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

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation: