Finding the friction before slipping

[Jack.525]

Homework Statement

There is a string that is attached to a bar as shown below in the picture. What is the coefficient friction between the bar and floor before bar starts slipping.
Reference https://www.physicsforums.com/threa...t-of-friction-using-torque-and-forces.723351/[/B]

Homework Equations

Moment which is
moment (torque) = F r (position)

The Attempt at a Solution

I have chosen a pivot point about the point where the bar contacts with the ground.


The equation for the torque about the point where bar contacts with the ground ->
- mg *1.4863 - T*1.814989 = 0
I found 1.814989 by using the cross product.

Then
Fx = 0
-Tsin21 - f(friction) = 0
-Tsin21 - u(coefficient of friction) *N = 0

Fy = 0
-mg + N + T*cos21 = 0

Now, I'm stuck and i don't how to proceed further. Also, I'm confused about this part ->
So the formula for friction is f = u*N, is N equals to mg ?

 

[haruspex]

So the formula for friction is f = u*N, is N equals to mg ?

Not always, and not in this instance.
The normal force from a solid surface is the minimum magnitude force necessary to prevent the object penetrating the surface.

The signs look a bit odd in your equations, but I'm not sure what conventions you've adopted. It might all come out ok.

 

[Jack.525]

Not always, and not in this instance.
The normal force from a solid surface is the minimum magnitude force necessary to prevent the object penetrating the surface.

The signs look a bit odd in your equations, but I'm not sure what conventions you've adopted. It might all come out ok.

So if normal force in this case is not equal to m*g, can i solve this problem with 5 unknowns?

 

[haruspex]

So if normal force in this case is not equal to m*g, can i solve this problem with 5 unknowns?

I assume you mean T, n, u, m and f (friction).
You have four equations.
It can happen that you have enough information to determine some unknowns but not all.
In the present case, T and m are the only unknowns which involve a mass dimension, so you can find the ratio of those but not their individual values. This leaves you with only four unknowns, effectively.

 

[ehild]

So if normal force in this case is not equal to m*g, can i solve this problem with 5 unknowns?

You will find that m cancels.

 

[haruspex]

You will find that m cancels.

Well, not exactly. See my post #4.

 

[ehild]

Well, not exactly. See my post #4.

When the bar just starts to slip the friction is μN. The task is to find μ. It is not needed to know T or m. It is a homogeneous system of equations, the determinant should be zero, you get μ from this condition.

 

[haruspex]

When the bar just starts to slip the friction is μN. The task is to find μ. It is not needed to know T or m. It is a homogeneous system of equations, the determinant should be zero, you get μ from this condition.

Sure, but Jack lists T and m as unknowns. So what will actually happen is that these will reduce to a single unknown T/m. That is not quite the same as saying m will cancel out.

 

[ehild]

Sure, but Jack lists T and m as unknowns. So what will actually happen is that these will reduce to a single unknown T/m. That is not quite the same as saying m will cancel out.

It is also needed to use N/m an unknown instead of N. That is, we can choose m arbitrary,
If you choose to solve the system of equation by eliminating N first then T you are left with an equation of form m f(μ) = 0, which can be divided by m.

 

[haruspex]

It is also needed to use N/m an unknown instead of N.

Yes, I missed that one.