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Stuck on a maths question about moments


Samuel
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Hi all, I have been working through my textbook in preparation for the a-level exams in autumn and have found a question I cannot solve and was hoping someone could take a look and let me know where I'm going wrong. I have attached my partial solution and the question bellow (Q6)(sorry they are sideways ahah)

IMG 0787[1]
IMG 0789[1]

Thanks Sam

 

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Zeeshan Ahmed
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Hi sam

Everything you wrote was correct, except the “8000 / cos(theta)”

This is a common mistake, you basically resolved it slightly wrong

Have a look at my diagram below, specifically the green part.

CEBA4249 9BC9 454C 97DE 75967BE05F03

Thw “8000N” going downwards should be the hypotenuse of the green triangle, so then you can do the “crush the angle” resolving to get 8000cos(theta) which would be perpendicular force to the rod.

Tell me if you’re still confused

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Samuel
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@zeeshan

OK thanks that makes sense. But how did you know that that was the right way to draw the diagram was it just from experience or does the length you're trying to find always have to be the adj? 

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Zeeshan Ahmed
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@samuel-4

When you're in that situation, always treat the weight going down as the "hypotenuse" - its kind of from doing lots of similar questions + logically it make sense

This is because when you resolve forces, the resolved force should be less than the original force.

However, if you don't treat the weight as the hypotenuse, when you resolve it you can end up with a force thats greater than the weight, which doesn't make sense.

Resolved forces should be smaller than the original force being resolved

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Samuel
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@zeeshan

Ok thanks again i'm a lot clearer on resolving now.

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Further_Maths_Student
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I understand the line of reasoning, but if you could explain why "resolved forces should be smaller than the original force" I feel like that would increase mt understanding

Thanks

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Samuel
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@further_maths_student

I think it is because you are trying to find how much of weight is acting perpendicular to the bridge and so it would not make  sense if this value was greater than that of the total weight.

 

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Leanorad
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@samuel-4

Correct

@further_maths_student

Its got to do with the idea that if you're pushing something or pulling something in a certain direction, it doesn't mean all that force is going to translate into the resolved version

image

Just because you're pushing this block with 100 newtons of force, depending on the angle you're pushing it at, its only gonna feel a fraction of it in the horizontal direction. The smaller the angle of theta you push it at, the more its gonna feel (cos theta tends to 1 and theta gets smaller and smaller). But it will always be less than 100 newtons.

Sorry if I got a bit too technical haha

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Further_Maths_Student
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@leanorad

Makes sense. Cheers for the diagram

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