Question for the mathematicians

[WorAl]

OK, struggling with this one a little so need some back up.
You have a box sitting on a flat surface.
You lift one edge up 5 degrees (two corners off the floor).

You then lift one other corner off the floor by 5 degrees. So you now have two corners at a known height from the floor and another (the furthest from the point on the floor) at a random height.

How do you work out the height of the unknown corner and what angle that point is in relation to the floor?

I hope my illustration helps, explain.

What is H and what is alpha? thank you PH

ETA, is alpha still 5 degrees?

Edited by WorAl on Tuesday 14th September 12:14

[StressedDave]

From your picture, H = 10 + 20 = 30 and I'd find alpha from tan^-1(H / sqrt(l^2+w^2)) where l and w are the length and width respectively. If you like a combination of trig and algebra you can probably get it to a cleaner answer, given that as you've drawn it, l is 20/sin 5 and w is 10/sin 5 so l = 2w.

If you need a proof - think in terms of two orthogonal vectors. Effectively you're raising the whole of the back line of the box by 10 then rotating it by 5 degrees at 90 degrees to the original lift, so effectively the height H is l sin 5 + w sin 5...

ETA... if you're a design engineer, why do you need to ask the mathematicians of PH for this?

Edited by StressedDave on Tuesday 14th September 12:27

[WorAl]

StressedDave said:

ETA... if you're a design engineer, why do you need to ask the mathematicians of PH for this?

It's an argument we're having in the office. If I didn't have such a stty CAD system it could have been solved in 2 seconds by actually drawing it out in 3D.

Just trying to settle it with external sources that's all.

[V8mate]

alpha is way more than 5 degrees. To keep the first 5 degree lift static along the front plane, the second lift is just piling angle on top.

[StressedDave]

As a proper engineer you shouldn't need external sources , certainly not for sub A-level stuff like that. As for needing a CAD system to prove it...

[Davel]

My thoughts exactly........

[WorAl]

Roll your eyes all you like, when there are 3 people arguing a point and they all have different points of view, how do you argue that you're right, even if you do perform calculations for them (when they are performing calculations for their "theory") without having external sources or physically drawing the thing out?

Edited by WorAl on Tuesday 14th September 12:54

[StressedDave]

You're supposed to be an engineer, and thus never knowingly wrong... time to man up

[Landlord]

I'm disgusted with you WorAl. You've sullied the name of design engineers the world over. You should be ashamed. Get out! Hang up your cardigan, retract your propelled pencil and take your tupperware lunch-box with you. Never darken these hallowed doors again.

Seeing as this particular thread is mainly inhabited by engineers, I should point out that I was being sarcastic. Also, I don't actually know whether he has any of the items listed with which to take as he leaves. Finally, I realise that it would be physically very difficult for a lone human of typical dimensions to darken a door enough to justify the state of "being darkened". Thank you.

[Famous Graham]

Hang on...by lifting the third corner, you'll lower the opposite one and raise the one in between them.

So the "first edge" corners will have changed and alpha will be 5.

[W00DY]

As in the first post H will be 30 and then alpha can be found using trig.

[V8mate]

Famous Graham said:

Hang on...by lifting the third corner, you'll lower the opposite one and raise the one in between them.

So the "first edge" corners will have changed and alpha will be 5.

Not if you maintain that first angle; as in my comment above. The long front edge becomes a 'hinge' as the second lift occurs.



O/T: Did the book arrive ok?

[shirt]

i deleted my post, really shouldn't eat lunch, browse ph and work things out at the same time.

i get alpha = 6.68degrees, h = 29.848mm.

also, m&s mocha frappe mousse is amazing and much better than maths.

[Famous Graham]

@V8

Yeah, poorly worded question, tbh

And not yet - I think it's in Edinburgh tho (had a missed delivery wossname last week but the local PO are ste and haven't got around to actioning my redelivery request yet).

Edited by Famous Graham on Tuesday 14th September 14:10

[Davel]

Davel said:

My thoughts exactly........

Ah but I'm crap at maths and can't even follow any of the arguements!

[Vladimir Pukin]

That's NumberWang!

[Spiritual_Beggar]

Vladimir Pukin said:

That's NumberWang!

[WorAl]

What StressedDave, V8 and Shirt said, thank you fellas.

For FG: The 5 degrees on each edge has to be maintained.

[Famous Graham]

WorAl said:

You then lift one other corner off the floor by 5 degrees.

Should have been

WorAl said:

You then lift one other corner off the floor and adjust until the original corners are still at 5 degrees. What are H and alpha

If it had been worded correctly, I'd have got it straight off. No need for calculators or anything.

Note : May not be true

[WorAl]

You are of course correct it could have been worded better, I wasn't sure how well it was written when I posted, but since you're the only person out of 7 so far to not understand it, it mustn't have been that confusing, especially with my epic picture.