A light spring with force constant 3.75 N/m is compressed by 7.40 cm as it is he

Question

A light spring with force constant 3.75 N/m is compressed by 7.40 cm as it is held between a 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, 0.045, and 0.407. (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.)

Explanation / Answer

The spring exerts on each block an outward force of magnitude

Fs = kx

k = spring constant = 3.75 N/m

x = 7.4 cm = 0.074 m

Fs = 0.2775 N

assume postive in right direction

for lighter block force in y direction

n = mg

n = 0.400 * 9.8 = 3.92 N

for heavier block

n = 7.84 N

part a )

for the block on the left

Fs = m*ax

-0.2775 = 0.400 * ax

ax = -0.69 m/s^2

for heavier block

+0.2775 = 0.800 * ax

ax = 0.347 m/s^2 = 0.35 m/s^2

part b )

mu = 0.045

for lighter block

friction force = f= mu*n = 0.045 * 3.92 N = 0.1764 N

for lighter block

-0.2775 + 0.1764 = 0.400 * ax

ax = -0.25 m/s^2

for heavier block

friction force = f = 0.045 * 7.84 = 0.3528 N

this is more than spring force so there is no motion

ax = 0

part c )

mu = 0.407

f = 0.407 * 3.92 = 1.59 N

static friction is more than spring force so there is no motion

ax = 0

for haevier block

f = 0.407 * 7.84 = 3.19 N

static friction is more than spring force so there will be no motion

ax = 0 m/s^2

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