A block of mass M slides on a frictionless surface with an initial speed of v 0 . On top of the block, there is a small block of mass m . The coefficient of friction between the blocks is μ . The system of blocks encounters an ideal spring with force constant k . The maximum value of k for which the blocks don't slip relative to each other is

Question

A block of mass M slides on a frictionless surface with an initial speed of v 0 . On top of the block, there is a small block of mass m . The coefficient of friction between the blocks is μ . The system of blocks encounters an ideal spring with force constant k . The maximum value of k for which the blocks don't slip relative to each other is, μ g v 0 2 m + M 2 m, μ g v 0 2 m + M, μ g v 0 2 m + M 2 M, μ g v 0 2 M - m

MARKS App · Accepted Answer

1 2 M + m v 0 2 = 1 2 k x 2 x = v 0 M + m k Also for the upper block f m a x = μ m g = m k m + M x μ g = k m + M v 0 m + M k ⇒ k m + M = μ g v 0 2 ⇒ k = μ g v 0 2 m + M

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