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Thread: Expression in Terms of Theta

  1. #1
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    Expression in Terms of Theta

    A crate weighing $\displaystyle w$ pounds sits on a ramp positioned at an angle of $\displaystyle \theta$ with the horizontal. The forces acting on this crate are modeled by the equation $\displaystyle Mw cos \theta = w sin \theta$ , where $\displaystyle M$ is the coefficient of friction. What is an expression for $\displaystyle M$ in terms of $\displaystyle \theta$ ?

    a) $\displaystyle M = tan \theta$

    b) $\displaystyle M = sec \theta$

    c) $\displaystyle M = cot \theta$

    d) $\displaystyle M = csc \theta$
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  2. #2
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    Quote Originally Posted by ThaBeretta View Post
    A crate weighing $\displaystyle w$ pounds sits on a ramp positioned at an angle of $\displaystyle \theta$ with the horizontal. The forces acting on this crate are modeled by the equation $\displaystyle Mw cos \theta = w sin \theta$ , where $\displaystyle M$ is the coefficient of friction. What is an expression for $\displaystyle M$ in terms of $\displaystyle \theta$ ?

    a) $\displaystyle M = tan \theta$

    b) $\displaystyle M = sec \theta$

    c) $\displaystyle M = cot \theta$

    d) $\displaystyle M = csc \theta$
    Divide through by $\displaystyle wcos(\theta)$:

    $\displaystyle M = \frac{wsin(x)}{wcos(x)}$

    w will cancel out and what does sin(x)/cos(x) equal
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  3. #3
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    $\displaystyle M = \frac{wsin(x)}{wcos(x)}$is equal to $\displaystyle tan \theta$ . Thus the answer is choice "a". Thanks again!
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