My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 1st, 2012, 04:35 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.
Attached Images
File Type: png k.png (143.4 KB, 1393 views)
summychan is offline  
 
October 1st, 2012, 11:47 AM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,208
Thanks: 516

Math Focus: Calculus/ODEs
Re: work

You want to solve:



for (taking the root ).
MarkFL is offline  
October 1st, 2012, 03:48 PM   #3
Member
 
Joined: Oct 2012

Posts: 30
Thanks: 0

Re: work

can i ask where is the 5x-x^2 come from?
summychan is offline  
October 1st, 2012, 04:05 PM   #4
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,208
Thanks: 516

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?
MarkFL is offline  
October 1st, 2012, 08:51 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(3-x)(2+x)] dx

that's my equation
summychan is offline  
October 1st, 2012, 09:13 PM   #6
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 628
Thanks: 92

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:
jks is offline  
October 1st, 2012, 09:15 PM   #7
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 628
Thanks: 92

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?
jks is offline  
October 1st, 2012, 09:18 PM   #8
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,208
Thanks: 516

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 .
MarkFL is offline  
October 1st, 2012, 09:28 PM   #9
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 628
Thanks: 92

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?
jks is offline  
October 1st, 2012, 09:33 PM   #10
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,208
Thanks: 516

Math Focus: Calculus/ODEs
Re: work

Yes, I get the same results.
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
work



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
when work be - and + r-soy Physics 1 October 11th, 2013 07:50 AM
I can't work this out... please someone help? dsbcourtney Advanced Statistics 3 July 20th, 2013 05:22 PM
can someone work this out Kinroh Algebra 9 May 7th, 2013 12:32 PM
No work. mathbalarka Number Theory 2 June 16th, 2012 03:53 PM
I can't work this out... please someone help? dsbcourtney Real Analysis 2 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.