- #1

klg.amit

- 12

- 0

## Homework Statement

A small body starts sliding down an inclined plane. The angle between the plane and the horizon is [tex]\alpha[/tex]. The coefficient of friction depends on the distance [tex]s[/tex] that the body travels according to [tex]\mu = \beta s[/tex].

Find the distance that the body travels until coming to a stop and its maximum speed.

**2. The attempt at a solution**

The force equation for the plane axis which I'm pretty sure I got correctly is

[tex] g\sin{\alpha} - \beta s g\cos{\alpha} = a [/tex]

That is after simplifying and substituting what is required. This is a differential equation which I'm not sure how to solve. First, is there any problem with treating the acceleration as the second derivative of the distance (rather than of the position, which appears the same in this case). Second when I do try to find a homogenous solution I get an imaginary root which I'm not sure is ok. Am I even on the right track ? Or is there something I'm totally missing ?