Equilibrium of Coplanar Forces

[Taniaz]

Homework Statement

In this experiment, a suspended metre-ruler lies in a series of equilibrium under non-parallel forces.

Homework Equations

The apparatus consists of the following. A metre rule suspended by strings which make an angle with the vertical. The strings run over pulleys which are clamped in retort stands. Slotted masses M are tied to the other ends of the strings and so a tension T = Mg is maintained in each string. Other slotted masses m are suspended by string tied centrally on the metre stick. Let the mass of the metre stick itself be n.

The Attempt at a Solution

I've setup the apparatus as required but I've been encountering a few issues. I've fixed the pulley as high as it can go on the retort stand. I've kept the distance from the string tied around on the metre stick to the stand around 10 cm on each side. It then says to place 600 g as M on both sides but says nothing about the mass in the centre m. When I place more than 300 g as M on both sides, the metre rule starts moving and reaches its maximum height and stops as it can't go any higher. So my first issue is I can't get it to 600 on both sides.
Secondly when I start adding weight in the centre as m, nothing happens. There's no gradual change in the setup moving downwards. And then when m reaches a particular mass, it just drops downwards.
The change in vertical length upon adding m is directly proportional to the mass m added but it doesn't seem. I've attached a picture of the setup.

 

[haruspex]

Your problem is that the points of attachment of the strings from the two end masses are still too close to the pulleys. This leaves only a narrow range of central masses that will lead to equilibrium, so you may easily add too much.

The change in vertical length upon adding m is directly proportional to the mass m added

Are you saying you think it should be proportional? Why?

 

[Taniaz]

I did try changing that distance too but it seemed to have no effect, I tried tying the string at distances of 10 cm, 15 cm, 20 cm and even 5 cm away from the central mass :/

 

[haruspex]

I did try changing that distance too but it seemed to have no effect, I tried tying the string at distances of 10 cm, 15 cm, 20 cm and even 5 cm away from the central mass :/

There's something unclear in the image. I can see where the string runs from the central mass over a pulley, but it then goes horizontally a short distance before descending to the side mass. Is it running over a second pulley that I cannot see?
If you had the strings attached very close to the ruler's centre, it should balance with the three masses equal (counting the ruler's mass as part of the central mass) and the strings at 30 degrees to the horizontal.

 

[Taniaz]

Yes it does, that's part of the pulley and it helps in clamping it to the retort stand. Is that the problem?

 

[haruspex]

Yes it does, that's part of the pulley and it helps in clamping it to the retort stand. Is that the problem?

No, that should be ok.
When you increase the central mass and let the system go, do you simply let go of it or lower it gently?
With 300g on each side, and the strings connected about 10cm from the centre, at what central mass does the ruler suddenly go all the way down, and by how much did you increase it at each step?

 

[Taniaz]

I simply let it go but it doesn't move until I add that particular mass which was about 500-600 g. The strings are not connected 10 cm from the centre, they're 10 cm or more from the other ends of the metre stick as per the instructions.
I tried pulling it down myself and when I stopped pulling it, it stopped moving and assumed this new position.

 

[haruspex]

I tried pulling it down myself and when I stopped pulling it, it stopped moving and assumed this new position.

Then there is too much friction somewhere. Check that the pulleys turn freely. You confirm that each of the two visible pulleys is actually a pair of pulleys, the smaller of the pair being hidden behind the clamp, yes? The strings are touching nothing except the masses and the perimeters of the pulleys?

 

[Taniaz]

For the ones I have, each pulley does not consist of a pair of pulleys, it's just the one that you can actually see in the picture. The strings are touching nothing but the masses. The masses sometimes hit the retort stand when I add the weights. What lengths of strings should I use? Does that play a role in this by any chance?

 

[haruspex]

For the ones I have, each pulley does not consist of a pair of pulleys, it's just the one that you can actually see in the picture. The strings are touching nothing but the masses. The masses sometimes hit the retort stand when I add the weights.

That does not fit with what I see in the image. I see each string attached to the ruler, passing up over a pulley, then continuing horizontally. It disappears behind part of the pulley arrangement, then reappears vertically down to the mass. What is it passing over or through in order to go from horizontal to vertical?

 

[Taniaz]

This is the type of pulley I have, the string actually goes over the horizontal part of the clamp before becoming completely vertical.