Centre of mass further mechanics 2 edexcel

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Piano enthusiast
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Question attached (from edexcel FM2 textbook) and working out attached too.
I seem to be getting the first bit of the question wrong - the numerical value of tanà.
I got the value:
tanà = (12+5√15)/21
But the book gives
Tanà = (√375)/25 = (√15)/5

This gives the final disparity in my answer:
m ≈ 0.0157M
Whereas book gives:
m ≈ 0.0343M

I'd greatly appreciate any help as to where I went wrong with the geometry
Many thanks
Last edited by Piano enthusiast; 1 month ago
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It's the challenge question at top, attached images for better visibility and I've attached the working out in the answers of the book but the book doesn't really say how it got the value for tanà
Last edited by Piano enthusiast; 1 month ago
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mqb2766
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The model solution uses simple pythagoras. The hypotenuse (squared) is 1000 as its 30^2 + 10^2 so the opposite (squared) is 1000-25^2 = 375. So tan(theta) = opp/adj = sqrt(375)/25.

Note theta here is the angle from the vertical to OG. So add on atan(10/30) to go from OG to OE to get "a".

This gives a~0.98 which satisfies the basic trig
25 = 30cos(a) + 10sin(a)
which would have been another way to derive it. Though pythagoras is a bit simpler.

Checking your solution now, but I suspect you've overcomplicated it a bit. Your solution also gives a~0.98. So I suspect they've equated theta and "a" whereas they're offset by atan(10/30).
Last edited by mqb2766; 1 month ago
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(Original post by mqb2766)
The model solution uses simple pythagoras. The hypotenuse (squared) is 1000 as its 30^2 + 10^2 so the opposite (squared) is 1000-25^2 = 375. So tan(a) = opp/adj = sqrt(375)/25.

This gives a~0.98 which satisfies the basic trig
25 = 30cos(a) + 10sin(a)
which would have been another way to derive it. Though pythagoras is a bit simpler.

Checking your solution now, but I suspect you've overcomplicated it a bit
Ah ok many thanks
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mqb2766
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(Original post by Piano enthusiast)
Ah ok many thanks
I was editing the previous post/still checking when you replied. Your angle is correct, though a bit longer.

It looks like the model solution has assumed that theta is "a" when comparing to the COM and is therefore wrong.

Note you could do
tan(A+B) = ...
to check whether your surd answer is equal to the sum of the two angles (tan). It will be, but its a useful check.
Last edited by mqb2766; 1 month ago
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(Original post by mqb2766)
I was editing the previous post/still checking when you replied. Your angle is correct, though a bit longer.

It looks like the model solution has assumed that theta is "a" when comparing to the COM and is therefore wrong.

Note you could do
tan(A+B) = ...
to check whether your surd answer is equal to the sum of the two angles (tan). It will be, but its a useful check.
Ah yes, tanA = (√15)/5 and tanB = 1/3,
Tan(A+B) gives the angle I originally got, so my answer was correct then?
This further mechanics 2 book has quite a few errors in the answers
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mqb2766
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(Original post by Piano enthusiast)
Ah yes, tanA = (√15)/5 and tanB = 1/3,
Tan(A+B) gives the angle I originally got, so my answer was correct then?
This further mechanics 2 book has quite a few errors in the answers
Yours looked about right, but I've not done a carefui/full working of the problem. The book has that wrong "typo" in the method, but the method seems ok otherwise and yours was basically the same.
Last edited by mqb2766; 1 month ago
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