October 1st, 2012, 03:35 AM  #1 
Member Joined: Oct 2012 Posts: 30 Thanks: 0  work
a) A tank (as shown in the diagram) is full of water. Find the work required to pump the water out of the spout. The density of water is 1000kg/m3. b) suppose that for the tank of part a, the pump breaks down after 4.7*10^5 J of work has been done. what is the depth of the water remaining in the tank? i have done part a but i have no idea how to do part b. Can anyone help with detail? Thanks a lot. 
October 1st, 2012, 10:47 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: work
You want to solve: for (taking the root ). 
October 1st, 2012, 02:48 PM  #3 
Member Joined: Oct 2012 Posts: 30 Thanks: 0  Re: work
can i ask where is the 5xx^2 come from?

October 1st, 2012, 03:05 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: work
I figured that would be familiar to you since you solved the first part of the problem...how did you solve the first part?

October 1st, 2012, 07:51 PM  #5 
Member Joined: Oct 2012 Posts: 30 Thanks: 0  Re: work
first use the Mass=density * volume F=mg displacement= (2+x) work = integrate from 0 to 3 [78400(3x)(2+x)] dx that's my equation 
October 1st, 2012, 08:13 PM  #6 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 614 Thanks: 83 Math Focus: Electrical Engineering Applications  Re: work
Leaving units out which is not a good idea, but at and at so where is the height from the bottom of the trough. integrate: 
October 1st, 2012, 08:15 PM  #7 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 614 Thanks: 83 Math Focus: Electrical Engineering Applications  Re: work
Darn it, hit submit instead of preview. But you should get the idea. One other thing, shouldn't the right side of the equation for part b) be the total work minus 470000? 
October 1st, 2012, 08:18 PM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: work
@summychan: Okay, your equation is just as valid, we just set it up differently. I let be the depth of the water, while you let be the distance the depth has decreased. Your approach is better for part b) as your integration moves from the top down, while mine moves from the bottom up, so you actually want to solve: for , where . 
October 1st, 2012, 08:28 PM  #9 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 614 Thanks: 83 Math Focus: Electrical Engineering Applications  Re: work
Just to check answers, using g = 9.8 m/s^2, I get a) = 1058400 J b) = 2.02856 m Are these the same results that you get? 
October 1st, 2012, 08:33 PM  #10 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: work
Yes, I get the same results.


Tags 
work 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
when work be  and +  rsoy  Physics  1  October 11th, 2013 06:50 AM 
I can't work this out... please someone help?  dsbcourtney  Advanced Statistics  3  July 20th, 2013 04:22 PM 
can someone work this out  Kinroh  Algebra  9  May 7th, 2013 11:32 AM 
No work.  mathbalarka  Number Theory  2  June 16th, 2012 02:53 PM 
I can't work this out... please someone help?  dsbcourtney  Real Analysis  2  December 31st, 1969 04:00 PM 