3. Work Suppose that you are gathering water from a well that is 10 meters deep

Question

3. Work Suppose that you are gathering water from a well that is 10 meters deep by pulling a rope attached to a bucket of water. To lift the bucket, we need to oppose the force due to gravity. For simplicity, let’s approximate g= 10 m/s2and assume the mass of the rope is negligible.

(a) Suppose that the mass of the bucket of water is constant , m= 40 kg. Find the work required to lift the bucket of water out of the well.

(b) Suppose the bucket has mass m(y) when it is at height y with y= 0 representing the bottom of the well and y= 10, the top. Express the work required to lift the bucket out of the well in terms of m(y).

(c) Suppose that the bucket has the same initial mass m(0) = 40 kg, but is continuously leaking so that its mass is reduced by a constant rate of 3 kg for every meter it is raised. Also, assume that the mass of the rope is 1 kg. Find the work required to lift the leaky bucket out of the well.

(d) Calculate the average force on the bucket in part (c).

Explanation / Answer

Work = (force)(distance)

If you are lifting a load, the force = weight = mg, and the distance = lifting height.

Work = (weight)(height)=(mg)h

An easy way to deal with the rope weight is to treat it as a concentrated load located at the center of gravity of the rope (i.e. at 25 m depth).

mrope=(0.2kgm)(50m)=10kg

So the total work done is:

(mgh)water+(mgh)rope=(20)(9.81)(40)+(10)(9.81)(25)

=12300Nm

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