On a frictionless surface two blocks of masses m and M move in the same direction with speeds v1 and v2 (v1 v2), with M ahead of m. An ideal spring of force constant K is fixed to the rear face of M. Find the maximum compression of the spring when the blocks interact.

Question

On a frictionless surface two blocks of masses m and M move in the same direction with speeds v1 and v2 (v1 > v2), with M ahead of m. An ideal spring of force constant K is fixed to the rear face of M. Find the maximum compression of the spring when the blocks interact.

Accepted Answer

(v1 - v2) * sqrt(mM/((M + m)K)). At maximum compression both blocks share a common velocity; the lost kinetic energy equals the spring PE. Using reduced mass mu = mM/(M+m), (1/2)K x² = (1/2) mu (v1 - v2)², giving x = (v1 - v2) sqrt(mM/((M+m)K)).

On a frictionless surface two blocks of masses m and M move in the same direction with speeds v1 and v2 (v1 > v2), with M ahead of m. An ideal spring of force constant K is fixed to the rear face of M. Find the maximum compression of the spring when the blocks interact.

Solution

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