A wooden block with mass 1.70 k g is placed against a compressed spring at the b

Question

A wooden block with mass 1.70kg  is placed against a compressed spring at the bottom of a slope inclined at an angle of 32.0? (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 6.70m  up the incline from A, the block is moving up the incline at a speed of 6.20m/s  and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is ?k = 0.40. The mass of the spring is negligible.

Part A) Calculate the amount of potential energy that was initially stored in the spring.

Explanation / Answer

net eork done = change in kinetic energy

Woekdone by spring = 0.5*k*x^2 = U1(initial potential energy)

work done by gravity Wg = -m*g*sin(32)*6.7 = -59.15 J

workdone by friction, wf = -mue*m*g*cos(32)*6.7 = 0.4*1.7*9.8*32 = -37.86 J


U1 + Wg + Wf = 0.5*m*v2^2 - 0.5*m*v1^2

U1 -59.15 - 37.86 = 0.5*1.7*6.2^2 - 0

U1 = 32.674+59.15+37.86 = 129.684 J

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