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Gravitational Energy

Gravitational Energy. Gravitational Work. The work done by the force of gravity only depends on the vertical distance. The path taken doesn’t matter It’s a conservative force There is a potential energy. y 2. d. F = - mg. h. h. q. y 1. Energy of Position. Raise a block

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Gravitational Energy

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  1. Gravitational Energy

  2. Gravitational Work • The work done by the force of gravity only depends on the vertical distance. • The path taken doesn’t matter • It’s a conservative force • There is a potential energy y2 d F = -mg h h q y1

  3. Energy of Position • Raise a block • The state of the block changes • Work is stored in a new position • Energy due to position is called potential energy (U). • An object has the potential to do work • The potential energy of gravity: U = mgy y2 Dy y1

  4. The hill is 2.5 km long with a drop of 800 m. The skier is 75 kg. The speed at the finish is 120 km/h. How much energy was dissipated by friction? Using Friction and Energy q

  5. Find the total change in kinetic energy. Find the total change in potential energy. The difference is due to friction and drag. DK = ½ mv2 - 0 = ½(75 kg)(130 m/s)2 = 5.4 x 105 J DU = mgh = (75 kg)(9.8 m/s2)(-800 m) = -5.9 x 105 J Wnon = DK + DU = -0.5 x 105 J Friction and Height

  6. No Absolute • Potential energy reflects the work that may be done. • The point U = 0 is arbitrary • At the top of a table of height h: • U = mg(y+h) • The same experiment is shifted by a constant potential mgh: • U = mgy + mgh = mgy + C y2 y y1 h

  7. Universal Gravitational Work • Gravity on the surface of the Earth is a local consequence of universal gravitation. • How much work can an object falling from very far from the Earth do when it hits the surface? r RE

  8. Universal Gravitational Potential • The work doesn’t depend on the path. • Universal gravity is a conservative force • The potential is set with U = 0 at an infinite distance. • Gravity acts at all ranges • Gravity is weakest far from the source

  9. The kinetic energy for a circular orbit is related to the potential energy. The total energy in a circular orbit can be described in terms of either the kinetic or the potential energy. Kinetic Energy in Orbit

  10. Escape Velocity • Negative total energy can be viewed as being captured by the force of gravity. • To get away from the influence of gravity requires zero or positive energy. • The minimum velocity is called the escape velocity. On earth,vesc= 11.2 km/s next

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