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Non-Conservative Forces

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 7.15 compares the effects of conservative and nonconservative forces. We often choose to understand simpler systems such as that described in Figure 7.15(a) first before studying more complicated systems as in Figure 7.15(b).

(a) A system is shown in three situations. First, a rock is dropped onto a spring attached to the ground. The rock has potential energy P E sub 0 at the highest point before it is dropped on the spring. In the second situation, the rock has fallen onto the spring and the spring is compressed and has potential energy P E sub s. And in the third situation, the spring pushes the rock into the air; then the rock has some kinetic and some potential energy, labeled as K E plus P E sub g prime. (b) A rock is at some height above the ground, having potential energy P E sub g, and as it hits the ground all of the rock’s energy is used to produce heat, sound, and deformation of the ground.

Figure 7.15 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.