Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Work, Power and Energy
0 votes

We have a cable that weighs 2lbs/ft attached to a bucket filled with coal that weighs 800lbs.The bucket is initially at the bottom of a 500 ft mine shaft.Determine the amount of work required to lift the bucket to the midpoint of the shaft.

$\begin{array}{1 1}387500ft-lb\\287500ft-lb\\187500ft-lb\\587500ft-lb\end{array} $

Can you answer this question?

1 Answer

0 votes
Answer : 387500 ft-lb
Assume $x$ to be the amount of cable that has been pulled up.
So at the bottom of the shaft $x=0$, at the midpoint of the shaft $x=250$ and at the top of the shaft $x=500$
Also at any point in the shaft there is $500-x$ feet of cable still in the shaft.
The force then for any $x$ is then nothing more than the weight of the cable and bucket at that point.This is,
$F(x)=$ weight of cable +weight of bucket/coal
$W=\int\limits_0^{250} F(x) dx$
$\;\;\;\;=\int\limits_0^{250} 1800-2xdx$
answered Sep 1, 2014 by sreemathi.v
edited Sep 2, 2014 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App