Statics : find coefficient of static friction

[tranj10]

Homework Statement

Find coefficient of static friction if shell starts to slip at θ = 60°

known - θ
unknowns - P, r, Normal force, weight

Homework Equations

friction = μ * normal force

The Attempt at a Solution

I do not know where to start. It looks like the picture wants you to assume P is always horizontal so it has no effect on the normal force which means friction is constant. If friction were constant though why would it start to slip?

 

[RTW69]

I haven't done this problem but here is a place to start.

Find the centroid of the shell. The gravitational force will act through the centroid. P is horizontal. Do a free body diagram. Sum forces in X and Y direction. Sum the moments around the contact point. Hopefully everything falls out but Coefficient of static friction which is probably related somehow to the angle.

 

[RTW69]

Yep, the method I outlined above will give you the correct answer. Treat this as a statics problem.

 

[tranj10]

ah yes. Your method worked perfectly for me, thank you.

 

[DeeNos]

As a scientist, it is important to always start with the basic principles and equations that govern the situation. In this case, we can use the equation for friction, which states that friction is equal to the coefficient of static friction (μ) multiplied by the normal force (N). The normal force is the force that is perpendicular to the surface and prevents the object from falling through the surface. In this case, the normal force is equal to the weight of the shell (mg), where m is the mass of the shell and g is the acceleration due to gravity.

Now, we can use the given information that the shell starts to slip at an angle of 60° to set up an equation. At this angle, the component of the weight parallel to the surface is equal to the friction force. Therefore, we can write:

mg * sinθ = μN

We know that N = mg * cosθ, so we can substitute that into the equation:

mg * sinθ = μ * mg * cosθ

We can cancel out the mass and rearrange the equation to solve for the coefficient of static friction:

μ = tanθ

Substituting the given angle of 60°, we get:

μ = tan60° = √3 ≈ 1.73

Therefore, the coefficient of static friction for this situation is approximately 1.73. This means that the friction force is 1.73 times the weight of the shell. If the friction force exceeds this value, the shell will start to slip.

It is important to note that this calculation assumes a few simplifying assumptions, such as a horizontal force P and a constant friction force. In reality, the situation may be more complex and the coefficient of static friction may vary depending on factors such as surface roughness and applied force. As a scientist, it is important to always consider these limitations and potential sources of error in our calculations.