A light spring of force constant 3.95 N/m is compressed by 8.00 cm and held betw

Question

A light spring of force constant 3.95 N/m is compressed by 8.00 cm and held between a 0.250 kg block on the left and a 0.420 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.
0.000 ___________m/s ____________m/s
0.100 ___________m/s ____________m/s
0.488 ___________m/s ____________m/s

Explanation / Answer

the spring constant of the spring is k = 3.95 N/m

the spring is compressed by d = 8.00 cm = 8.00 x 10^-2 m

the mass of the two blocks are m1 = 0.250 kg and m2 = 0.420 kg

let v1 and v2 be the speed of the blocks

we know that

(1/2)m1v1^2 = (1/2)kd^2

or v1^2 = (k/m1) x d^2

or v1 = (k/m1)^1/2 x d

similarly,

v2 = (k/m2) x d

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