A light spring with force constant 3.40 N/m is compressed by 7.40 cm as it is he

Question

A light spring with force constant 3.40 N/m is compressed by 7.40 cm as it is held between a 0.300-kg block on the left and a 0.600-kg block on the right, both resting on a horizontal surface. The spring exerts a force on each block, tending to push the blocks apart. The blocks are simultaneously released from rest. Find the acceleration with which each block starts to move, given that the coefficient of kinetic friction between each block and the surface is 0, 0.060, and 0.422. (Let the coordinate system be positive to the right and negative to the left. Indicate the direction with the sign of your answer. Assume that the coefficient of static friction is the same as the coefficient of kinetic friction.)

(a)    ? = 0

(b)    ? = 0.060

(c)    ? = 0.422

Explanation / Answer

a) for heavier block
kx = ma
a = kx/m = 3.4*7.4E-2/0.6=0.419 m/s^2

for lighter block, a = 3.4*7.4E-2/0.3 = 0.839 m/s^2

b) now u = 0.06

so

kx - friction = ma

so for heavier block
3.4*7.4E-2 - 0.06*0.6*9.81 = 0.6*a
a=-0.169 but this makes no sense so this means a = 0

for lighter block

3.4*7.4E-2 - 0.06*0.3*9.81 = 0.3*a
a=0.25 m/s^2

c) now u = 0.422

heavier block will still be a = 0

light block
3.4*7.4E-2 - 0.422*0.3*9.81 = 0.3*a
a=-3.3 which makes no sense
so a = 0

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