Determining the coefficient of friction? (example inside)

[Nonchalant]

Homework Statement

A physics student is performing an experiment to determine the coefficient of friction between a physics textbook and a 2.5 m wooden ramp. He places the textbook, which has a mass of 1.2 kg, on the inclined ramp and gradually increases the angle of the incline. At an angle of 30 degrees, the textbook starts to slip. It slides down the ramp in 4.0 s. Determine the coefficient of friction.

Homework Equations

The Attempt at a Solution

Well i was working on it with my friend in class, and he came up with

friction = tan 30 degrees = 0.58

but then, I don't think that's all to it right? Any help please?

 

[G01]

The coefficient of static friction is indeed:

$$\mu_s=\tan\theta$$ where $$\theta$$ is the angle at which the block starts to slip.

You can work on deriving this yourself by starting with the following information:

At the angle where the block just starts to slip the component of gravity along the hill (x direction) much equal the force of static friction:

$$F_{gx}=F_{static f}$$

Can you fill in for the forces above and solve for the coefficient? If you can, you should end up with the expression given by your friend.

 

[Moetasim]

I would suggest that the student's approach is a good start, but there are a few other factors to consider when determining the coefficient of friction in this experiment. First, it is important to note that the coefficient of friction is a dimensionless quantity that represents the ratio of the force of friction to the normal force between two surfaces. In this case, the normal force would be equal to the weight of the textbook, which is 1.2 kg multiplied by the acceleration due to gravity (9.8 m/s^2), giving a normal force of 11.76 N.

Next, it is important to consider the motion of the textbook down the ramp. The student mentioned that the textbook slides down the ramp in 4.0 s, which means it is experiencing a constant acceleration down the ramp. This acceleration is related to the angle of incline and the coefficient of friction through the equation a = gsinθ - μcosθ, where θ is the angle of incline and μ is the coefficient of friction. Since we know the angle of incline (30 degrees) and the acceleration (calculated from the time and distance), we can rearrange this equation to solve for μ.

Finally, it is important to consider any sources of error in the experiment. For example, the surface of the ramp and the textbook may not be perfectly smooth, which could affect the coefficient of friction. Additionally, the textbook may have been placed on the ramp at slightly different angles each time, leading to variations in the results.

In conclusion, determining the coefficient of friction between the textbook and the ramp requires considering the normal force, the motion of the textbook down the ramp, and potential sources of error. By taking these factors into account, the student can arrive at a more accurate value for the coefficient of friction.