How could we solve for the peak height using conservation of energy? A small lea

Question

How could we solve for the peak height using conservation of energy?

A small lead ball, attached to a 1.5-m rope, is being whirled in a circle that lies in the vertical plane. The ball is whirled at a constant rate of three revolutions per second and is released on the upward part of the circular motion when it is 0.75 m above the ground. The ball travels straight upward. In the absence of air resistance, to what maximum height above the ground does the ball rise? Since the lead ball makes three complete revolutions of 9.42 m each second the speed is: The lead ball would travel upward at 28.26 m/s and come down at the rate of gravity -9.81 m/s2 Average travel at 14.13 m/s for 2.88 seconds makes a distance, d = 14.13 m/s * 2.88 sec = 40.69 m The total height is distance + 0.75 m = 40.69 m + 0.75 m = 41.44 m

Explanation / Answer

at peak height, velocity will be zero

so using conservation of energy

mgh + 1/2mv2 = mghp

hp = (gh + 0.5*v^2)/g

hp = (9.8*0.75 + 0.5*28.26^2)/9.8

hp = 406.66/9.8

hp = 41.496m

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