Question

A pail in a water well is hoisted by means of a frictionless winch, which consists of a spool and a hand crank. When Jill turns the winch at her fastest water-fetching rate, she can lift the pail the 26.0 m to the top in 12.0 s. Calculate the average power supplied by Jill's muscles during the upward ascent. Assume the pail of water when full has a mass of 6.50 kg. W

Answer 1

140.83 W

Step-by-step explanation:

From the question given above, the following data were obtained:

Height (h) = 26 m

Time (t) = 12 s

Mass (m) = 6.50 Kg

Power (P) =?

Power is simply defined as the rate at which energy is used up. Mathematically, it is expressed as:

Power (P) = Energy (E) / Time (t)

But:

Energy (E) = mass (m) × acceleration due to gravity (g) × height (h)

E = mgh

P = E/t

P = mgh / t

With the above formula i.e

P = mgh / t

We can obtain the power supplied by Jill's muscles as follow:

Height (h) = 26 m

Time (t) = 12 s

Mass (m) = 6.50 Kg

Acceleration due to gravity (g) = 10 m/s²

Power (P) =?

P = mgh / t

P = 6.5 × 10 × 26 / 12

P = 140.83 W

Therefore, the power supplied by Jill's muscles is 140.83 W