A light spring with force constant 3.90 N/m is compressed by 7.44 cm as it is he

Question

A light spring with force constant 3.90 N/m is compressed by 7.44 cm as it is held between a 0.225 kg block on the left and a 0.450 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.)

(a) ? = 0
heavier block? m/s2
lighter block ? m/s2

(b) ? = 0.070
heavier block ? m/s2
lighter block ? m/s2

(c) ? = 0.152
heavier block ?m/s2
lighter block ?m/s2

Explanation / Answer

(A)

A(heavier block) =3.9*0.0744/0.45 = 0.6448 m/s^2

A(lighter block) = 3.9*0.0744/0.225 =1.2896 m/s^2

(B)

A(heavier block) =(3.9*0.0744-0.45*9.8*0.07)/0.45 = -0.042 m/s^2

As acceleration cannot be negative

A(heavier block) =0 m/s^2

A(lighter block) = (3.9*0.0744-0.225*9.8*0.07)/0.225 =0.6036 m/s^2

(C)

A(heavier block) =(3.9*0.0744-0.45*9.8*0.152)/0.45 = -0.8448 m/s^2

As acceleration cannot be negative

A(heavier block) =0 m/s^2

A(lighter block) = (3.9*0.0744-0.225*9.8*0.152)/0.225 =-0.2 m/s^2

As acceleration cannot be negative

A(lighter block) =0 m/s^2

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