Block A of mass mA is moving horizontally with speed Va along a frictionless surface
Block A of mass mA is moving horizontally with speed Va along a frictionless surface. It collides elastically with block B of mass mB that is initially at rest. After the collision block B enters a rough surface at x =0 with a coefficient of kinetic friction that increases linearly with distance μ(x) = bx for 0 ≤ x ≤ d, where b is a positive constant. At x=d block B collides with an unstretched spring with spring constant k on a frictionless surface. The downward gravitational acceleration has magnitude g.
What is the distance the spring is compressed when block B first comes to rest? Express your answer in terms of Va, mA, mB, b, d, g, and k.
STEPS should be used to solve this problem:
1) Find speeds of both blocks after collision (note collision is elastic as given).
2) Find the work done by friction on block B.
3) Find the speed of block B at the end of the rough surface.
4) Find the distance compressed in spring.
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