A 1.26-kg block is held in place against the spring by a 26-N horizontal externa

Question

A 1.26-kg block is held in place against the spring by a 26-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= 1.6 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 0.26. 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:

a)7.0 cm b) 9.8cm c)8.4cm d)4.2cm e)5.6cm

Explanation / Answer

m = mass of block = 1.26 kg

F = external force = 26 N

x = compression of spring =

k = spring constant

v1 = speed after saperation from spring = 1.2 m/s

using conservation of energy

spring potential energy = kinetic energy

(0.5) k x2 = (0.5) m v12

k x2 = 1.26 (1.2)2

k x2 = 1.8144

k = 1.8144 / x2     eq-1

also , spring force = F

kx = 26

(1.8144 / x2) x = 26

x = 0.0698

x = 7 cm

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