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Math Help - Find angle for max weight on incline

  1. #1
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    Find angle for max weight on incline

    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.
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  2. #2
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    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).
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  3. #3
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    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?
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