Prove mathematically that force of friction is non conservative force (3 marks)
Answers
Here is your answer in breaf :-
The majority of conversions of one type of energy to another have very simple and obvious math which shows that Energy is Conserved. However, when any form of energy is converted into heat, then more complicated forms of the Conservation of Energy are involved. Friction is a process where kinetic energy is (partially) converted into heat. So if the “simple math” is used, then it appears that Energy is not Conserved. But if the more complete forms of the Laws of Thermodynamics are used, then it is obvious that Energy IS conserved.
One of your other answerers partially described it. In math terms, in mechanical situations, the “Conservation of Energy” is defined for a mathematical Field, where processes can go in either direction. But heat is different, and the more complicated math is necessary, as forms of heat are usually not reversible.
Forces that do not store energy are called non-conservative of dissipative forces. Friction force is an example of a non-conservative force because it do not store energy rather than storing it. Frictional force oppose the motion of the object i.e.
Forces are either conservative or nonconservative. Conservative forces were discussed in Conservative Forces and Potential Energy. A
nonconservative force is one for which work depends on the path taken. Friction is a good example of a nonconservative force. As illustrated in Figure 1, work done against friction depends on the length of the path between the starting and ending points. Because of this dependence on path, there is no potential energy associated with nonconservative forces. An important characteristic is that the work done by a nonconservative force adds or removes mechanical energy from a system. Friction , for example, creates
thermal energy that dissipates, removing energy from the system. Furthermore, even if the thermal energy is retained or captured, it cannot be fully converted back to work, so it is lost or not recoverable in that sense as well.
Figure 1. The amount of the happy face erased depends on the path taken by the eraser between points A and B, as does the work done against friction. Less work is done and less of the face is erased for the path in (a) than for the path in (b). The force here is friction, and most of the work goes into thermal energy that subsequently leaves the system (the happy face plus the eraser). The energy expended cannot be fully recovered.
How Nonconservative Forces Affect Mechanical Energy
Mechanical energy may not be conserved when nonconservative forces act. For example, when a car is brought to a stop by friction on level ground, it loses kinetic energy, which is dissipated as thermal energy, reducing its mechanical energy. Figure 2 compares the effects of conservative and nonconservative forces. We often choose to understand simpler systems such as that described in Figure 2a first before studying more complicated systems as in Figure 2b.
Figure 2. Comparison of the effects of conservative and nonconservative forces on the mechanical energy of a system. (a) A system with only conservative forces. When a rock is dropped onto a spring, its mechanical energy remains constant (neglecting air resistance) because the force in the spring is conservative. The spring can propel the rock back to its original height, where it once again has only potential energy due to gravity. (b) A system with nonconservative forces. When the same rock is dropped onto the ground, it is stopped by nonconservative forces that dissipate its mechanical energy as thermal energy, sound, and surface distortion. The rock has lost mechanical energy.
Figure 3. A person pushes a crate up a ramp, doing work on the crate. Friction and gravitational force (not shown) also do work on the crate; both forces oppose the person’s push. As the crate is pushed up the ramp, it gains mechanical energy, implying that the work done by the person is greater than the work done by friction.
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during friction some of the energy is wasted in the form of hestand sound, so the kinetic energy does not remains conserved.
the force in which kinetic energy is not conserved is non conservative force and in case of friction also the kinetic energy is not conserved ,therefore fricrion is non conservative force.