A 2.10 mass is pushed against a horizontal spring of force constant 26.0 on a fr

Question

A 2.10 mass is pushed against a horizontal spring of force constant 26.0 on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring in any way. When the spring has been compressed enough to store 11.5 of potential energy in it, the mass is suddenly released from rest. Find the greatest speed the mass reaches. What is the greatest acceleration of the mass?

Explanation / Answer

The greatest speed occurs when the potential = zero so K = 11.6J => 1/2*m*v^2 = K so v = sqrt(2*K/m) = sqrt(2*11.5/2.5) = 3.03m/s The greatest acceleration occurs when the mass is released The force is k*x and we get x from 1/2*k*x^2 so x = sqrt(2*U/k) = sqrt(2*11.5/2500) = 0.0959m So F = k*x = 2500*0.0959 = 240N So a = F/m = 240N/2.5kg = 95.9m/s^

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