   Chapter 11.4, Problem 31E

Chapter
Section
Textbook Problem

# Optimization A force of 180 pounds acts on the bracket shown in the figure. (a) Determine the vector A B ⇀ and the vector F representing the force. (F will be in terms of θ .)(b) Find the magnitude of the moment about A by evaluating ‖ A B ⇀ × F ‖ .(c) Use the result of part (b) to determine the magnitude of the moment when θ = 30 ∘ .(d) Use the result of part (b) to determine the angle θ when the magnitude of the moment is maximum. At that angle, what is the relationship between the vectors F and A B ⇀ ? Is it what you expected? Why or why not?(c) Use a graphing utility to graph the function for the magnitude of the moment about A for 0 ∘ ≤ θ ≤ 180 ∘ . Find the zero of the function in the given domain. Interpret the meaning of the zero in the context of the problem

(a)

To determine

To calculate: The vector AB and the vector F representing the force of 180 pounds as shown below figure: Explanation

Given:

A force of 180 pounds acts on the bracket shown in the figure,

Calculation:

The free body diagram of above figure is given below:

Since one foot is equal to 12 inches. Now, converts the length of AB and AC from inches to feet.

From the above diagram, the length of AC is

AC=(15 inches)(1 feet12 inches)=54feet

And, length of BC is

BC=12 inches(1 feet12 inches)=1 feet

The vector AB is given as;

(b)

To determine

To calculate: The magnitude of the moment about A by evaluating the expression AB×F.

(c)

To determine

To calculate: The magnitude of the moment about A by evaluating AB×F when θ=30°.

(d)

To determine

To calculate: The angle θ when magnitude of the moment is maximum. At that angle determine the relationship between the vectors F and. Is it what you expected? why or why not?

(e)

To determine

To graph: Draw the function for the magnitude of the moment about A for 0θ180°. Find the zero of function in a given domain, interpret the meaning of zero in the context of the problem.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 