KineticEnergy

# KineticEnergy - Kinetic Energy How do work and energy...

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Kinetic Energy How do work and energy relate to each other? Consider an object with mass m being acted on by a force F . Then, if the speed of the object increases from v 1 to v 2 as it moves from x 1 to x 2 , we can write ( 29 1 2 2 1 2 2 2 x x a v v - + = solving for a , we get ( 29 1 2 2 1 2 2 2 x x v v a - - = so the force is ( 29 1 2 2 1 2 2 2 x x v v m F - - = Using (10.2), we find that the resulting work is ( 29 ( 29 ( 29 ( 29 2 1 2 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 1 2 ) ( mv mv v v m x x x x v v m x x F W - = - = - - - = - = (11.1) The quantity ½ mv 2 on the right hand side of (11.1) is called the kinetic energy of the object. Kinetic energy is the energy an object has due to its motion. It is one of three types of energy that can be associated with an object. The other two are the potential energy , which is the energy an object has due to its position inside a force field , and the rest energy , which is the energy an object has due to its existence . Returning to (11.1), we see that it tells us that W = K 2 K 1 = K (11.2) i.e., the work done by an external force on an object is equal to the change in the

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