Question

A crane lifts a mass m to the 10th floor of a building in a certain time. It then raises the same mass to the 20th floor of the same building in double the time. How much more energy and power are required? Assume that the height of all floors is equal.

Answer 1

Let h0 be the height of each level, and t be the time it takes to get to the 10th floor.

Energy:

Energy to reach the 10th floor, E₁ = mg × (10h₀)

Energy to reach the 20th floor, E₂ = mg × (20h₀)

`(E_2)/(E_1) = (20h_0)/(10h_0) = 2`

So, E₂ = 2E₁

As a result, the amount of energy needed is doubled.

Power:

Power to reach the 10th floor, `P_1 = (E_1)/t = (mg xx 10h_0)/t`

Power to reach the 20th floor (in double the time, 2t),

`P_2 = (E_2)/(2t)`

= `(mg xx 20h_0)/(2t) = (mg xx 10h_0)/t`

So, P₂ = P₁

As a result, the same amount of electricity is needed in both situations (no additional power is needed).

Therefore, it takes twice as much energy but the same amount of power to lift the mass to the 20th floor.