Finding the Weight of a Rope and Bucket

In summary, the question asks for the work done in raising a bucket of water, weighted 20 kg, attached to one end of a 5 meter rope hanging over the edge of a well. The rope has a uniform density of 1 kg/m and the force needed to raise the bucket can be found using the equation W=\int F(x)xdx. The work done is equal to the change in potential energy, which can be calculated using the equation change in PE = work done. Using calculus, the work done can be expressed as the integral from 0 to 5 of (\rho y + 20)(5-y)dy, where y represents the change in height of the bucket.
  • #1
glennpagano
17
0

Homework Statement



A rope is 5 meters long and hangs over the edge of a well. It has a bucket of water weighted 20 kilograms attached to one end. For Simplicity, use g=10N/kg

Suppose the rope has a uniform density of [tex]\rho[/tex] = 1kg/m

Homework Equations



W=[tex]\int[/tex] F(x)xdx


The Attempt at a Solution



I could not figure out what the force would be I would think it would be (Mrope+Mbucket)g
Mass of the rope would be ([tex]\rho[/tex])(v)=Mrope
 
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  • #2
Welcome to PF!

Welcome to PF! :smile:

(have a rho: ρ and an integral: ∫ :wink:)

Does the question ask for the work done in raising the bucket 5 m ?

If so, remember that the rope doesn't rise 5 m … it stops as it gets to the top.

Use work done = change in PE. :wink:
 
  • #3
I know I can do change in PE but this is for my calculus and my teacher wants me to use calculus I did some more work and found this so far. F(y)=(Mrope+Mbucket) Mrope=[tex]\rho[/tex]v. Now I have to find change in y for that I got (5-y) Now my equation for work is the integral from 0 to 5 of ([tex]\rho[/tex]y+20)(5-y)
 

FAQ: Finding the Weight of a Rope and Bucket

How do you find the weight of a rope and bucket?

To find the weight of a rope and bucket, you will need a scale. First, weigh the empty bucket on the scale. Then, tie the rope to the bucket and hang it on the scale. The weight shown on the scale will be the weight of the rope and bucket combined.

Can I use any type of scale to find the weight of a rope and bucket?

Ideally, you should use a scale that can accurately measure small weights, such as a kitchen scale. A bathroom scale may not be precise enough for this task.

Do I need to account for the weight of the rope itself?

Yes, the weight of the rope must be included in the final weight measurement. The rope is part of the overall weight of the rope and bucket.

How can I ensure an accurate measurement?

To ensure an accurate measurement, make sure the scale is properly calibrated and that the rope and bucket are securely attached to the scale. Double check that the scale is reading zero before adding the rope and bucket.

Is there a formula for finding the weight of a rope and bucket?

The formula for finding the weight of a rope and bucket is simply the weight of the empty bucket plus the weight shown on the scale with the rope and bucket attached. There is no need for a complex formula or calculations.

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