a 25 lb block has an initial speed of vo=10ft/s when it is midway between springs A and B. After striking spring B, it rebounds and slides across the horizontal plane toward spring A, etc. If the coefficient of kinetic friction between the plane and the block is mew k= 0.4, determine the distnace traveled by the block before it comes to rest.

Question

a 25 lb block has an initial speed of vo=10ft/s when it is midway between springs A and B.  After striking spring B, it rebounds and slides across the horizontal plane toward spring A, etc.  If the coefficient of kinetic friction between the plane and the block is mew k= 0.4, determine the distnace traveled by the block before it comes to rest. 
ka=10lb/in and kb=60lb/in?

drwls · Answer

Forget the springs. The block stops sliding when the total distance travelled is X such that

friction work done = (Kinetic friction force) * X = Initial K.E.

The kinetic friction force is 0.4*25 = 10 lbf

The initial kinetic energy is
(1/2)(W/g)V^2 = 38.8 ft lb.
(Note than I had to convert the weight to mass in slugs by dividing by g)

X = 38.8 ft-lb/10 lb = 3.88 feet