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M2 Statics - Help

In the attached solution, (to the also attached question), I don't understand how they've got the perpendicular distance to 'T' as '2asin30'? (for part a)

It's probably something very obvious but I'm so used to doing the standard 'ladder against wall' type question that I've forgotten how to do these slightly non-standard questions.

Thanks in advance.
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Hey,

So the distance to 2 from A when they've taken moments, is 2a. That's where that part comes from, As T has to be perpendicular it isn't touching that angle of 30 degrees anymore, and remember cos always touches the angle. You could use sin30 or cos60 and you'd get the same result :smile:

Hope that helped
Reply 2
Avatar for nerak99
nerak99
13
The moment is the perpendicular distance to the line of action of the force multiplied by the Force.

In the diagram if you extend the line of action of T to the left to form a Right Angled Triangle with 2a as the hypotenuse you will get to a point where the line of action of T and a line to the point A form the right angle of the Traingle which has 2a as the hypotenuse. Call this point X.

It is the distance AX which is 2aSin30. Times by T to get the moment.

Hope that's clear.
Original post by nerak99
The moment is the perpendicular distance to the line of action of the force multiplied by the Force.

In the diagram if you extend the line of action of T to the left to form a Right Angled Triangle with 2a as the hypotenuse you will get to a point where the line of action of T and a line to the point A form the right angle of the Traingle which has 2a as the hypotenuse. Call this point X.

It is the distance AX which is 2aSin30. Times by T to get the moment.

Hope that's clear.


' if you extend the line of action of T to the left to form a Right Angled Triangle with 2a as the hypotenuse' Not quite sure I understand this. Diagram please?
Original post by nerak99
The moment is the perpendicular distance to the line of action of the force multiplied by the Force.

In the diagram if you extend the line of action of T to the left to form a Right Angled Triangle with 2a as the hypotenuse you will get to a point where the line of action of T and a line to the point A form the right angle of the Traingle which has 2a as the hypotenuse. Call this point X.

It is the distance AX which is 2aSin30. Times by T to get the moment.

Hope that's clear.


Is this correct?

Or is the right angle meant to be between the line AX and the line of action of T?

(@Zacken ?)
(edited 7 years ago)
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Updated diagram. Is this correct? @nerak99 @Zacken


Edit: Damn, this can't be right cause 2a isn't the hyptotenuse and thus 2asin30 wouldn't give the distance AX. Does this mean the right angle should be between the line AX and the line of action of T? Can anyone do a correct diagram please?
(edited 7 years ago)
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SOMEONE PLEASE REPLY!!! Is this the correct way??
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Reply 7
Avatar for nerak99
nerak99
13
Hey sorry. Went to bed. Find attached a diagram which I hope makes it clear.

The difficult issue is defining the line of action and the perpendicular distance. If you imagine passing some point, your point of closest approach is the perpendicular distance we are after. For all sorts of reasons this forms a right angle between the line of action and the line from that point to the place about which we are taking moments.
Photo on 17-06-2016 at 09.05.jpg93.6KB

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