In Figure 1 , an engine that delivers power P is attached to a pulley that lifts a box of mass m0 a vertical distance of y0 at a constant speed in time t0 . If, as shown in Figure 2 the engine again delivers power P , how long would it take the engine to raise a box of mass 3m0 the same vertical distance y0 at a constant speed? Options:
1/3 t0
t0
root(3 t0
3t0
9t0

t = 3 t₀

Explanation:

The formula for the power delivered by the engine can be given in terms of the change in the potential energy of the box as follows:

P = P.E/t = mgy/t

where,

P = Power delivered by the engine

m = mass of box lifted = m₀

g = acceleration due to gravity

y = vertical distance or height box covered = y₀

t = time taken = t₀

Therefore,

P = m₀gy₀/t₀

t₀ = m₀gy₀/P   equation (1)

Now, if we change the mass of box as:

m = 3m₀

y = y₀ (constant)

P = Constant

Then,

P = 3m₀gy₀/t

t = 3m₀gy₀/P

using equation (1):

t = 3 t₀

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explanation: