Question

A block of mass m starts from rest at height h on a frictionless inclined plane. The block slides down the plane. Travels a distance d on a rough horizontal surface (before coming to rest for the first time) with co-efficient of kinetic friction μ & compresses a spring with force constant k through a distance x before momentarily coming to rest. Then the block travels back across the rough surface, sliding up the plane. The correct expression for the maximum height h' which the block reaches on its return

• A. h' = $h-2\mu d$
• B. h' = $h+2\mu d$
• C. h' = $h+2\mu d+\frac{k}{mg}{x}^2$
• D. h' = $h-2\mu d-\frac{k}{mg}{x}^2$

Answer 1

The correct option is A h' = $h-2\mu d$

W_G + W_SF + W_FF=∆ K.E

Mg(h-h') +0 + μmg(-2d) = 0

h - h' - 2 μd = 0

h' = h - 2μd