A 1.73-kg block is held in place against the spring by a 76-N horizontal externa

Question

A 1.73-kg block is held in place against the spring by a 76-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 = 1.5 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 0.37. The velocity of the block is v_3 = 1.4 m/s at C. The block moves on to D, where it stops. The height h of the ramp is closest to

Explanation / Answer

from the conservation of energy

(1/2) kx2   =   (1/2) mv2

from the hooks law

k =F/x

so,

(F/x) x2 = m v2

x = mv^2/ F = 1.73(1.2)^2/76

=0.032m

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