A 1.35-kg block held in place against the spring by a 60-N horizontal external f

Question

A 1.35-kg block held in place against the spring by a 60-N horizontal external force as shown below. The external force is removed, and the Mock U projected with a velocity V_1 = 1.5 m/s upon separation from the spring. The block descends a ramp and has a velocity V_2 = 2.1 m/s at the bottom. Although the track is frictionless between points A and B, the block enters a rough section after B, where coefficient of Kinetic friction is 0.39. The block moves on to D, where it stops. Find the spring constant k of the spring and the length S of the rough section. Each to at least two significant figures.

Explanation / Answer

when the spring is relaxed and the block is detached, the potential energy in the spring

is transferred to the block.

if compression of the spring is x,

then k*x=60..(1)

potential energy stored=0.5*k*x^2

kinetic energy of the block in the beginning=0.5*1.35*1.5^2=1.51875 J

==> 0.5*k*x^2=1.51875..(2)

dividing equation 2 by equation 1,

0.5*x=0.0253==>x=0.050625

==>k=60/x=1185.18 N/m

part b:

friction force=friction coefficient*normal force=0.39*1.35*9.8=5.1597 N

then if the box is stopped after distance s,

then work done against friction=kinetic energy of the box at the point B

==>5.1597*s=0.5*1.35*2.1^2

==>s=0.58 m

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