Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    My exam's in a few hours, and I just figured out I'm extremely crappy at horizontal circular motion questions.

    Here are a couple I can't do:

    A particle, of mass m, is suspended from a fixed point O by a light elastic string, of natural length l and modulus X. The particle moves with constant angular speed W in a horizontal circular path with the string making a constant angle @ with the downward direction of the vertical. Show that e, the extension of the string, is given by
    Xe = W²lm(l+e)
    Deduce that the motion described cannot take place unless W²<X/(lm)
    Show further that, for a given value of W, the depth of the horizontal circle below O is independant of X.

    A conical pendulum consists of a light inextensible string which has one end attached to a fixed point A. A particle P of mass m is attached to the other end of the string. The particle P moves with constant speed comleting 2 orbits of its circular path every second and the tension in the string is 2mg.
    Find to the nearest cm
    a) the radius of the circular path of P
    b) the length of the string

    Help!!!
    Offline

    12
    ReputationRep:
    if it's from one of the past papers why dont you try neos site if it is back to operate.
    Offline

    15
    ReputationRep:
    A particle, of mass m, is suspended from a fixed point O by a light elastic string, of natural length l and modulus X. The particle moves with constant angular speed W in a horizontal circular path with the string making a constant angle @ with the downward direction of the vertical. Show that e, the extension of the string, is given by
    Xe = W²lm(l+e)
    Resolving up: [email protected] = mg
    Resolving horiontally: F=ma
    [email protected] = mrW^2
    Hookes law gives: T=Xe/l

    Substitution gives: (Xe/l)[email protected] = mrW^2.
    Taking the total length of the string to be l+e, hence the radius is (l+e)[email protected] (resolving dimensions horizontally)

    (Xe/l)[email protected] = m(l+e)[email protected]^2
    Xe/l = m(l+e)w^2
    Xe = lm(l+e)w^2

    Deduce that the motion described cannot take place unless W²<X/(lm)
    For a tension to be present there must be an extension. Hence e>0.
    Taking Xe=lmw^2(l+e)
    Xe = l^2mw^2 + lmw^2e
    Xe - lmw^2e = l^2mw^2
    e[X-lmw^2] = l^2mw^2
    e = [l^2.mw^2]/[X-lmw^2]
    E>0
    Hence: [l^2.mw^2]/[X-lmw^2]>0
    As the numerator is always >0:
    X - lmw^2 > 0
    X > lmw^2
    or, X/lm > w^2 and w^2 < x/lm

    Show further that, for a given value of W, the depth of the horizontal circle below O is independant of X.
    Xe=lm(l+e)w^2
    w^2 = Xe/lm(l+e), T=mg/[email protected], Xe/l = mg/[email protected], X = mgl/[email protected]
    w^2 = [e/lm(l+e)][mgl/[email protected]]
    w^2 = [g/(l+e)[email protected]]
    [email protected]^2 = g/(l+e)
    Using trigonometry, let the depth by y. [email protected] = y/(l+e)
    yw^2/(l+e) = g/(l+e)
    yw^2 = g
    y = g/w^2.
    Offline

    15
    ReputationRep:
    A conical pendulum consists of a light inextensible string which has one end attached to a fixed point A. A particle P of mass m is attached to the other end of the string. The particle P moves with constant speed comleting 2 orbits of its circular path every second and the tension in the string is 2mg.
    Find to the nearest cm
    a) the radius of the circular path of P
    2orbits per sec means 4pi radians per sec [remember w is always in radians per second]
    w=4pi.
    Resolving vertically, let the angle theta be the angle between the string and the vertical: [email protected] = mg
    [email protected] = 1/2.
    Resolving horizontally: f=ma
    [email protected] = mr(4pi)^2
    [email protected] = r(4pi)^2
    [email protected]/(4pi)^2
    r=0.107489...
    r=11cm.

    b) the length of the string
    [email protected] = r
    y = r/[email protected]
    y = 2g/(4pi)^2
    y =0.12412m
    y=12cm.

    Feel free to ask if you have any other questions.

    Edit: Btw, you don't need to panic. We proabably won't have anything like the first question in the exam. The most they'll ask is for you to use the fact T>0 to prove an inequality, which is good because it serves as a quick answer check.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thanks Gaz! You're a life saver. I just tried doing a few more horizontal circular motion questions, and I got the right answers.

    Two questions, though... I don't really understand what "depth" is. Why are you using [email protected]? And in the second question, where'd the [email protected] come from?
    Offline

    15
    ReputationRep:
    (Original post by shift3)
    Thanks Gaz! You're a life saver. I just tried doing a few more horizontal circular motion questions, and I got the right answers.

    One question though... I don't really understand what "depth" is. Why are you using [email protected] (both questions)?
    No worries, it's all practice for me too.
    Depth is the distance of the centre of the horizontal circle below the point the string is fastened to.
    I've let y=the length of the string.
    Hence [email protected] would be the depth and [email protected] would be the radius.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Oh. I thought y was some other variable.

    Thanks again... I'm repping you ASAP.
    Offline

    15
    ReputationRep:
    (Original post by shift3)
    Oh. I thought y was some other variable.

    Thanks again... I'm repping you ASAP.
    Heh, no worries. I find that if i'm getting into trouble with a question i'll often make up a variable to simplify things as i can always cancel it out later.
    I hope the exam goes well. The butterflies are setting in now.
 
 
 
Turn on thread page Beta
Updated: January 12, 2005

University open days

  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 Feb '19
  • Sheffield Hallam University
    City and Collegiate Campus Undergraduate
    Sun, 3 Feb '19
Poll
Brexit: Given the chance now, would you vote leave or remain?
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.