energy when the Voyager probe (720kg) travelled from the Earth’s surface to beyond the edge of the solar system, 16 billion km away (1.6 x1013m!) G =6.67 × 10-11m3kg-1s-2 mE = 5.97 × 1024 kg

  10. Along any equipotential line an object will have the same gravitational potential energy per unit mass. This quantity Ep/m is called the gravitational potential. Field lines • We can draw lines that are perpendicular to the field lines on our diagram. These are called equipotential lines.

  11. 2x105m • Calculate the gravitational potential at a distance 2x105m from a 5x1020kg mass? • Calculate the potential at a distance of 1x1020m? • Calculate the change in gravitational potential energy if a 1kg object moved between the points: • Calculate ∆GPE if the object has a mass of 49kg 5x1020kg Gravitational potential • The Gravitational potential at any point is equal to the work done in bringing a unit mass from infinity to that point. This is a useful quantity as it is independent of the mass of object in the field, but can be used to calculate the potential energy for any mass at any point in a field.

  12. Gravitational potential energy Earlier we defined gravitational potential as the gravitational potential energy per unit mass, therefore V=Ep/m or Ep=Vm This equation gives the gravitational potential energy of test mass mat a point that is distance r from mass M. When we used the equation G.P.E = mgh we were calculating the change in potential energy, but we get around this by creating a reference point with which all other G.P.E’s are compared.

  13. Gravitational fields Force per unit mass Potential energy per unit mass

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