a book math solution that got me confused (m2)

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thebrahmabull
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Here's the question and solution:
Image

What got me confused is that they labeled 45degree in such a place which seems to suggest pcos45 as the red line below:

Image

But here's what I think: in the expression for M(A), if pcos45 was the red line then it would pass through A and so would the green line so neither of them can be pcos45 when taking moments about A. Therefore in the M(A) expression pcos45 must be either the blue line or the orange line. I believe the orange line does not exert any moment here so it must be the blue line. Someone please say if I am right or wrong.
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davros
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(Original post by thebrahmabull)
Here's the question and solution:
Image

What got me confused is that they labeled 45degree in such a place which seems to suggest pcos45 as the red line below:

Image

But here's what I think: in the expression for M(A), if pcos45 was the red line then it would pass through A and so would the green line so neither of them can be pcos45 when taking moments about A. Therefore in the M(A) expression pcos45 must be either the blue line or the orange line. I believe the orange line does not exert any moment here so it must be the blue line. Someone please say if I am right or wrong.
I'm not quite sure what method you've been taught, but since P acts along CD, when you take moments about A you want the perpendicular distance from A to CD, so what you should be doing is drawing a straight line that meets CD at right angles and then working out the length of that line from the sides and angles you already know.
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thebrahmabull
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(Original post by davros)
I'm not quite sure what method you've been taught, but since P acts along CD, when you take moments about A you want the perpendicular distance from A to CD, so what you should be doing is drawing a straight line that meets CD at right angles and then working out the length of that line from the sides and angles you already know.
Thanks for the response! I haven't been taught, I am self teaching by looking at books and so it gets frustrating some times. What I was thinking is that the thrust in the rod P can be broken down into its horizontal and vertical component. m(A): pcos45 (the blue line force aka the vertical component of p) x 1 = 40g x 1.5

Is there anything wrong doing it this way?
Also I wanted to know that if the orange force (the horizontal component of p)would exert a moment about A. Thanks again.
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davros
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(Original post by thebrahmabull)
Thanks for the response! I haven't been taught, I am self teaching by looking at books and so it gets frustrating some times. What I was thinking is that the thrust in the rod P can be broken down into its horizontal and vertical component. m(A): pcos45 (the blue line force aka the vertical component of p) x 1 = 40g x 1.5

Is there anything wrong doing it this way?
Also I wanted to know that if the orange force (the horizontal component of p)would exert a moment about A. Thanks again.
It's a long time since I studied Mechanics formally, so I wouldn't want to say absolutely that there isn't another method of thinking about things.

But what I would say is this: you are generally going to find life a lot easier if you do things the 'official' way - at least when you start out learning new topics. So somewhere in your book (either M1 or M2, whenever they introduce this topic) you should have a definition of taking a moment of a force about a point which should involve working out the perpendicular distance to the line of action of the force from the point. This is the definition I would stick to in the beginning. Later on, when you're more comfortable with the topic, you can experiment and see if you can arrive at the same result by a different route.

Looking at components of a force is generally most helpful when you're resolving e.g. when you have forces acting in all directions and you want to simplify things by looking at what happens in 2 perpendicular directions, typically up-down and left-right.
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thebrahmabull
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(Original post by davros)
It's a long time since I studied Mechanics formally, so I wouldn't want to say absolutely that there isn't another method of thinking about things.

But what I would say is this: you are generally going to find life a lot easier if you do things the 'official' way - at least when you start out learning new topics. So somewhere in your book (either M1 or M2, whenever they introduce this topic) you should have a definition of taking a moment of a force about a point which should involve working out the perpendicular distance to the line of action of the force from the point. This is the definition I would stick to in the beginning. Later on, when you're more comfortable with the topic, you can experiment and see if you can arrive at the same result by a different route.

Looking at components of a force is generally most helpful when you're resolving e.g. when you have forces acting in all directions and you want to simplify things by looking at what happens in 2 perpendicular directions, typically up-down and left-right.
Thanks! I will try to follow what you said
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Ayman!
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(Original post by thebrahmabull)
Also I wanted to know that if the orange force (the horizontal component of p)would exert a moment about A. Thanks again.
If you're talking about the force going through C, yes, it does exert a moment as the perpendicular distance from the pivot is 1 m.
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