Moments question Mechanics June 2010 Watch

RBoss
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Hi all, was hoping someone could explain where I went wrong on this moments question on an OCR paper. The correct answer is 110N, I've attached both the question and my working

Thanks!

Attachment 536507536509Attachment 536507536509
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ak111
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The weight is 45g.
You can work out the angle theta by using the 0.15m length they've given you at the bottom to form a right angled triangle with the 0.3m.
Then take moments about P.
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voltz
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(Original post by RBoss)
Hi all, was hoping someone could explain where I went wrong on this moments question on an OCR paper. The correct answer is 110N, I've attached both the question and my working

Thanks!

Attachment 536507536509Attachment 536507536509
So you've made a simple error which has complicated this.

First, looking at the definition of a moment:
"Force multiplied by the PERPENDICULAR distance from the pivot"

If you look at the diagram, the force F is perpendicular the the slab of length 0.600m, so we dont have to resolve any angle.

Simple, equal 0.600F to the clockwise moment and solve for F which will give you the answer of 110N.

Hope this helped
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RBoss
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(Original post by voltz)
So you've made a simple error which has complicated this.

First, looking at the definition of a moment:
"Force multiplied by the PERPENDICULAR distance from the pivot"

If you look at the diagram, the force F is perpendicular the the slab of length 0.600m, so we dont have to resolve any angle.

Simple, equal 0.600F to the clockwise moment and solve for F which will give you the answer of 110N.

Hope this helped
I'm definitely overlooking something very obvious xD

I only formed the second equation cos theta = weight/F (using vertical resultant force = 0) in an attempt to eliminate the cos theta part from the moments equation, as the weight is not acting perpendicularly to the slab/slope. Surely only the normal component of the weight to the slope needs to be considered in the moments equation?
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Joinedup
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(Original post by RBoss)
I'm definitely overlooking something very obvious xD

I only formed the second equation cos theta = weight/F (using vertical resultant force = 0) in an attempt to eliminate the cos theta part from the moments equation, as the weight is not acting perpendicularly to the slab/slope. Surely only the normal component of the weight to the slope needs to be considered in the moments equation?
note: lengths on the exam paper diagram aren't to scale which could cause confusion.

You seem to have overlooked that the vertical component of F should be W/2... though you wrote it on line 1. Not sure if you've confused yourself by trying to make the vertical forces always equal W - but you don't want to do that when you're taking moments, There's a vertical component at the pivot but you can worry about that separately if you need to.

W=45*g = 441 N
cos ϴ = 1/2

fwiw I resolved F vertically and said

cos ϴ = F/Fvert
Fvert cos ϴ = F
W/2 cos ϴ = F

F=W/4
=110 N (3sf)

(there was no need to resolve horizontally for this question)

---
if would also work if you prefer to resolve parallel and perpendicular to the slab
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RBoss
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(Original post by Joinedup)
note: lengths on the exam paper diagram aren't to scale which could cause confusion.

You seem to have overlooked that the vertical component of F should be W/2... though you wrote it on line 1. Not sure if you've confused yourself by trying to make the vertical forces always equal W - but you don't want to do that when you're taking moments, There's a vertical component at the pivot but you can worry about that separately if you need to.

W=45*g = 441 N
cos ϴ = 1/2

fwiw I resolved F vertically and said

cos ϴ = F/Fvert
Fvert cos ϴ = F
W/2 cos ϴ = F

F=W/4
=110 N (3sf)

(there was no need to resolve horizontally for this question)

---
if would also work if you prefer to resolve parallel and perpendicular to the slab
Aha, yes. I was looking too much at the parallel/perpendicular components, without considering Fv = W/2, as the gradient of the slope is the same, and F has twice the vertical distance of W... *facepalm*

That's a major bit of thinking space recovered though - thanks a lot for the clear explanation
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