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# M2: Centre of Mass question watch

1. Hi all,
This question has been bothering me for days and I just cannot solve it :

In the OCR Mechanics 2 book it is on page 86, it is Ex 5B, Question 7.

The object shown is made of two plates of the same width and thickness welded together. The object is placed on a horizontal floor with the plates at equal angles to the horizontal. BD is of length 10cm. What is the greatest possible length for AC if the object is to stand on the floor in equilibirum.
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2. Well, I get 42.36cm.

If that checks with your book's answers I'd be happy to give hints as to how I arrived at it. Having said that my methods are probably a little bit unusual.
3. Yeah your right, the book says 42.4(3sf)

Any hints would be great

Hints:

When the length is a maximum about which point will it be about to tip?

Let the length AC = x.

Let the angle with the horizontal be

Now work out the sum of the moments about the point it is going to tip, and set it equal to zero.
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Secondly say that AC is k times the length of BD.

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Third, call the distance DC L.

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Finally use all that and a bit more to write an equation equating clockwise and anticlockwise moments
6. (Original post by ghostwalker)
Agreed.

Well OP, there you go, two sets of hints.

Incidentally, I did not find it necessary to consider the angle at all.
7. An interesting feature, is that the angle cancels out (in my working), so the maximum length is independent of the angle.

So, at maximum length, if you fixed a pivot at the point about which it would tip, and a hinge at the join then you can slilde the free base back and forth, and the centre of gravity always remains over the pivot!
8. Thanks for the help but I still cant seem to crack it. I'll try and go through it step by step.

I think that when AC gets really long, it will tip to the left, so am I right in thinking A is tipping towards the floor?

Following the other post I tried taking moments about D.
5 mg sin(theta) + ... I wasnt sure how to take into account the weight of AC.

I think if I call AC x, then the weight will act at x/2 .

Thanks for the help so far guys, my morale has been lifted already just knowing that this problem can be solved lol.
9. My scanner wont work so instead of my sketch plus original doodles you get this.

Attachment 74063

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