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# Help me. Thanks all! watch

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1. 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.
2. Where's this from? It seems hard !!!
3. 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(@)
4. It's quite far from Alevel, isn't it?
5. (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.
6. (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....

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