Calculate how much work Wf in J the farmer does on the bucket of water (via the rope) to raise it to ground level.

Question

A farmer is using a rope and pulley to lift a bucket of water from the bottom of a well that is h_y = 12.5 m deep. The farmer uses a force F₁ = 48.5N to pull the bucket of water directly upwards. The total mass of the bucket of water is m_b a) Calculate how much work Wf in J the farmer does on the bucket of water (via the rope) to raise it to ground level.

b) Calculate how much work Wg in J gravity does on the bucket filled with water as the farmer lifts it up the well.

c) Calculate the net work W_net in J done on the bucket of water by the two forces F1 and Fg.

Answer 1

Before starting this question always remember that work is always conserved in isolated systems (Net work in isolated systems = 0 Joules):

a) To calculate the work done by the farmer, you will use the equation

W = F*d*cosθ

where F is the force exerted, d is the distance traveled by the object, and θ is the angle between the direction of the force and the direction the object travels in

Looking at the problem, we can see that the farmer exerts a force through the rope of 48.5 N upwards, so F = 48.5 N.

We can also see that the bucket travels upwards 12.5 m, so d = 12.5 m

Lastly, since both the force AND the distance are upwards, there is no angle between the two, so θ = 0º.

Now it's time to plug all these numbers in and calculate an answer:

W_f = F₁*d*cosθ = (48.5 N)*(12.5 m)*cos(0º)

W_f = 606.25 N*m

Since 1 Newton-meter is the same as 1 Joule, we get our final answer

W_f = 606.25 J

b) We don't know how heavy the bucket is, so we can't calculate this answer the same way. However, we can use the fact that energy is conserved to help us answer this question.

We can isolate the bucket by labeling all the forces acting on it: F₁ which is the force from the farmer, and F_g which is the force from gravity.

Since energy must be conserved (W_net = 0 J), we can add the work from both forces together to be 0 Joules.

W_net = 0 J

W_f + W_g = 0 J

Now let's plug in our answer from part a and solve for the work done by gravity:

(606.25 J) + W_g = 0 J

W_g = 0 - 606.25

W_g = -606.25 J

This might seem odd, but is correct! Forces can do negative work so long as the direction of the force and the direction of the distance moved are in opposite directions. And since gravity points down while the bucket moved up, gravity will do negative work!

c) By showing that this is an isolated system we have already proved that W_net = 0 J!