Gravitational Energy

Gravitational Work  The work done by the force of gravity only depends on the vertical distance. The path taken doesn’t matterThe path taken doesn’t matter It’s a conservative forceIt’s a conservative force There is a potential energyThere is a potential energy d F =  mg h  h y2y2 y1y1

Energy of Position  Raise a block The state of the block changesThe state of the block changes Work is stored in a new positionWork is stored in a new position  Energy due to position is called potential energy (U). An object has the potential to do workAn object has the potential to do work The potential energy of gravity: U = mgyThe potential energy of gravity: U = mgy y1y1 yy y2y2

Using Friction and Energy  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? 

Friction and Height  Find the total change in kinetic energy.  Find the total change in potential energy.  The difference is due to friction and drag.   K = ½ mv  = ½(75 kg)(130 m/s) 2  = 5.4 x 10 5 J   U = mgh  = (75 kg)(9.8 m/s 2 )(-800 m)  = -5.9 x 10 5 J  W non =  K +  U  = -0.5 x 10 5 J

No Absolute  Potential energy reflects the work that may be done. The point U = 0 is arbitraryThe point U = 0 is arbitrary  At the top of a table of height h: U = mg(y+h)U = mg(y+h)  The same experiment is shifted by a constant potential mgh: U = mgy + mgh = mgy + CU = mgy + mgh = mgy + C y1y1 h y2y2 y

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 RERE

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

Kinetic Energy in Orbit  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.

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. next On earth, v esc = 11.2 km/s