A light spring of force constant 3.75 N/m is compressed by 8.00 cm and held betw

Question

A light spring of force constant 3.75 N/m is compressed by 8.00 cm and held between a 0.250 kg block on the left and a 0.490 kg block on the right. Both blocks are at rest on a horizontal surface. The blocks are released simultaneously so that the spring tends to push them apart. Find the maximum velocity each block attains if the coefficient of kinetic friction between each block and the surface is the following. In each case, assume that the coefficient of static friction is greater than the coefficient of kinetic friction. Let the positive direction point to the right.

(a) For the 0.250 kg block:
At µk = 0.000, the maximum velocity is _____ m/s
At µk = 0.100, the maximum velocity is _____ m/s
At µk = 0.454, the maximum velocity is _____ m/s

(b) For the 0.490 kg block:
At µk = 0.000, the maximum velocity is _____ m/s
At µk = 0.100, the maximum velocity is _____ m/s
At µk = 0.454, the maximum velocity is _____ m/s

Explanation / Answer

spring constant k = 3.75 N/m compressed distance x = 8.00 cm = 8.00 * 10^-2 m when m1 = 0.250 kg then m1 * a = k * x or a = (k * x/m1) where a is acceleration speed of the block when u_k has some value is v^2 - u^2 = 2u_k * a * x Here,u = 0 or v = (2u_k * a * x)^1/2 similarly when m2 = 0.490 kg then a1 = (k * x/m2) speed of block m2 when u_k has some value is v1 = (2u_k * a1 * x)^1/2

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