Questions on Mechanics (moments)

[faisal]

in the context of the lever, archimedes is recorded as saying
''give me a long enogh lever and i will move the earth''
explain in terms of moments the point archimedes was making
how can i tackle this question?, i know the principle of moments the sum of the clockwise direction=the sum of the anti clockwise (in equalibrium) i don't know how i can apply it to this question.
the second part of the question states
Comment on how pratical Atchimedes suggestion really is?

 

[arildno]

The magnitude of the FORCE we are able to generate has definite limits, but does that set a limit on how large MOMENT we may generate?

 

[dextercioby]

Just to verify yourcalcuations,IIRC the length of lever to really move the Earth out of it's trajectory should be something round 10^{20}m (it may as well be Km) which would have one end under the Earth & the other out of our Galaxy...


Daniel.

 

[clive]

I thought Arch. said "Give me a place to stand on, and I will move the earth"

 

[faisal]

The magnitude of the FORCE we are able to generate has definite limits, but does that set a limit on how large MOMENT we may generate?

i don't understand, can you elaborate ?

 

[dextercioby]

What's the definition of the force's moment...??(In vector form,please)

Daniel.

 

[supersix2]

A moment is the cross product of force and distance or the magnitude of the moment is Fd*sin(b) where b is the angle between the force and the moment arm (lever). Think of it this way:
If you want to push a door open you would push perpendicular to the door at the farthest point from the hinge giving you the maximum moment on the door. If you were to push the door at some angle other than 90 degrees to it you would have a smaller moment because only a component of the force would be acting on the moment arm.

Now think of it this way. You can only apply a certain amount of force because of certain physical constraints (such as your own strength) but you need to move a very heavy object. The answer is to multiply the force you can generate by some number to move the large object (i.e. a lever) . So as Archimede's was saying "Give me a big enough lever and I can move the Earth" it would be theoretically possible.

So what is a moment?

Its F x r (F is your force vector and r is your distance vector.)

The magnitude being Fd*sin(b) or if your force is exactly perpendicular to the moment arm simply Fd.