A tank in the shape of an inverted right circular cone has height 5 meters and radius 3 meters. It is filled with 3 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is 1100kg/m^3 Your answer must include the correct units
2 answers
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When h=3, r = 9/5 so the volume of liquid is
1/3 πr^2 h = 1/3 π (9/5)^2 * 3 = 81π/25 m^3
so the weight is 1100 * 9.81 * 81π/25 N
The center of gravity of the liquid is at height 3/4, so the weight must be lifted through a height of 4.25 m
That makes the work 1100 * 9.81 * 81π/25 * 4.25 = 466,816 J
If no one comes by while I'm away, to post the calculus way to solve this, I'll take care of that later. But just think of the work involved in lifting a disc of thickness dh through a distance of 5-h.
1/3 πr^2 h = 1/3 π (9/5)^2 * 3 = 81π/25 m^3
so the weight is 1100 * 9.81 * 81π/25 N
The center of gravity of the liquid is at height 3/4, so the weight must be lifted through a height of 4.25 m
That makes the work 1100 * 9.81 * 81π/25 * 4.25 = 466,816 J
If no one comes by while I'm away, to post the calculus way to solve this, I'll take care of that later. But just think of the work involved in lifting a disc of thickness dh through a distance of 5-h.
1 answer