Question

What is the maximum height a 100-w engine can lift a 100-kg man in 3.00 minutes?

Answer 1

18.4 m

Step-by-step explanation:

The force that the engine must apply at least to lift the man must be equal to the weight of the man:

`F=mg=(100 kg)(9.8 m/s^2)=980 N`

The work done by the engine is the product of the force applied, F, and the height at which the man is lifted, h:

`W=Fh` (1)

while the power of the engine is defined as:

`P=(W)/(t)`

where

P = 100 W

t = 3.00 min = 180 s

From this equation, we find the work:

`W=Pt=(100 W)(180 s)=18,000 J`

And solving (1) for h, we find the maximum height:

`h=(W)/(F)=(18,000 J)/(980 N)=18.4 m`