How to more accurately determine an angle?

[spike spiegel]

A recent lab involved finding the coefficient of static friction. A book was on a table. A brass weight was placed on the book and one end of the book was raised until the weight began to slide. The angle between the book and the table was found by measuring the height and hypotenuse of the triangle formed and using trigonometry. What would be a more accurate method of finding the angle?

 

[PhysiPhile]

Are you asking how would you calculate the angle at which the book would slide?

The measurement you made is the most "accurate" because it's experimental and takes into account variables that you will ignore when doing a simple force balance equation. (i.e. when the gravitational force component in the direction of the sliding book equals the frictional force)

 

[AlephZero]

Coulomb's "laws" of static and dynamic friction are only rough approximations to the "real world". There isn't really much point trying to measure friction coefficients "accurately" (with errors less than about 10%, say) because the result depends on many things that you can't control in a simple experiment.

 

[Studiot]

Hello spike;

Since you say you did this as a lab I assume this was a question asked as part of the assignment.

A purely mechanical answer would be to use what is known as a 'sine bar'.
This is a mechancial engineer's improvement of the method you describe - look it up on google.

An opto-mechanical answer would be to shine a light parallel to the sliding surface onto a vertical scale some distance away thus magnifying both the hypotenuse and vertical measurements therby increasing the accuracy.

An electronic method would be to attach an electronic inclinometer to the lifted plane and read out the angle.

There are other ways but these plus google should give you a start.

 

[asteriatic]

One potential method to more accurately determine the angle in this scenario would be to use a protractor. The protractor would allow for a direct measurement of the angle between the book and the table, rather than relying on calculations using the height and hypotenuse of the triangle formed. Additionally, using multiple trials with varying weights and angles could help to reduce any potential errors and provide a more precise measurement of the angle. Furthermore, ensuring that the surface of the table and the book are completely level and that the weight is evenly distributed on the book could also help to improve the accuracy of the measurement.