A light spring with force constant 3.50 N/m is compressed by 7.80 cm as it is he

Question

A light spring with force constant 3.50 N/m is compressed by 7.80 cm as it is held between a 0.300-kg block on the left and a 0.600-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, 0.067, and 0.429. (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

heavier block m/s2

lighter block m/s2

(b) = 0.067

heavier block m/s2

lighter block m/s2

(c) = 0.429

heavier block m/s2

lighter block m/s2

Explanation / Answer

There are only two relevant forces acting on the blocks. The force exerted by the spring which is pushing them apart, and the frictional force which is opposing the spring force.

The kinetic coefficient of friction is K

The Spring force = (3.50Newtons/meter)(0.078meters) = 0.273 Newtons

The frictional force on the left block = (9.8 Newtons/kg)(0.30kg)K = 2.94 K Newtons

The frictional force on the right block = (9.8 Newtons/kg)(0.60kg)K = 5.88 K Newtons

The initial acceleration of each block is initial force/mass. Note that the spring force on each block must be greater than the frictional force, or the block wont accelerate (acc=0).

For the left block, acceleration = (0.273 - 2.94 K) / 0.30

For the right block, acceleration = (0.273 - 5.88 K) / 0.60

k = 0, left block acc. = 0.91 m/s^2, right block acc. = 0.455m/s^2
k = 0.067, left block acc. = 0.844 m/s^2, right block acc. = 0.201m/s^2
k = 0.429, left block acc. = 3.294 m/s^2, right block acc. = 0.0345 m/s^2

Calculation may be wrong but concept is right

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