Turn on thread page Beta

Help me. Thanks all! watch

Announcements
    • Thread Starter
    Offline

    1
    ReputationRep:
    A uniform sphere, of mass m and radius a, rolls without slipping down a line of greatest slope of a plane inclined at angle @ to the horizontal. Show that the minimum value of the coefficient of fraction between the sphere and the plane is 2/[email protected]

    Spent 2 days on it.... I've given up. :mad:
    Offline

    12
    ReputationRep:
    Where's this from? It seems hard !!!
    Offline

    8
    ReputationRep:
    Let N be the normal reaction exerted by the plane on the sphere. Let F be the frictional force, acting up the slope, exerted by the plane on the sphere. Let p be the angular acceleration of the sphere.

    Resolving perpendicular to the plane,

    mg cos(@) = N

    Resolving parallel to the plane, using the fact that the acceleration of the sphere's centre is pa,

    mg sin(@) - F = mpa

    Considering the rotation of the sphere,

    (applied moment) = (moment of inertia)p
    Fa = (2/5)ma^2 p

    --

    F
    = (2/5)map
    = (2/5)[mg sin(@) - F]

    F = (2/7)mg sin(@)

    mu
    >= F/N
    = (2/7)mg sin(@)/[mg cos(@)]
    = (2/7)tan(@)
    Offline

    12
    ReputationRep:
    It's quite far from Alevel, isn't it?
    Offline

    8
    ReputationRep:
    (Original post by BCHL85)
    It's quite far from Alevel, isn't it?
    It is part of the topic "General Motion of a Rigid Body" in Edexcel M6.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Jonny W)
    Let N be the normal reaction exerted by the plane on the sphere. Let F be the frictional force, acting up the slope, exerted by the plane on the sphere. Let p be the angular acceleration of the sphere.

    Resolving perpendicular to the plane,

    mg cos(@) = N

    Resolving parallel to the plane, using the fact that the acceleration of the sphere's centre is pa,

    mg sin(@) - F = mpa

    Considering the rotation of the sphere,

    (applied moment) = (moment of inertia)p
    Fa = (2/5)ma^2 p

    --

    F
    = (2/5)map
    = (2/5)[mg sin(@) - F]

    F = (2/7)mg sin(@)

    mu
    >= F/N
    = (2/7)mg sin(@)/[mg cos(@)]
    = (2/7)tan(@)
    Damn Jonny W, you DA MAN!!! It's so simple! hehe.. I feel dumb now....
 
 
 
Turn on thread page Beta
Updated: January 11, 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
  • Aston University
    Postgraduate Open Day Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 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.