Turn on thread page Beta
    • Thread Starter
    Offline

    3
    ReputationRep:
    Consider the following problem: Water starts running out of a small hole in the bottom of a bowl so that the depth of the water in the bowl at time t is x. The rate at which the volume of water is decreasing is proportional to x.

    Why did the book represent the relationship as: -dV/dt ∝ x. knowing that as x decreases the volume decreases as well. Thus putting a negative sign will make the decrease in x cause an increase in V.
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by Rana1997)
    Consider the following problem: Water starts running out of a small hole in the bottom of a bowl so that the depth of the water in the bowl at time t is x. The rate at which the volume of water is decreasing is proportional to x.

    Why did the book represent the relationship as: -dV/dt ∝ x. knowing that as x decreases the volume decreases as well.

    dV/dt is the rate of increase in V with respect to t - it could be positive or negative, and -dV/dt is the rate of decrease, which again could be positive or negative. In this example dV/dt will be negative and -dV/dt positive.

    But, it doesn't overly matter here, since this is "proportional to", rather than "equal to". To turn it into an equation you'd need to add the coefficient of proportionality (-dV/dt = kx). With the minus sign that constant will be positive; without it, it would be negative.

    Thus putting a negative sign will make the decrease in x cause an increase in V.
    That doesn't follow.

    As x gets smaller towards zero, -dV/dt will tend to zero, i.e. the rate at which the volume changes will tend to zero.

    If you work through and solve the equation, you will find that there is no problem either way, except without the -ve sign the coefficient of proportionality will be negative, and although that's not wrong per se., it's usual, if not an actual requirment, that it's +ve.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 30, 2016
The home of Results and Clearing

2,965

people online now

1,567,000

students helped last year

University open days

  1. London Metropolitan University
    Undergraduate Open Day Undergraduate
    Sat, 18 Aug '18
  2. Edge Hill University
    All Faculties Undergraduate
    Sat, 18 Aug '18
  3. Bournemouth University
    Clearing Open Day Undergraduate
    Sat, 18 Aug '18
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.