Calculating Work on a Bucket Hanging in a Well

[mjjaques]

Homework Statement

An old oaken bucket of mass 6.75 kg hangs in a well at the end of a rope. The rope passes over a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to raise the bucket slowly a distance of 4.00 m. (a) How much work do you do on the bucket in pulling it up? (b) How much work does gravity do on the bucket? (c) What is the total work on the bucket?

m=6.75 kg, s=4.00 m

Homework Equations

F=ma, W=Fs

The Attempt at a Solution

I know that this should be easy, right? It's just one-dimensional movement... but how do I know what the force of tension is? I drew a free body diagram for the bucket - the only forces are F_G and F_T, but I only know that F_T is greater than F_G (if it's accelerating upward). I don't know how to actually find the force of tension acting on the bucket.

 

[gneill]

Is the bucket accelerating if it's being "raised slowly"? I think that you can presume a constant speed over the 4.00 m.

 

[mjjaques]

So, if F_T=mg then, wouldn't the answer to part (a) be (6.75 kg)(9.8 m/s²)(4.00 m) = 264.6 J? But that would make the total work equal zero, with gravity doing -264.6 J. The back of the book says the answers are (a): 3.60 J, (b): -.900 J, (c): 2.70 J

 

[gneill]

Well, it's a mystery. 3.60 J is enough energy to raise a 6.75 kg bucket about 5.4 cm.

 

[rwisz]

To find the force of tension, you can use the equation F=ma, where F represents the force of tension, m is the mass of the bucket, and a is the acceleration. In this case, the acceleration is zero since the bucket is moving at a constant velocity. Therefore, the force of tension is equal to the force of gravity acting on the bucket, which is given by the equation FG=mg, where g is the acceleration due to gravity (9.8 m/s^2). Once you have determined the force of tension, you can use the equation W=Fs to calculate the work done on the bucket. Remember to use the displacement of 4.00 m as the distance (s) in this equation. To find the work done by gravity, you can use the equation W=Fs again, but this time the force (F) will be equal to the force of gravity (FG). Finally, to find the total work, you can simply add the work done by tension and the work done by gravity. I hope this helps!