💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

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)?

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

01:02

Frank L.

04:28

Clarissa N.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

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

Baylor University

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:10

An object with weight $W$ …

04:40

00:35

An object with weight $ W …

01:49

The force $F($ in Newtons)…

01:07

The forces acting on an ob…

00:19

The forces acting on a…

03:56

In Fig. $6-23,$ a sled is …

01:35

Holding on to a towrope mo…

05:14

A rope with mass $m_{r}$ i…

02:56

A uniform beam of length $…

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.

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

An object with weight $W$ is dragged along a horizontal plane by force actin…

An object with weight $W$ is dragged along a horizontal planeby a force …

An object with weight $ W $ is dragged along a horizontal plane by a force a…

The force $F($ in Newtons) required to move a box of mass $m \mathrm{kg}$ in…

The forces acting on an object weighing $W$ units on an inclined plane posit…

The forces acting on an object weighing units on an inclined plane…

In Fig. $6-23,$ a sled is held on an inclined plane by a cord pulling direct…

Holding on to a towrope moving parallel to a frictionless ski slope, a 50 $\…

A rope with mass $m_{r}$ is attached to a block with mass $m_{b}$ as in Figu…

A uniform beam of length $L$ and mass $m$ shown in Figure PI2.16 is inclined…