A light spring of force constant 3.55 N/m is compressed by 8.00 cm and held betw

Question

A light spring of force constant 3.55 N/m is compressed by 8.00 cm and held between a 0.250 kg block on the left and a 0.600 kg block on the right. Both blocks are at rest on a horizontal surface. The blocks are released simultaneously so that the spring tends to push them apart. Find the maximum velocity each block attains if the coefficient of kinetic friction between each block and the surface is the following. In each case, assume that the coefficient of static friction is greater than the coefficient of kinetic friction. Let the positive direction point to the right.

Uk .250 kg block .600 kg block

0.00 ___________m/s _____________m/s

0.10 ___________m/s _____________m/s

0.40 ___________m/s _____________m/s

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 = (3.55 Newtons/meter)(0.08meters) = 0.284 Newtons

The frictional force on the left block = (9.8 Newtons/kg)(0.25kg)K = 2.45 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 = (0.284 - 2.45 K) /0.25

For the right block, acceleration = (0.284 - 5.88 K) /0.6

Lets plug in the 3 different Ks

k = 0, left block acc. = 1.136 m/s^2, right block acc. = 0.47 m/s^2
k = 0.1, left block acc. = 0.156 m/s^2, right block acc. = -0.51 m/s^2
k = 0.4, left block acc. = -2.784 m/s^2, right block acc. = -3.45 m/s^2

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