Turn on thread page Beta
    • Thread Starter
    Offline

    18
    ReputationRep:
    A and B are two fixed points on a smooth horizontal table. A particle P is in equilibrium, attached to A by means of a light elastic string of natural length l and modulus of elasticity lamda and to B by means of a light elastic string of natural length 3l and modulus of elasticity lamda. Given that the extension in the string AP is 0.5l, find the distance AB.

    A particle P of mass 2kg is attached to the mid-point of a light elastic string of natural length 2m and modulus of elasticity 20N. One end of the string is attached to point A of a ceiling and the other end is attached to point B on the floor 3m vertically below A. Calculate the tension in AP and the tension in PB.

    A ball of mass 0.5kg is attached to one end of a cord of unstretched length 0.6m whose other end is fixed. When a horizontal force of magnitude QN is applied to the ball holding the ball inn equilibrium, the cord increases its length by 10% and is inclined at an angle of arcsin 3/5 to the downward vertical. Calculate the value of Q and the modulus of the cord.

    I found 1-11 okay but 12-15 got me.

    I really appreciate this.
    Offline

    0
    ReputationRep:
    i)AP a=l L=L x=(1/2)l

    BP a=3l L=L Let d be the distance AB=>x=d-(9/2)l

    Equilibrium=>equal tensions

    T=((L(1/2)l)/l)=(1/2)L (i)
    T=((L(d-(9/2)l))/3l) (ii)

    (i)=(ii)=>(1/2)L=((L(d-(9/2)l))/3l)=>(3/2)l=d-(9/2)l=>d=6l

    Newton.
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by Newton)
    i)AP a=l L=L x=(1/2)l

    BP a=3l L=L Let d be the distance AB=>x=d-(9/2)l

    Equilibrium=>equal tensions

    T=((L(1/2)l)/l)=(1/2)L (i)
    T=((L(d-(9/2)l))/3l) (ii)

    (i)=(ii)=>(1/2)L=((L(d-(9/2)l))/3l)=>(3/2)l=d-(9/2)l=>d=6l

    Newton.
    Thankyou, could you explain the part in bold?
    Offline

    0
    ReputationRep:
    (Original post by Widowmaker)
    Thankyou, could you explain the part in bold?

    A_________________P_____________ _______________B
    |<-------->|<----->|<--------->|<---------------->|
    _____l______ (1/2)l______x_____________3l_______ __

    d=l+(1/2)l+x+3l=>x=d-(9/2)l

    Newton.
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by Newton)
    A_________________P_____________ _______________B
    |<-------->|<----->|<--------->|<---------------->|
    _____l______ (1/2)l______x_____________3l_______ __

    d=l+(1/2)l+x+3l=>x=d-(9/2)l

    Newton.
    Ah I see.
    There are two other questions if you have time.
    Offline

    0
    ReputationRep:
    ii) Let the tension in AP=T1 and PB=T2

    L=20N, x=1m, a=2m

    =>T=(Lx/a)=10N

    By looking at the situation you have an obvious systematic equation

    T1=T2+2g => T1-T2=2g (i)

    The net tension in each part of the string, T=10N

    For the top half T1-2g=10 (ii) and for the bottom T2+2g=10 (iii)

    (ii)+(iii)=>T1+T2=20 (iv)

    (i)+(ii)=>2T1=39.8=>T1=19.8N

    Substituting back into (iv):

    T2=20-19.8=0.2N

    Newton.
    Offline

    0
    ReputationRep:
    [email protected]=(3/5)=>[email protected]=(4/5), [email protected]=(3/4)

    The string is unstretched when l=0.6m=>a=0.6m

    After the force has been applied:

    Vertically:

    [email protected]=mg=>(4/5)T=0.5g=>T=0.625gN=6.125

    10% of 0.6m=0.06

    Therefore:

    (L0.06/0.6)=0.1L=6.125=>L=61.25N

    Horizontally:

    [email protected]=Q

    =>(3/5)(6.125)=Q=3.675N

    Newton.
 
 
 
Turn on thread page Beta
Updated: February 7, 2005

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.