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A level Mechanics question help!!!

This is my question : A rough circular cylinder of radius 4a is fixed to a rough horizontal plane with its axis horizontal. A uniform rod AB, of weight W and length 6aroot3, rests with its lower end A on the plane and a point C of the rod against the cylinder. The vertical plane through the rod is perpendicular to the axis of the cylinder. The rod is inclined at 60 to the horizontal. The coefficient of friction between the rod and the cylinder is
(Root3)/3 and the coefficient of friction between the rod and the plane is p. Given that friction is limiting at both 4 and C,
(b) find the value of p. I am confused on where the friction at C would be acting, is it parallel up the plane? I’m also struggling to resolve forces horizontally and vertically for the whole system as I don’t know how to split the normal reaction and friction at C into horizontal and vertical components. I can’t find the mark scheme anywhere so please help!!!

Reply 1

Original post
by Autumnfoxy
This is my question : A rough circular cylinder of radius 4a is fixed to a rough horizontal plane with its axis horizontal. A uniform rod AB, of weight W and length 6aroot3, rests with its lower end A on the plane and a point C of the rod against the cylinder. The vertical plane through the rod is perpendicular to the axis of the cylinder. The rod is inclined at 60 to the horizontal. The coefficient of friction between the rod and the cylinder is
(Root3)/3 and the coefficient of friction between the rod and the plane is p. Given that friction is limiting at both 4 and C,
(b) find the value of p. I am confused on where the friction at C would be acting, is it parallel up the plane? I’m also struggling to resolve forces horizontally and vertically for the whole system as I don’t know how to split the normal reaction and friction at C into horizontal and vertical components. I can’t find the mark scheme anywhere so please help!!!

IMG_0862.jpgThis is the question.

Reply 2

Original post
by Autumnfoxy
This is my question : A rough circular cylinder of radius 4a is fixed to a rough horizontal plane with its axis horizontal. A uniform rod AB, of weight W and length 6aroot3, rests with its lower end A on the plane and a point C of the rod against the cylinder. The vertical plane through the rod is perpendicular to the axis of the cylinder. The rod is inclined at 60 to the horizontal. The coefficient of friction between the rod and the cylinder is
(Root3)/3 and the coefficient of friction between the rod and the plane is p. Given that friction is limiting at both 4 and C,
(b) find the value of p. I am confused on where the friction at C would be acting, is it parallel up the plane? I’m also struggling to resolve forces horizontally and vertically for the whole system as I don’t know how to split the normal reaction and friction at C into horizontal and vertical components. I can’t find the mark scheme anywhere so please help!!!

At C, rod-cylinder friction would act along AB and would be a function of the normal reaction at that point. Resolving those forces horizontally, friction would act at 60 and the normal at 30 as should be clear if you drew a horizontal line through C and took the 60 degree angle to that point using simple angle relationships. Similar for resolving vertically - sketch the forces and the horizontal / vertical legs of the right triangles as usual.

However, Id probably go for moments as a way to work out what happens at C and its kind of hinted at in the first part by getting AC, then work out what happens at A.
(edited 10 months ago)

Reply 3

Original post
by mqb2766
At C, rod-cylinder friction would act along AB and would be a function of the normal reaction at that point. Resolving those forces horizontally, friction would act at 60 and the normal at 30 as should be clear if you drew a horizontal line through C and took the 60 degree angle to that point using simple angle relationships. Similar for resolving vertically - sketch the forces and the horizontal / vertical legs of the right triangles as usual.
However, Id probably go for moments as a way to work out what happens at C and its kind of hinted at in the first part by getting AC, then work out what happens at A.

Awesome Thank you so much!!!!!

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