Be familiar with the Atwood machine

[path_finder]

Consider two masses, m1 and m2, connected by a light inextensible string which is suspended from a light frictionless pulley, as shown in Fig.31.
Let us again apply Newton's second law to each mass in turn.
Without being given the values of m1 and m2, we cannot determine beforehand which mass is going to move upwards.
Let us assume that mass m1 is going to move upwards: if we are wrong in this assumption then we will simply obtain a negative acceleration for this mass.
The first mass is subject to an upward force T, due to the tension in the string, and a downward force m1g, due to gravity.
These forces cause the mass to move upwards with acceleration a = (T/m1) - g
The second mass is subject to a downward force m2g, due to gravity, and an upward force T, due to the tension in the string.
These forces cause the mass to move downward with acceleration a = g - (T/m2)
Now, the upward acceleration of the first mass must match the downward acceleration of the second, since they are connected by an inextensible string.
Hence, equating the previous two expressions, we obtain
T = g x (2x m1 x m2) / (m1 + m2)
a = g x (m2 - m1) / (m1 + m2)
As expected, the first mass accelerates upward (i.e., a>0) if m2 > m1, and vice versa.
Note that the acceleration of the system is less than the full acceleration due to gravity, g, since both masses contribute to the inertia of the system, but their weights partially cancel one another out.
In particular, if the two masses are almost equal then the acceleration of the system becomes very much less than g.
Incidentally, the device pictured in Fig.31 is called an Atwood machine, after the eighteenth Century English scientist George Atwood, who used it to ``slow down'' free-fall sufficiently to make accurate observations of this phenomena using the primitive time-keeping devices available in his day.

(excerpt from the following page: http://farside.ph.utexas.edu/teaching/3 ... ode48.html)

[path_finder]

And now someone should be able to explain to me the functioning of this old Atwood machine...

[DrWhat]

path_finder, where did you find this machine image?

Thanks

Damian

[path_finder]

Dear DrWhat,
From the book of Johann Joachim Becher 'Technica Curiosa, sive mirabilia artis' (page 732), published in Nürnberg 1664

The full book can be downloaded here (80Mo)
http://books.google.fr/books/download/P ... 0R7RwBme1g

The cover is here:
http://books.google.fr/books?id=RSsjwCR ... sQ6AEwAjge

Just the drawing can also be seen here (at the middle of the page):
http://www.hp-gramatke.net/perpetuum/en ... ge0220.htm