A light spring with force constant 3. 75 N/m is compressed by 8. 32 cm as it is

Question

A light spring with force constant 3. 75 N/m is compressed by 8. 32 cm as it is held between a 0. 251 kg block on the left and a 0. 502 kg block on the right, both resting on a horizontal surface. The spring exerts a force on each block, tending to push them 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 the following values. (Let the coordinate system be positive to the right and negative to the left. Be sure to include the sign to indicate the direction of the acceleration. ) mu = 0 heavier block lighter block mu = 0. 070 heavier block lighter block mu = 0. 147 heavier block lighter block

Explanation / Answer

Spring force on each block=3.75*0.00832=0.0312N

Let heavier block be M and lighter block be m.

a)a=F/M=0.0312/0.502=0.0622m/s2

a=F/m=0.0312/0.251=0.1243m/s2

b)Spring force on heavier block=0.0312

Maximum friction=Mg=0.344N

Since maximmum fricition>spring force, heavier block remains stationary.

a=0

For lighter block,

Maximum friction=mg=0.172N,

Since maximmum fricition>spring force, lighter block remains stationary.

a=0.

c)From b) it is clear that both blocks will be stationary since friction will be even greater here.

a=0

a=0

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