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## #1 2012-04-12 20:50:50

hammana
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### Applied Math (a ladder, a cylinder)

Hi bobbym

I am proposing 2 exercises, associating theory with practice. They assume a basic knowledge of mechanics. Feel free to delete what you think is inappropriate in this forum.

It is observed that a ladder, uniform in design, length=6 m, mass=10 Kg, slips down whenever its angle with the floor exceeds 60°. We assume there is no friction on the wall.

a - If the ladder makes an angle of 65° with the floor, how far can a man of 60 Kg climb along the ladder before the ladder slips

b - What is the minimum angle of the ladder with the floor that allows the man to climb safely to the top of the ladder.

Consider a cylinder of wood, density=0.7 Kg/dm^3, length=100 cm, section square 10x10 cm, floating in a basin of water.

a - Why the cylinder can not remain floating vertically

b - A square slice of copper 10x10 cm, density = 8.92 Kg/dm^3, is fixed at the bottom of the cylinder. What is the minimum thickness of the copper slice, calculated to +/- .1 mm, that will allow the cylinder to float vertically (It is easier to use a trial and error method, or Excel or a computer for the calculation.)

c - A square slice of copper, 10x10 cm, 2.5 cm thick, is fixed at the bottoom of the cylinder, What is the height of the emerging part of the cylinder when it is at rest

d - The cylinder is pushed down until its top is at the water level, then left to oscillate freely. Neglecting the friction forces , and assuming g=9.8 m/sec^2, What is the period of its oscillations, Find the function y(t) giving the emerging part as a functio of time.

Last edited by hammana (2012-04-12 22:06:08)

## #2 2012-04-12 21:23:18

bobbym

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### Re: Applied Math (a ladder, a cylinder)

Hi hammana;

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #3 2012-04-12 21:58:43

hammana
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### Re: Applied Math (a ladder, a cylinder)

Hi bobbym

I think I made a wrong manipulation. Is it all right now?

## #4 2012-04-12 22:09:22

bobbym

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### Re: Applied Math (a ladder, a cylinder)

Hi;

Yes, it looks fine. Also the topic is acceptable. Thanks for posting it.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.