What are the minimum and maximum values of theta for the moment equation?

[Altairs]

Homework Statement

The 70N force acts on the end of the pipe at B. determine the angles theta between 0 and 180 of the force that will produce maximum and minimum moments about point A.

Homework Equations

FBD is attached.

The Attempt at a Solution

I made the following equation then took its derivative and put it equal to 0. The problem here is that I only get one value of theta. the one which gives the maximum value of the moment. there isn't any other value of tan coming withing 0-180. How do I get the minimum value of theta from this method. Wasn't I automatically supposed to get two value of theta from the first derivative and then I could I have gone further to second derivative to check if it was min or max. I am stuck.

Equation :- $$M = (70cos\theta * 0.9) + (70sin\theta * 0.7)$$
Derivative :- $$= -63sin\theta + 49cos\theta$$

 

[tiny-tim]

I made the following equation then took its derivative and put it equal to 0. The problem here is that I only get one value of theta. the one which gives the maximum value of the moment. there isn't any other value of tan coming withing 0-180. How do I get the minimum value of theta from this method. Wasn't I automatically supposed to get two value of theta from the first derivative and then I could I have gone further to second derivative to check if it was min or max. I am stuck.

Equation :- $$M = (70cos\theta * 0.9) + (70sin\theta * 0.7)$$
Derivative :- $$= -63sin\theta + 49cos\theta$$

Hi Altairs!

(btw, I haven't seen the picture yet)

erm … sometimes it's maths, and sometimes it's just looking at the reality.

It often helps to draw a diagram (roughly).

The graph of the moment should look like a hill.

At 0º, the derivative is 49, which is positive; at 180º, it is -49, which is negative.

So the moment is already increasing at 0º, and is still decreasing at 180º.

So one of them may be a minimum …
​

 

[Altairs]

Sorry. Can't get it. Would be easier with a few equations.

 

[tiny-tim]

Hi Altairs!

(Still can't get the picture - I keep getting the please-log-in screen! )

At 0º, the moment is 63; it goes up until tantheta = 7/9; then it goes down until, at 180º, it is -63.

So the maximum is at tantheta = 7/9, them minimum is at 180º.