Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    3
    ReputationRep:
    This is q10 Exercise 3B Advanced Maths for AQA Mechanics M1:
    ----------------------------------------------------------
    A particle of mass 4kg is suspended from a point A on a vertical wall by means of a light inextensible string of length 130cm.
    a) A horizontal force,P, is applied to the particle so that it is held in equilibrium a distance of 50cm from the wall. Find the value of P and the tension in the string.

    b) By drawing a triangle of forces, or otherwise, find the magnitude and direction of the minimum force which would hold the particle in this position, and the tension in the string which would result.
    ----------------------------------------------------------
    I've managed part a) but part b) has me foxed.

    I've said, let the force applied to the particle be F at an angle alpha to the horizontal. Let T = tension in the string and F the force needed to keep the particle in equilibrium. From part a) the cos of angle of the string to the horizontal is 5/13 and its sin is 12/13.

    So I get 5T/13 = Fcos(alpha)
    and 12T/13 + Fsin(alpha)= 4x9.8

    I have 2 equations with 3 unknowns. I'm missing something.
    Offline

    16
    ReputationRep:
    You should indeed have a whole choice of "F"s, now you have to pick the smallest in magnitude. I suggest eliminating alpha and seeing if the resulting expression for F in terms of T has a minimum.
    • Thread Starter
    Offline

    3
    ReputationRep:
    Thanks for the reply.

    I think my algebra/pure maths isn't up to eliminating alpha. I've tried rearranging to get F sin(alpha). Then I squared both sides of each equation so that I could use sin2 + cos2 =1 but now I have only 1 equation with two unknowns.

    I would appreciate another clue.
    Offline

    16
    ReputationRep:
    The sin^2 + cos^2 =1 trick should help you on your way to getting F in terms of T, have you managed that? If so, see what the smallest value that F can take is.
    • Thread Starter
    Offline

    3
    ReputationRep:
    Hi again

    No, as of yet I've not worked out the sum of the squares of the equations because I thought that I'd get nowhere with only one equation and two unknowns.

    So once I've got there I'm going to have F2 = some huge expression involving Ts and T2 by the looks of things. So then will I solve the quadratic for zero (that's a minimum F)?

    Will get on to that equation, now you think I'm on the right lines, but I might be some time as I now have to go to work.
    Offline

    16
    ReputationRep:
    Yes, you should get F^2= some function of T. You can then complete the square to find the smallest value of F^2 (it shouldn't be zero, you're essentially trying to find the minimum of the graph F^2), and the value of T that will give it. Of course, the smallest value of F^2 might not always correspond to the smallest valid value of F, but plug in your found value of T and you'll get a valid F out.
    • Thread Starter
    Offline

    3
    ReputationRep:
    Oh, lovely.

    Yes managed to find minimum T by differentiating (T2 -96T/13 + 16) rather than completing the squares.

    Once I'd found T I put that back into F2 so kept getting the wrong answer. Then I realised my mistake and found the correct F by using the correct T.

    As usual these things take a while but I'm learning such a lot with TSR's help.

    Thanks
    Offline

    10
    ReputationRep:
    (Original post by maggiehodgson)
    Oh, lovely.

    Yes managed to find minimum T by differentiating (T2 -96T/13 + 16) rather than completing the squares.

    Once I'd found T I put that back into F2 so kept getting the wrong answer. Then I realised my mistake and found the correct F by using the correct T.

    As usual these things take a while but I'm learning such a lot with TSR's help.

    Thanks
    kind of a long time ago but do u by any chance remember how you got the answer to part a
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by girl :D)
    kind of a long time ago but do u by any chance remember how you got the answer to part a
    Yes, I keep all my maths.

    I am attaching a picture of the diagram I used. I've hidden the workings (TSR rules - just hope the sketch isn't too much)

    Let me know if you need further help.
    Attached Images
  1. File Type: pdf Scan0002.pdf (364.3 KB, 44 views)
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What's your favourite Christmas sweets?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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.