Question

3. You raise a bucket of water from the bottom of a deep well. If your power output is 100 W, and the mass of the bucket and the water in it is 4.00 kg, with what speed can you raise the bucket? Ignore the weight of the rope.

Answer 1

Answer:

2.55 m/s

Explanation:

The power output can be rewritten as:

$P=Fv$ (1)

where

F is the force applied

v is the speed at which the bucket is raised

If we want to raise the bucket at constant speed, we must apply a force equal and opposite to the weight of the bucket, which is equal to the product between its mass (4.00 kg) and the gravitational acceleration (9.8 m/s^2):

$F=mg=(4.00 kg)(9.8 m/s^2)=39.2 N$

We know that the power output is P = 100 W, so we can re-arrange eq.(1) to find the speed:

$v=\frac{P}{F}=\frac{100 W}{39.2 N}=2.55 m/s$