A powered winch pulls a 75.5-kg box up a frictionless ramp of height h = 5.35 m

Question

A powered winch pulls a

75.5-kg

box up a frictionless ramp of height

h = 5.35 m

by a cable as shown in the figure below. The ramp rises at an angle

? = 26.0

A powered winch pulls a 75.5-kg box up a frictionless ramp of height h = 5.35 m by a cable as shown in the figure below. The ramp rises at an angle ? = 26.0° above the horizontal. The box, starting from rest at the bottom, steadily accelerates at 1.80 m/s2 to a final speed of 6.63 m/s at the top. (a) the average power P delivered by the winch (via the cable's tension) to the box while being pulled up the ramp (b) the instantaneous power P delivered by the winch to the box at the top of the ramp

Explanation / Answer

T - mgsin theta = ma

T = mg sin theta + ma

T = 75.5x 9.8 x sin 26 + 75.5 x 1.8

T = 460.25 N

instantaneous power = force x velocity = 460.25 x 6.63 = 3051.46 W

time taken to rise up

v = at

t = 6.63 / 1.8

t = 3.68 s

total energy imparted to the block = Potential energy = mgh = 75.5 x 9.8 x 5.35 = 3958.46 J

time taken = 3.68 s

Average power = Energy / time = 3958.46/3.68 = 1075.66 W

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