Coefficient of friction between wrench jaws and cylinder

• battleaxe
In summary, the given problem involves finding the critical value of the coefficient of friction between the pipe and the jaws of an adjustable pipe wrench for it to work correctly in the shown position. The solution depends on geometry and involves measuring friction angles or components of associated triangles and then calculating the friction coefficient. To find the normal force, an arbitrary value for the applied force can be used and the answer can be taken as a factor of that force.
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!)

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

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

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

1. What is the coefficient of friction between wrench jaws and cylinder?

The coefficient of friction between wrench jaws and cylinder refers to the measure of the amount of resistance or force required to move the two surfaces against each other. It is a dimensionless number that can range from 0 to 1, with a lower value indicating less resistance and a higher value indicating more resistance.

2. How is the coefficient of friction between wrench jaws and cylinder determined?

The coefficient of friction can be determined through experiments or calculations using the formula: μ = F/N, where μ is the coefficient of friction, F is the force required to move the surfaces against each other, and N is the normal force exerted by the surfaces on each other.

3. What factors can affect the coefficient of friction between wrench jaws and cylinder?

The coefficient of friction can be affected by various factors such as the material and surface properties of the wrench jaws and cylinder, the roughness of the surfaces, the amount of lubrication present, and the applied force between the surfaces.

4. Why is the coefficient of friction important in determining the effectiveness of a wrench?

The coefficient of friction is important because it indicates the amount of force that is needed to create movement between the wrench jaws and the cylinder. A higher coefficient of friction would require more force, making it more difficult to loosen or tighten a bolt or nut. A lower coefficient of friction would require less force, making the wrench more effective in its use.

5. Can the coefficient of friction between wrench jaws and cylinder change over time?

Yes, the coefficient of friction can change over time due to wear and tear on the surfaces, changes in temperature or humidity, or the introduction of lubricants. It is important to regularly check and maintain the surfaces to ensure the most effective use of the wrench.

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