A glider on a nearly frictionless air track is connected to an ideal spring fixed at…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A glider on a nearly frictionless air track is connected to an ideal spring fixed at one end. The glider oscillates with amplitude A and period T. At the instant the glider passes through the equilibrium position moving to the right, a very short, horizontal impulse is delivered in the same direction, instantly doubling the glider’s speed without appreciably changing its position.
Neglect any effects of the impulse duration on the spring.
(a) Express the new total mechanical energy of the system in terms of the original total mechanical energy E0.
(b) Derive an expression for the new amplitude A′ of oscillation in terms of the original amplitude A.
(c) Discuss whether the period of oscillation changes as a result of the impulse, and justify your answer without invoking the small-angle or small-amplitude approximations.
(d) Compare the maximum kinetic energy and maximum potential energy before and after the impulse. Explain how each extreme changes and why.