Help with force and motion with friction problems

AI Thread Summary
To determine the coefficient of kinetic friction for a box sliding down a 30.5° ramp with an acceleration of 1.43 m/s², start by applying Newton's second law (F = ma). Break the weight of the box into two components: the perpendicular component (mgcos(30.5)) and the parallel component (mgsin(30.5)). The frictional force opposing the motion is the product of the normal force and the coefficient of kinetic friction (u). It is important to note that the mass of the box is not needed to solve the problem. This approach will help in calculating the coefficient of kinetic friction effectively.
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Help with "force and motion with friction" problems!

A box slides down a 30.5° ramp with an acceleration of 1.43 m/s2. Determine the coefficient of kinetic friction between the box and the ramp.

I simply don't understand how to do this because I was absent from school fro a few days.. If someone could walk me through I would be most grateful!
 
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First I'm going to have to assume that the ramp is angled 30.5 degrees from the horizontal.

It's not terribly difficult. You know that F = ma.
You are going to have to split the weight of the object into two components, perpendicular and parallel to the plane, these are mgcos(30.5) and mgsin(30.5) respectively.

The drag force (due to friction) is the normal reaction force (perpendicular to the plane) multiplied by the coefficient of kinetic friction which we will call u. This will be parallel to the plane, and will always oppose the direction of movement.

Try it now, let me know how you go.

Hint: You do not need to know the mass of the object to solve this.
 

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