If -52 J of net work is done on a system by all forces while the system does -15 J of work against nonconservative forces, then by how much do the PE and the KE of the system change?
The PE of the system is equal to the work done by the system against conservative forces. Work done against conservative forces can be regained in the form of KE when the system is 'released'. For example work done against gravity in lifting an object might be regained in the form of KE when the object is dropped; work done by an object against a spring or a rubber band as it is stretched might be regained as the elastic object is released.
The amount of work done BY the system and the work done ON the system are equal and opposite. Thus the -52 Joules of work are done ON the system and 52 Joules of work are done BY the system.
The amount of work done BY the system against nonconservative forces and the amount of work done ON the system by nonconservative forces are equal and opposite. -15 Joules are done BY the system against nonconservative forces 15 Joules are done ON the system by nonconservative forces..
The work done BY the system against conservative forces is the change in the PE of the system. For example in lifting an object against gravity a system will do positive work against conservative forces, which will increase the potential energy of the system (as the object drops back to its original position this potential energy might be 'reclaimed' in the form of KE). If an object falls gravity does positive work ON it so the work done BY the object against gravity is negative, which means that the PE change is negative.
If we let `dWnoncons stand for the net work done BY the system against nonconservative forces, and `dPE for the work done BY the system against conservative forces, then the net work done BY the system is `dWnet = `dWnoncons + `dPE.
`dKE + `dPE + `dWnoncons = 0.
In the present example we see that
Thus the remaining 52 J - -15 J = 67 J of the work done BY the system is done against conservative forces. This is the change in the PE of the system.
To understand this, again think of the example of work done against the conservative force of gravity. If this work is positive, as in the case of a rising object, PE increases; if this work is negative, as in the case of a falling object, PE decreases.
The KE of the system in this example changes by a net amount equal to the work done on the system, which is -52 Joules.
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