Potential Energy
When we throw a ball upwards with an initial velocity, it rises to a certain height and becomes stationary for a moment. What happens to the lost kinetic energy? We know with our experience that the ball returns back in our hands with a speed equal to its initial value. The initial kinetic energy is somehow stored and is later fully recovered in the form of kinetic energy. The ball must have something at the new height that it does not have at the previous level. That something by virtue of its position is Potential Energy . Potential energy is the energy associated with the relative positions of two or more interacting particles. Potential energy fits well the idea of energy as the capacity to do work. For example, the gravitational potential energy of an object raised off the ground can be used to compress or expand a spring or to lift another weight. As a coil spring unwinds, or a straight spring returns to its natural length, the stored potential energy can be used to do work. For example, if a block is attached to a compressed spring, the elastic potential energy can be converted into kinetic energy of the block as (Fig.1)
In the above discussion we have seen that in the case of gravity and elastic spring, the kinetic energy imparted initially is stored as potential energy for a short time which is regained, later on. But this is not true in all cases.
For example , consider block placed at rest on a rough horizontal surface. If we impart it some initial kinetic energy, it starts sliding on the surface, the frictional force does negative work on the block, decreasing its kinetic energy to zero. But it does not come back to own hand no matter how long we wait! The Frictional Force has used up the kinetic energy in a non reversible way. The forces, such as gravity and spring force, which does work in a reversible manner is called a conservative force . In contrast, the force such a frictional force, which does work in an irreversible manner is called a non-conservative force . Any constant force (both in magnitude and direction) is always a CONSERVATIVE FORCE.
`text(Important :)`
(a) The work done by a conservative force is independent of path. It depends only on the initial and final positions. In contrast, the work done by a non-conservative force depends on the path.
(b) The work done b y a conservative force around any closed path is zero.
`text(The Potential energy is defined only for conservative forces.)`
The change in potential energy as a particle moves from point A to point B is equal to the negative of the work done by the associated conservative force
`DeltaU=U_B-U_A=-W_C`
Using definition of work
`U_B-U_A=-int_A^BF_Cds......(1)`
From equation (1) , we see that starting with potential energy `U_A`, we end up with potential energy. `U_B` at point B , because `W_C` has the same value for all paths. When a block slides along a rough floor, the work done by the force of friction on the block depends on the length of the path taken ti'om point A to point B . There is no unique value for the work done. So one cannot assign unique values for potential energy at each point. Hence, non-conservative force can not have potential energy. When the forces within a system are conservative, external work done on the system is stored as potential energy and is fully recoverable.
Note : The potential energy is always defined with respect to a reference point.
In the above discussion we have seen that in the case of gravity and elastic spring, the kinetic energy imparted initially is stored as potential energy for a short time which is regained, later on. But this is not true in all cases.
For example , consider block placed at rest on a rough horizontal surface. If we impart it some initial kinetic energy, it starts sliding on the surface, the frictional force does negative work on the block, decreasing its kinetic energy to zero. But it does not come back to own hand no matter how long we wait! The Frictional Force has used up the kinetic energy in a non reversible way. The forces, such as gravity and spring force, which does work in a reversible manner is called a conservative force . In contrast, the force such a frictional force, which does work in an irreversible manner is called a non-conservative force . Any constant force (both in magnitude and direction) is always a CONSERVATIVE FORCE.
`text(Important :)`
(a) The work done by a conservative force is independent of path. It depends only on the initial and final positions. In contrast, the work done by a non-conservative force depends on the path.
(b) The work done b y a conservative force around any closed path is zero.
`text(The Potential energy is defined only for conservative forces.)`
The change in potential energy as a particle moves from point A to point B is equal to the negative of the work done by the associated conservative force
`DeltaU=U_B-U_A=-W_C`
Using definition of work
`U_B-U_A=-int_A^BF_Cds......(1)`
From equation (1) , we see that starting with potential energy `U_A`, we end up with potential energy. `U_B` at point B , because `W_C` has the same value for all paths. When a block slides along a rough floor, the work done by the force of friction on the block depends on the length of the path taken ti'om point A to point B . There is no unique value for the work done. So one cannot assign unique values for potential energy at each point. Hence, non-conservative force can not have potential energy. When the forces within a system are conservative, external work done on the system is stored as potential energy and is fully recoverable.
Note : The potential energy is always defined with respect to a reference point.