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Problem 38 Hard Difficulty
An object with weight $W$ is dragged along a horizontal plane by a force acting along a rope attached to the object. $\\$
If the rope makes an angle $\theta$ with the plane, then the magnitude of the force is $\\$
$$
F=\frac{\mu W}{\mu \sin \theta+\cos \theta}
$$ $\\$
where $\mu$ is a constant called the coefficient of friction. $\\$
(a) Find the rate of change of $F$ with respect to $\theta$. $\\$
(b) When is this rate of change equal to $0 ?$$\\$
(c) If $W=50$ Ib and $\mu=0.6$, draw the graph of $F$ as a function of $\theta$ and use it to locate the value of $\theta$ for which $d F / d \theta=0 .$ Is the value consistent with your answer to part (b)?
Answer
a) $\frac{d F}{d \theta}=\frac{\mu W(\sin \theta-\mu \cos \theta)}{(\mu \sin \theta+\cos \theta)^{2}}$
b) $\theta=\arctan \mu$
c) SEE SOLUTION
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Christabel M.
October 11, 2020
Differentiate with respect to t. y = a cos(t) + t^2 sin(t)
David Base G.
October 26, 2020
Finally, now I'm done with my homework
Catherine A.
October 27, 2020
it gives us more lesson to learn
Top Calculus 1 / AB Educators
Anna Marie V.
Campbell University
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Watch More Solved Questions in Chapter 3
Video Transcript
the problem given to us here we want to find the derivative of the trigger metric function. So first we're asked to find the rate of change of F. With respect to data. So here we're going to be using the question rule. So we're gonna have that D. F. E. Data. No mm is equal to below times the derivative of the high. So that's going to be um minus high time to the River of love. So what we end up getting is new which are Detroit is M. New W. Times Sine of theta minus new coast science data. Yeah. And then this is all going to be over new sign data plus coastline data. This whole thing is squared. That's the collection role. So that's how we express this. And then we also want to know when this is equal to zero. We see that's when the arc tangent of. We have the arc tangent of mu um So we can graph this function as well and see that this will be a consistent relationship.
California Baptist University
Top Calculus 1 / AB Educators
Anna Marie V.
Campbell University
Kayleah T.
Harvey Mudd College
Caleb E.
Baylor University
Kristen K.
University of Michigan - Ann Arbor
