15) A 0.92-kg block is held in place against the spring by a 53-N horizontal ext

Question

15) A 0.92-kg block is held in place against the spring by a 53-N horizontal external force. The external force is removed, and the block is projected with a velocity v1-1.2m/s when it separates from the spring, as shown in the figure. The block descends a ramp and has a velocity v2 = 1.9 m/s at the bottom of the ramp. 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 between the block and the rough surface is 0.25. The block moves on to D, where it stops. By how many centimeters was the spring initially compressed? Vi Smooth B Rough A) 6.3 cm B) 1.3 cm C) 3.8 cm D) 2.5 cm E) 5.0 cm

Explanation / Answer

given

m = 0.92 kg

kx = 53 N

V1 = 1.2 m/sec

V2 = 1.9 m/sec

but using kx = 53 N

we have equilibrium

1/2 k x2 = 1/2 m V12

k x2 = m V12

kx ( x ) = m V12

53 x = 0.92 X 1.22

x = 0.92 X 1.22 / 53

x = 0.024996 m

or

x = 2.4996 cm

so x = 2.5 cm ( rounded off value )

Option D is correct

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