Figure 7.26 shows a cart striking a spring. In Figure 7.26a, consider the motion of the cart along the direct path from the initial position \(x_{1}\), which is the position at which the cart makes initial contact with the free end of the spring, to the position \(x_{2}\) (path A). In Figure \(7.26 b\), consider the motion along the path from \(x_{1}\) to the position of maximum compression \(x_{3}\) and then back to \(x_{2}\) (path B). Show that the change in the cart's kinetic energy is the same for both paths if the interaction caused by the spring is reversible.

Data from Figure 7.26

Transcribed Image Text:

(a) Cart moves directly from x, tox www path A (b) Cart moves from x, to x, viax www. path B