Calculating Coefficient of Friction In the System

[junkie_ball]

Homework Statement

When the converyor belt was first installed safety checks were carried out to determine the limit of angle for safety. It was found that at an angle of 30 degrees the crates start to slip down.

Calculate the coefficient of friction between the crates and the belt? (Diagram as shown in the question attached) I also assume they are looking for the static coefficient not the slipping as the question isn't very clear?

Homework Equations

Friction = Pressing Force x Constant

or μ= Pressing Force/Friction

The Attempt at a Solution

Vertical force acting on the crate (H in my free body diagram)

H = Gravity x mass
H = 9.81 x 200
H = 1962N

Parallel downwards to the surface of the plane force acting on the crate (O in my free body digram)

O = H x Sin θ
O = 1962 x Sin 30
O = 981N

Therefore i can assume the friction force acting in the opposite direction to 'O' is 981N

Force acting into the surface of the plane (A in my free body diagram)

A = H x Cos θ
A = 1962 x Cos 30
A = 1699.14N

This is my pressing force.

To calculate the coefficient of friction between the crates and belt is

μ = 1699.14 / 981
μ = 1.73

This is my first attempt at calculating a coefficient do would really appreciate if someone could review this and check I'm on the right lines.

 

[climb515c]

Max Static friction is given by (μs*normal force), normal force in your diagram is "A" so set O=A and solve for μs. Looks good, up until the end. You have 1699.14/981 flipped, should be 981/1699.14. However its best to solve the problem in variables first and then plug in your values at the end. In this problem (mg) drops out and it simplifies nicely.

 

[junkie_ball]

Max Static friction is given by (μs*normal force), normal force in your diagram is "A" so set O=A and solve for μs. Looks good, up until the end. You have 1699.14/981 flipped, should be 981/1699.14. However its best to solve the problem in variables first and then plug in your values at the end. In this problem (mg) drops out and it simplifies nicely.

Hi thanks for the reply i see where i mixed my final equation up. I took a quick glance at my course material and they have written the equation back to front. I'm starting to seriously worry about the quality of the course materials with the errors i have come across so far.