The pair of blocks, which are connected by a cord, are released from rest when the spring is unstretched. The static and kinetic coefficients of friction are .2 and .1, respectively.
The following things are to be found using the work-energy methods:
1) Maximum Velocity of the blocks
2) Stretch of the spring at the maximum velocity of the blocks
3) Maximum displacement of the blocks during motion
4) Will the blocks rebound from the position of part 3?
Please see the attached file for the diagram.
mass of the block kept on the horizontal table m1 = 10 lb
mass of the hanging block m2 = 5 lb
coeff. static friction mu_s = 0.2
coeff. of kinetic friction mu_k = 0.1
spring constant K = 20 lb/ft = 20*32 = 640 lb.(ft/s^2)/ft
g = 32 ft/s^2
1 & 2.) Let us assume the velocity of the blocks be v at x stretching of the spring.
Hence, by energy law,
work done against friction force + K.E. + spring energy = decrease in P.E. of the hanging block
=> mu_k*m1*g*x + ...
This solution is provided in 353 words. It uses step-by-step calculations to solve each problem using energy and Newton's law.