Optimization A force of 180 pounds acts on the bracket shown in the figure. (a)

Chapter 11, Problem 31

(choose chapter or problem)

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

(a) Determine the vector \(\overrightarrow{A B}\) and the vector F representing the force. (F will be in terms of \(\theta\).)

(b) Find the magnitude of the moment about A by evaluating \(\|\overrightarrow{A B} \times \mathbf{F}\|\).

(c) Use the result of part (b) to determine the magnitude of the moment when \(\theta=30^{\circ}\).

(d) Use the result of part (b) to determine the angle \(\theta\) when the magnitude of the moment is maximum. At that angle, what is the relationship between the vectors F and \(\overrightarrow{A B}\)? Is it what you expected? Why or why not?

(e) Use a graphing utility to graph the function for the magnitude of the moment about A for \(0^{\circ} \leq \theta \leq 180^{\circ}\). Find the zero of the function in the given domain. Interpret the meaning of the zero in the context of the problem.

Text Transcription:

overrightarrow A B

theta

theta=30^circ

0^circ leq theta leq 180^circ