A light spring of force constant 4.00 N/m is compressed by 8.00 cm and held betw

Question

A light spring of force constant 4.00 N/m is compressed by 8.00 cm and held between a 0.250 kg block on the left and a 0.540 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.

Explanation / Answer

given:
spring of force constant = 4 N/m
compression = 8.00 cm
masess of the blocks = 0.250 kg and 0.540 kg
Force acting on the 0.540 kg
is the spring force kx = 4*0.08 = 0.036 N.
The maximum kinetic frictional force on this mass is
-*mg = -0.1*0.54*9.8
= - 0.5292 N.
The static frictional force is still greater than this.
The spring force (0.036) is less than this value.
Hence the mass will not move and is at rest always.
Since the mass 0.54 at the right is at rest,
All the stored energy of the spring is used to give kinetic energy to the mass 0.250 kg
kx² = mu²
u = x * (k/m) = x * (k/m) = - 0.8* (4/0.25) = - 3.2 m/s
Minus to indicate that it moves toward left side.

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