1How is the unbalanced torque produced? Is there any error in my force diagram ? The perpendicular distances of the tension from axis is coming out to be equal.
When a body is weighed on an ordinary balance we demand that the arm should should be horizontal if the weights on two pans are equal. Suppose the equal are put on two pans, the arm released. Is the torque of the two weights about the middle point(point of support) zero? If so, why does the arm rotate and finally become horizontal?
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1Is it always true?
Now suppose we make a balance such that the COM of the attached mass coincides with the axis. Will the balance remain at an inclination?
1As subhomoy pointed out, the centre of mass of the attached mass does not lie on the beam. It is lower.
I think its clear from my second figure.
49exactly i was developing on the element told by swordfish and so never thought of re-mentioning it..! :)
and the COM of the attached mass does not coincide with the point of suspension! :)
it is a bit down! :)
thus there is a stable equilibrium! :)
1If the mid point of the attached mass coincides with the axis the the torque produced due to the two equal halves of the attached mass would be equal.
1refer this
http://img11.imageshack.us/img11/9684/baler.jpg
P.S. Your force diagram is correct. But your force diagram for the balance is incorrect [3] (you missed the element I told)
49chalo..that what i was thinking..something is missing! :P
ok so now..
the 2 arms have generally equal lengths..putting equal mass on either, makes equal torque if and only if the arms are positioned horizontal...else there is unbalanced torque..
suppose the thing is tilted in right side, there is net anticlockwise torque..the system accelerates aunty-clockwise (:P)..
now the system becomes horizontal...torque is zero but the system has (angular)velocity (inertia of motion-(rotation)) and so doesnot stop and though it has zero torque acting, overshoots in the aunty clockwise direction...and now clockwise torque develops and opposes motion makes it stop and then makes movement in clockwise direction...then overshooting in clockwise direction and development of aunty clockwise torque..stop of motion and then starting of anticlockwise motion...
Thoeritically this oscillating motion would never stop..
but practically it does due to loss in (rotational) kinetic energy as air friction does negative work on the system (damping) :)
1Understanding comes later. First you told that the question is complete. You should have either posted the full complete question or have written 'refer this question on so and so page '.
I had to check in the book. You missed the most important thing- the arms are kept at an angle with the horizontal and released. Without it, there won't be any oscillating motion.
Back to your question, torque due to two equal weights seperately can never be 0. The total torque due to these equal weights is 0 always. In reality, there is a small mass attached at the point of support such that it has 0 moment when the balance is horizontal. But when it is displaced, this weight provides a restoring torque. So the beam becomes horizontal finally.
There might be other constructions of the balance too, but I told what I have seen.
1Does this sentence make sense to you?
"Suppose the equal are put on two pans, the arm released."