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Two blocks of masses M = 1 kg and m = 2 kg are connected by an ideal spring of spring constant k = 100 N/m and placed on a rough horizontal surface. The spring is initially at its natural length and the coefficient of friction for both blocks is mu = 1/sqrt(8). Block M is given an initial speed while block m remains at rest. Find the maximum initial speed of M (in m/s) such that block m never moves. (Take g = 10 m/s².)
- 1
- 2
- sqrt(2)
- 0.5
Correct answer: 1
Solution
Maximum spring compression before m slides: x_max = mu*m*g/k = (1/sqrt(8))*2*10/100 = sqrt(2)/20 m. Energy equation for M: (1/2)(1)v0² = (1/2)(100)(sqrt(2)/20)² + (1/sqrt(8))(1)(10)(sqrt(2)/20) = 1/4 + 1/4 = 1/2. Thus v0 = 1 m/s.
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