Hookes law problem - mechanics problem - CIE past papers

Announcements Posted on
Four things that unis think matter more than league tables 08-12-2016
    • Thread Starter
    Offline

    2
    ReputationRep:
    So today as i was practicing past papers, I came upon this question and honestly i coudnt get how they got the answer, here it is

    A light elastic string has natural length 3m and modulus of elasticity 45N. A particle P of weight 6N is attached to the mid-point of the string. The ends of the string are attached to fixed points A and B which lie in the same vertical line with A above B and AB = 4. The particle P is released from rest at the point 1.5m vertically below A.
    Calculate the distance P moves after its release before first coming to instantaneous rest at a point vertically above B. (you may assume that at this point the part of the string joining P to B is slack).

    I'd reaaally appreciate your help guys.
    Online

    3
    ReputationRep:
    (Original post by Roe1777)
    So today as i was practicing past papers, I came upon this question and honestly i coudnt get how they got the answer, here it is

    A light elastic string has natural length 3m and modulus of elasticity 45N. A particle P of weight 6N is attached to the mid-point of the string. The ends of the string are attached to fixed points A and B which lie in the same vertical line with A above B and AB = 4. The particle P is released from rest at the point 1.5m vertically below A.
    Calculate the distance P moves after its release before first coming to instantaneous rest at a point vertically above B. (you may assume that at this point the part of the string joining P to B is slack).

    I'd reaaally appreciate your help guys.
    What have you tried? At what point do you get stuck? Post your working, please.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Zacken)
    What have you tried? At what point do you get stuck? Post your working, please.

    l=3, (lmabda)= 45N, PB = ?

    45 * (3-1.5-PB)^2 / 2*3 = 6 (PB)
    45 * (2.25 + PB^2 - 3PB)/6 = 6PB
    7.5 * (2.25 + PB ^ 2 - 3PB) = 6PB
    PB ^ 2 - 3.8PB + 2.25 = 0
    = 3.06 , 0.735

    I attempted to equate PE with EE since PE is decreasing (moving downwards) and EE is increasing (tension is increasing in the part AP of the string), but the correct answer was 1.22m.
    Offline

    3
    ReputationRep:
    (Original post by Roe1777)
    l=3, (lmabda)= 45N, PB = ?

    45 * (3-1.5-PB)^2 / 2*3 = 6 (PB)
    45 * (2.25 + PB^2 - 3PB)/6 = 6PB
    7.5 * (2.25 + PB ^ 2 - 3PB) = 6PB
    PB ^ 2 - 3.8PB + 2.25 = 0
    = 3.06 , 0.735

    I attempted to equate PE with EE since PE is decreasing (moving downwards) and EE is increasing (tension is increasing in the part AP of the string), but the correct answer was 1.22m.
    What do you mean by PB? P moves from 1.5 m below A down to an arbitrary point above B.

    At the start, the part of the string from B to P has length 2.5, so it has some EE. Your equation should therefore include 2 EE terms.

    I suggest that you consider the two halves of the string as being two separate strings of natural length 1.5 m.
 
 
 
Write a reply… Reply
Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: September 21, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
Do you think you'll achieve your predicted A Level grades?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read here first

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
Study resources

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

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