Question

a 1kg block collides with horizontal lite string block compresses the spring 4m from the rest position what is the speed of blivk at the instant of collision

Answer 1

A 1.0kg1.0kg block collides with a horizontal weightless spring of spring constant 2.0N/m2.0N/m. The block compresses the spring 4.0m4.0mfrom the rest position.Assuming that the coefficient of kinetic friction between the block and horizontal surface of 0.25,0.25, what was the speed of the block at the instant of collision



a)7.18m/sb)6.23m/sc)5.21m/sd)4.52m/sa)7.18m/sb)6.23m/sc)5.21m/sd)4.52m/s



A)

 

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Let ′v′′v′ be the velocity of block at the time of collision.

KEKE of block=(Elastic energy store in spring )+ energy spent in doing work against friction

1212mv2=12mv2=12kx2+μkmgxkx2+μkmgx

1212×1×v2=12×1×v2=12×2×42+(.25)×1×9.8×4×2×42+(.25)×1×9.8×4

1212v2=16+9.8v2=16+9.8

v2=2×25.8v2=2×25.8

v=7.18m/sv=7.18m/s

Hence  a is the correct answer.