This is about 2 to 3 times the wattage of typical household light bulbs(60-100W)

Question

This is about 2 to 3 times the wattage of typical household light bulbs(60-100W) Assume that there are no non-conservative forces on the rock, and so its mechanical energy is conserved. Subscript 1 represents the rock as it leaves the volcano and subscript 2 represents the rock at it highest point. The location as the rock leaves the volcano is the zero location for PE (y = 0) we have y = 0 y = 500m and V = 0 solve for V? The power output is the energy transferred to the launched rocks per unit time. The launching energy of a single rock is 1/2 MV And so the energy of 1000 rock is 1000(l/2MV) Divide this energy by the time it takes to launch 1000 rocks find the power output needed to launch the rocks?

Explanation / Answer

using law of conservation of energy

Total energy at the leaving point = total energy at the heighest point

0.5*m*v1^2 = m*g*h

m cancels

v1 = sqrt(2*g*h) = sqrt(2*9.8*500) = 99 m/sec

b) time of ascent is t = V1/g = 99/9.8 = 10.1 sec

then

power output is P = energy / time taken = 1000*0.5*M*99/10.1 = 4900*M

M is the mass of the rock

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