Find angle for max weight on incline

Shaz · #1 $Old$ October 23rd, 2009, 11:24 AM

So I have been given a problem to do that involves an incline with an angle $\theta$ . 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 $\theta$ with the horizontal slope by a force F is
$W = \frac{F * (cos\theta + \mu*sin\theta)}{\mu}$
where $\mu$ is the coefficient of friction. Find $\theta$ so that W is a maximum.

rn443 · #2 $Old$ October 23rd, 2009, 12:36 PM

Quote:

Originally Posted by Shaz $View Post$

So I have been given a problem to do that involves an incline with an angle $\theta$ . 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 $\theta$ with the horizontal slope by a force F is
$W = \frac{F * (cos\theta + \mu*sin\theta)}{\mu}$
where $\mu$ is the coefficient of friction. Find $\theta$ so that W is a maximum.

Differentiate W by theta and set it equal to zero. You'll end up getting theta = arctan(mu).

Shaz · #3 $Old$ October 24th, 2009, 09:17 PM

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?