Coefficient of friction between wrench jaws and cylinder

[battleaxe]

Homework Statement

The figure shows an adjustable pipe wrench, drawn to scale. The geometry of the mechanism is arranged so that the jaws clamp more tightly as force is applied to the handle. Friction between the jaws and the pipe transfers a torque from the jaws to the pipe.

Find the critical value of the coefficient of friction between the pipe and the jaws for the wrench to work correctly in the position shown. A graphical solution is required.

Note:
The required coefficient may be different for each jaw. The solution depends on geometry only - measure friction angles or components of associated triangles, then calculate the friction coefficient.

Homework Equations

$F = \mu N$

$\mu = \tan \theta$

$M = Fr$

The Attempt at a Solution

The friction force on the jaws acts upwards on the right hand side and downwards on the left, with each value being F/2. The normal force acts along the line of the handle. Once that value is known, or drawn on, just measure the angle and use $\mu = \tan \theta$.

I'm stuck on what to do about the normal force - how can I know what it's magnitude is? It's supposed to be a fairly easy question, I'm not sure what I'm missing.

(Also it's my first time posting so please let me know if I need to add/change anything, thanks!)

 

[theodoros.mihos]

Use an arbitrary value, i.e. F=1 so take the answer as F factor.

 

[battleaxe]

Use an arbitrary value, i.e. F=1 so take the answer as F factor.

But I still don't know what N is...