A light spring with force constant 3.40 N/m is compressed by 7.80 cm as it is he

Question

A light spring with force constant 3.40 N/m is compressed by 7.80 cm as it is held between a 0.350-kg block on the left and a 0.700-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, 0.051, and 0.413. (Let the coordinate system be positive t 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. If the block does not move, enter 0.) mu = 0 heavier block lighter block mu = 0.051 heavier block lighter block mu = 0.413 heavier block lighter block

Explanation / Answer

The spring exerts on each block an outward force of magnitude

|Fs| = kx = 3.4 x 0.078 = 0.2652 N

for the light block on the left , the vertical force

Fg = mg = 0.350 * 9.8 = 3.43 N

and sum of all force in y direction = Fy = 0

N - 3.43 N = 0

N = 3.43 N

for heavier block

N = mg = 6.86 N

part a )

for the block on the left

Fx = max

-0.2652N = 0.350a

a = -0.7577 m/s^2

for heavier block

0.2652 = 0.7 *a

a = +0.378857 m/s^2

part b )

for the block on the left fk = mu_k*N = 0.051 * 3.43 = 0.17493 N

Fx = ma

-0.2652 + 0.17493 = 0.350* a

a = -0.2579

for heavier block on the right

fk = mu_k*N = 0.051*6.86 = 0.34986 N , The maximum force of static friction would be larger,so there is no motion

a = 0

part c )

for lighter block on left

fk = mu*N = 0.413 * 3.43 = 1.41659

The maximum force of static friction would be larger so no motion

a = 0 m/s^2

for heavier block

a = 0 m/s^2

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