# Thread: Find angle for max weight on incline

1. ## Find angle for max weight on incline

So I have been given a problem to do that involves an incline with an angle $\displaystyle \theta$. I have been staring this thing down all day and am thinking I have to take the derivative of W. But don't know how to start it.

Any help to get this problem started would be great. Maybe an outline of what I am going to need to do.

Problem:
The largest weight W that can be pulled up a plane inclined at an angle $\displaystyle \theta$ with the horizontal slope by a force F is
$\displaystyle W = \frac{F * (cos\theta + \mu*sin\theta)}{\mu}$
where $\displaystyle \mu$ is the coefficient of friction. Find $\displaystyle \theta$ so that W is a maximum.

2. Originally Posted by Shaz
So I have been given a problem to do that involves an incline with an angle $\displaystyle \theta$. I have been staring this thing down all day and am thinking I have to take the derivative of W. But don't know how to start it.

Any help to get this problem started would be great. Maybe an outline of what I am going to need to do.

Problem:
The largest weight W that can be pulled up a plane inclined at an angle $\displaystyle \theta$ with the horizontal slope by a force F is
$\displaystyle W = \frac{F * (cos\theta + \mu*sin\theta)}{\mu}$
where $\displaystyle \mu$ is the coefficient of friction. Find $\displaystyle \theta$ so that W is a maximum.
Differentiate W by theta and set it equal to zero. You'll end up getting theta = arctan(mu).

3. Ah ha, I see. The F and mu are treated as constants. Caught me off guard.

So I took the second derivative and found it to be the maximum weight on that angle. Sound right?