A light spring with force constant 3.10 N/m is compressed by 7.40 cm as it is he

Question

A light spring with force constant 3.10 N/m is compressed by 7.40 cm as it is held between 0.400-kg block on the left and a 0.800-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, 0.033, and 0.395. (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. If the block does not move, enter 0.)

(a)     = 0

(b)     = 0.033

(c)     = 0.395

Explanation / Answer

The spring exerts on each block an outward force of magnitude

|Fs| = kx = 3.10 * 0.074 = 0.2294 N

assume +x direction to the right . For the light block on the left, the vertical forces are given by

Fg = mg = 0.400 * 9.8 = 3.92 N

N = mg = 3.92 N

for heavier block

N = mg = 0.800 * 9.8 = 7.84 N

part a )

for the block on the left

sum of Fx = max = -0.2294 = (0.400)a

a = -0.5735 m/s^2

for heavier block

0.2292 = 0.800a

a = 0.28675 m/s^2

part b )

for the block on the left f = mu*N = 0.033 * 3.92 = 0.12936 N

sum of all force in x direction = max

-0.2292 + 0.12936 = (0.400)a

a = -0.2496 m/s^2

for heavier block f = mu*N = 0.25872 N

the maximum force of static friction would be larger , so no motion would begin

a = 0

part c )

f = mu.N = 0.395 * 0.400 * 9.8 = 1.5484 N

static friction is larger than spring force so block would not move

a = 0

for heavier block a = 0

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