PotentialEnergy - Potential Energy Conservative and...

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Potential Energy Conservative and Dissipative Forces Before moving on to the second type of energy, let us look at conservative and dissipative forces. Recall that we defined the work to be = 2 1 x x x d F W What would happen if we then traversed a second path, only this time going from x 2 to x 1 ? In some of the cases, we would find that the total work done would become zero. This is the hallmark of a conservative force . Specifically, we say that a force is conservative if 1. It is independent of the path of the body and depends only on the starting point and ending point, 2. It is completely reversible, and 3. When the starting and ending points are the same, the total work is zero. If the force is not conservative, it is called a dissipative force . Example : The force of gravity is a conservative force. Let a box of mass m be moved around the path shown below and acted on only by gravity. 1 2 3 4 m mg h Can break the work up into 4 pieces W 12 , W 23 , W 34 , W 41 . Then
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0 0 0 0 0 41 34 23 12 41 34 23 12 = + + + - = + + + = = = = - = mgh mgh W W W W W W mgh W W mgh W Definition of Potential Energy Whenever a force is conserved, we can define a potential energy for that force as follows: - = 2 1 x x x d F U (12.1) This is interpreted physically as the potential energy due to the force at position x 2 relative to x 1 . Example : What is the gravitational potential energy of an object of mass m at a distance h above the ground? h m Define the ground to be at x 1 = 0. Then since the force is constant mgh mgh x F U = - - = - = ) (
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Work-Energy Theorem Now let’s use (11.2) to find an important relationship between work and
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PotentialEnergy - Potential Energy Conservative and...

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