A light spring with force constant 3.70 N/m is compressed by 7.60 cm as it is he

Question

A light spring with force constant 3.70 N/m is compressed by 7.60 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) ? = 0.080 heavier block ? m/s2 lighter block ? m/s2 (c) ? = 0.148 heavier block 0 m/s2 lighter block 0 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 = (3.7Newtons/meter)(0.076meters) = 0.2812 Newtons The frictional force on the left block = (9.8 Newtons/kg)(0.225kg)K = 2.205 K Newtons The frictional force on the right block = (9.8 Newtons/kg)(0.450kg)K = 4.41 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 = (0.2812 - 2.205 K) / 0.225 For the right block, acceleration = (0.2812 - 4.41 K) / 0.450 Lets plug in the 3 different Ks k = 0, left block acc. = 1.25 m/s^2, right block acc. = 0.624 m/s^2 k = 0.080, left block acc. = 0.4657 m/s^2, right block acc. = 0.0 m/s^2 (i.e -0.159111) k = 0.148, left block acc. = 0.0 m/s^2 (i.e -0.2006) , right block acc. = 0.0 m/s^2 9 (i.e -0.82551)

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