The 30- lb block has an initial speed of vo = 12 ft/s when it is midway between

Question

The 30- lb block has an initial speed of vo = 12 ft/s when it is midway between springs A

and B. After striking spring A (kA = 440 lb/ft), it rebounds and slides across the horizontal plane

and strikes spring B and then, rebounds and stops midway (i.e., back to the initial position).

Determine the total distance traveled by the block until it stops at the final position and the

stiffness kB of the spring B. The coefficient of kinetic friction between the plane and the block is

mk = 0.26. Neglect the size of the block.

The 30- lb block has an initial speed of vo = 12 ft/s when it is midway between springs A and B. After striking spring A (kA = 440 lb/ft), it rebounds and slides across the horizontal plane and strikes spring B and then, rebounds and stops midway (i.e., back to the initial position). Determine the total distance traveled by the block until it stops at the final position and the stiffness kB of the spring B. The coefficient of kinetic friction between the plane and the block is mk = 0.26. Neglect the size of the block

Explanation / Answer

accn due to friction=-mug=0.26*32ft/s2

final velocity before hitting Ka V=sqrt(3.66^2-2*2.55*1.7*0.3)=10.75ft/s

maximum compression of Ka,0.5m*v^2=.5*kax^2+mu*mg*x; so, x=2.29

final velocity while leaving V2=sqrt(V^2-mu*g*2x); V2=2.54 m/s

net distance travelled for it to stop completely after release from ka=1.26m=4.13ft

data seems to be wrong it not doing the same

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