Conservation of energy

Physics Tutorial

Conservation of energy

Intro

When a system is isolated from the dissipative force, then the total energy of the system remains constant with time. One of the example of it is friction force. Its direction always oppose the motion of the system and at certain amount of time, the system energy will be reduced because of work done by this force. Remember that the total energy of the system is equivalent to total kinetic energy plus total potential energy and internal energy (this will be discussed more in thermodynamics).This dissipative force is one kinds of many non-conservative force, which the work done by it can be calculated by specified path. To generalize, the work done by this dissipative force, also known as non-conservative force is equal to the change of total energy for given end and initial points. Notice that if the force is path independent, then there is a potential energy associated with it so it corresponds to the potential energy term.

Sample Problem

Which of the following statements is true regarding the non-conservative force?

There exist a potential energy function associated to the force


The force should not be the function of the position


Work done by this force on the particle in the closed path is zero


The work done by this force is always negative


The kinetic energy of the system may be increased because of this force


Solution

Because it is path-independent, one should realize that, even though the initial and final position are the same, it still need a specified path to calculate the work. So it may be a non-zero work.

Only for the conservative force that have a relation with potential energy

The work done by the force may be positive. For example if you have a two blocks, with one above the other and the system have considerable friction, and you push the upper block, then the friction on the lower by the upper will be do the positive work.

The force may be function of the position. You will learn in the later course that the conditions of the force being a non-conservative in terms of mathematics.

Because the work done may be positive, according to the conservation of energy theorem, the kinetic energy may be increase too.



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