Rolling & Pulley Homework: Find Max Mass for Cylinder to Roll

[Carbon123]

Homework Statement

A solid cylinder is attached by a rope on its center.It has mass of 5kg and is lying on a table.The other end of the rope is a block of mass m2 which is not on the table .if the coeficient of friction between cylinder and table is 0.2.Find the maximum mass 2 so that the cylinder rolls without slipping.

Homework Equations

F=ma τ=I α

The Attempt at a Solution

Because it is rolling without slipping;f=1/2*5*a
T-f=5*a m2g-T=m2a and the a of cylinder centre is the same as a of the object.but i am stuck with bot knowing the accelleration.And is the coerficient of friction of any use ?

 

[haruspex]

The description is not crystal clear. I take it the cylinder is lying on the table with the rope either attached at the highest point or wrapped around it. Either way, the rope is horizontal at height 2r above the table, yes?

Because it is rolling without slipping;f=1/2*5*a

How do you get that? What are all the horizontal forces on the cylinder?

 

[ehild]

The description is not crystal clear. I take it the cylinder is lying on the table with the rope either attached at the highest point or wrapped around it. Either way, the rope is horizontal at height 2r above the table, yes?

How do you get that? What are all the horizontal forces on the cylinder?

The problem text says that " A solid cylinder is attached by a rope on its center."

 

[haruspex]

The problem text says that " A solid cylinder is attached by a rope on its center."

That can mean any of several things. Attached to the centre of the disc at one end; or, if attached to the centre of the side of the cylinder, at what height from the ground (given that the cylinder is lying on its side)? I would guess it means at the highest point, and going off horizontally (tangentially).

 

[ehild]

That can mean any of several things. Attached to the centre of the disc at one end; or, if attached to the centre of the side of the cylinder, at what height from the ground (given that the cylinder is lying on its side)? I would guess it means at the highest point, and going off horizontally (tangentially).

I think this is the set-up: the rope is attached to the axis of the cylinder :

 

[ehild]

Homework Statement

A solid cylinder is attached by a rope on its center.It has mass of 5kg and is lying on a table.The other end of the rope is a block of mass m2 which is not on the table .if the coeficient of friction between cylinder and table is 0.2.Find the maximum mass 2 so that the cylinder rolls without slipping.

Homework Equations

F=ma τ=I α

The Attempt at a Solution

Because it is rolling without slipping;f=1/2*5*a
T-f=5*a m2g-T=m2a and the a of cylinder centre is the same as a of the object.but i am stuck with bot knowing the accelleration.And is the coerficient of friction of any use ?

You know that the maximum friction can be f=μ(5g).

 

[haruspex]

I think this is the set-up: the rope is attached to the axis of the cylinder :
View attachment 104049
View attachment 104048

That is indeed another possibility. But one thing it cannot be is attached, literally, to the centre of the cylinder.

 

[ehild]

That is indeed another possibility. But one thing it cannot be is attached, literally, to the centre of the cylinder.

You are right. But the problem makers usually think in two dimension :) The OP followed that scheme shown in my picture, his only problem was that he eliminated the known force of friction, and so he had two many unknowns.

 

[haruspex]

problem makers usually think in two dimension

That argues in favour of my interpretation, which only requires the cylinder to be shown and thought of as a disc. But I accept that your reading is at least as likely.

 

[Carbon123]

Ehild's picture is the problem i was trying to interpret.Is such problwm solvable? I don't know if the variable a and m2 can be solved with the dynamics equation.

 

[ehild]

Ehild's picture is the problem i was trying to interpret.Is such problwm solvable? I don't know if the variable a and m2 can be solved with the dynamics equation.

Remember the problem text

Find the maximum mass 2 so that the cylinder rolls without slipping.

You did not calculate with the friction although the coefficient of friction was given. If the cylinder rolls, there is static friction between the cylinder and the table. The static friction is f<μmg, m is the mass of the cylinder, 5 kg and μ=0.2. If the cylinder has so big acceleration, that the force of friction reaches μmg, the cylinder is on the verge to slip. You know that maximum force of friction. Instead of eliminating it from the equations, determine the acceleration a and the mass m2 from the condition that f= 5*0.2*g