It is interesting to do the above experiment also with a steel marble (or ball bearing). You will need the mass of the marble as well to calculate its initial kinetic energy. As noted in Kinetic Energy and the Work-Energy Theorem, the work-energy theorem states that the net work on a system equals the change in its kinetic energy, or W net = ΔKE W net = ΔKE size 12. We will see that the work done by nonconservative forces equals the change in the mechanical energy of a system. Now let us consider what form the work-energy theorem takes when both conservative and nonconservative forces act. 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. (b) A system with nonconservative forces. The spring can propel the rock back to its original height, where it once again has only potential energy due to gravity. When a rock is dropped onto a spring, its mechanical energy remains constant (neglecting air resistance) because the force in the spring is conservative. (a) A system with only conservative forces. As noted in Chapter 7.Figure 7.15 Comparison of the effects of conservative and nonconservative forces on the mechanical energy of a system. Comparison of the effects of conservative and nonconservative forces on the mechanical energy of a system. We often choose to understand simpler systems such as that described in Figure 2(a) first before studying more complicated systems as in Figure 2(b). Figure 2 compares the effects of conservative and nonconservative forces. 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. Mechanical energy may not be conserved when nonconservative forces act. How Nonconservative Forces Affect Mechanical Energy The energy expended cannot be fully recovered. 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). Less work is done and less of the face is erased for the path in (a) than for the path in (b). 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. 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. Friction, for example, creates thermal energy that dissipates, removing energy from the system. An important characteristic is that the work done by a nonconservative force adds or removes mechanical energy from a system. Because of this dependence on path, there is no potential energy associated with nonconservative forces. As illustrated in Figure 1, work done against friction depends on the length of the path between the starting and ending points. Friction is a good example of a nonconservative force. A nonconservative force is one for which work depends on the path taken. Conservative forces were discussed in Chapter 7.4 Conservative Forces and Potential Energy. Show how the principle of conservation of energy can be applied by treating the conservative forces in terms of their potential energies and any nonconservative forces in terms of the work they do.įorces are either conservative or nonconservative.Define nonconservative forces and explain how they affect mechanical energy.
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