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Old Jan 15th 2011, 12:54 AM   #1
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Hi, I have some questions in mechanics and I need some help.

1. In a container with constant volume, we have an ideal gas. The average kinetic energy of molecules is Wk. We heat the gas, so the temperature doubles. What is average kinetic energy of molecules now?

2. The body with weight Fg hangs on strings. With what force is each string stretched?

3. We drop a stone from 3 m. What is the speed of the stone, just before in hits the floor, if the loses of energy, due to air drag are 20%?
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Old Jan 15th 2011, 08:42 AM   #2
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We know that PV = 1/3 Nmc^2 and PV = NkT (where c is the mean velocity of gas particles)

We can simplify this to:

mc^2 = 3kT


1/2 mc^2 = 3/2 kT

Which means that

K.E. is directly proportional to temperature T.


Resolve the tensions in each string.The vertical components of both tensions add up to Fg. The horizontal components of both tensions add on to zero (each is equal to a certain F that I introduced).

The vertical component provided by one string is Tsin(45) = Fg/2.
The same vertical component is provided by the other string.

Along the horizontal, we have Tcos(45) = F

And T^2 = (Fg/2)^2 + F^2

Of course, that's the 'calculation' part of it. If you can 'see' it right from the start, you get the answer easily. But that's something you see after quite some practice.

Find the potential energy of the stone.
Hence, find the kinetic energy the stone normally gets after falling 3 m without air resistance.
Find the kinetic energy that the stone actually has, after accounting for air resistance.
Convert kinetic energy to a speed.

Can you give those a try?

[Note that there is nothing involving torque whatsoever in those questions.]
Jerry (Got my results!)
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