A block of mass is released from rest at the top of a friction-free ramp of vertical…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A block of mass 0.80kg is released from rest at the top of a friction-free ramp of vertical height h. The bottom of the ramp is at the left end of a horizontal track that is 1.2m long and has a coefficient of kinetic friction μk=0.25. At the right end of the horizontal track is an ideal light spring of force constant k=150Nm−1 that is fixed to a rigid wall. The block slides across the rough horizontal surface, compresses the spring a maximum distance x, momentarily comes to rest, and is then pushed back toward the ramp. Ignore any friction after the block leaves the rough surface during the return trip.
Unless otherwise stated, express algebraic answers first, then substitute numbers.
(a) Derive an algebraic expression for the speed vB of the block at the bottom of the ramp just as it reaches the horizontal track in terms of h and fundamental constants.
(b) Starting from point B at the bottom of the ramp, write an energy balance for the motion across the horizontal track to the instant of maximum compression of the spring. From this, obtain an expression for the minimum ramp height h required to achieve a specified maximum compression x.
(c) For a desired maximum compression of x=0.20m, calculate the corresponding numerical value of h.
(d) Suppose the coefficient of kinetic friction is doubled while all other quantities remain unchanged. Qualitatively describe how the required ramp height would change, and then compute the new numerical value of h needed to obtain the same compression x=0.20m. Explain your reasoning.