A 1.06-kg block is held in place against the spring by a 13-N horizontal externa

Question

A 1.06-kg block is held in place against the spring by a 13-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v 1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v 2= 1.7 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.21. The velocity of the block is v 3 = 1.4 m/s at C. The block moves on to D, where it stops. The initial compression of the spring is closest to: 14 cm. 12 cm. 17 cm. 7.2 cm. 9.6 cm.

Explanation / Answer

equating force we have

kx =13N

and by energy conservation we have 0.5kx2= 0.5mv2

v=1.2, m=1.06kg

0.5kx*x =0.5 *1.06*1.22

0.5*13*x=0.5*1.06*1.2*1.2

we get x=0.117m

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