Normal and tangential forces on a cylinder

[Karol]

Homework Statement

The walls are smooth, calculate the reactions. the cylinder weighs 100[N].
Now the 60⁰ wall is rough with a friction coefficient 0.4. what are the reactions

Homework Equations

Friction: F=μN

The Attempt at a Solution

I made the first step and it was good: N₁=287.9, N₂=253.2
But with friction there is another force, tangential, but the results in the book are the same.

 

[siddharth23]

You got the first one correct? Because I'm getting different answers.

As for the second part, what I think, is that the cylinder is stationary, in equilibrium. There is no resultant force on it. So which direction will you consider the friction to act in?

 

[Nathanael]

You got the first one correct? Because I'm getting different answers.

I agree with Karol's answers.

But with friction there is another force, tangential, but the results in the book are the same.

If the cylinder is in equilibrium when there is no friction, and then the only change that is made is that a coefficient of friction is added, then why would a force of friction act?

Edit:

Friction: F=μN

For the case of static friction, that is only the maximum, not the applied force.

 

[siddharth23]

Ok I'll check the first part again.

 

[Karol]

If the cylinder is in equilibrium when there is no friction, and then the only change that is made is that a coefficient of friction is added, then why would a force of friction act?

I may agree if μ is added later. but the forces can arrange themselves differently (only magnitudes) to accommodate the changes.
Maybe because there is no relative movement without the friction force anyway it isn't created.

 

[siddharth23]

See the image I've uploaded. The surface is rough and has a coeffecient of friction 'μ'. A force 'F' pushes the block towards the right side but its motion is hindered by the wall. Now even though a force of friction would act on the block, in this case it won't as the system is in equilibrium. There is no scope for the block to move.

 

[haruspex]

Maybe because there is no relative movement without the friction force anyway it isn't created.

More accurately, it would be because there is no tendency to move.
However, the question is not really correct. While there need not be a frictional force, there could be one. You could find a solution to the equations in which the walls exert a greater normal force and, to balance that, a small frictional force. In the real world, this corresponds to the cylinder being jammed in.