Massless pulley and acceleration

[iloveannaw]

Homework Statement

In the following situation (see attachment) both pulleys and the string have zero mass. If m_{2} > m_{1} we would expect a net force and therefore an acceleration in the direction of the net force. But if pulley 2, which is moveable, has no mass the sum of the forces acting on it is zero. How does this affect the acceleration of the blocks (which I would expect to have same acceleration - ideal string etc.)?

Homework Equations

Newton's II

 

[shyta]

a moveable pulley 2 only means that it move along the string, without a change in its x coordinate. i.e. meaning it will only move up or down depending whether m1 > or < m2.

what is your workings?

 

[iloveannaw]

hi thanks, i realize it will only move vertically - my question is since both blocks should have the same acceleration, pulley 2 will also have that acceleration (whatever it may be) but since no net force can act on that pulley how can it have an acceleration?

does this mean that the acceleration is zero?

thanks

 

[shyta]

correct me if I am wrong but massless objects are an ill-defined concept to begin with. Considering F = ma
a= F/0 or infinity in other words.

I wouldn't say it's 0 acceleration.

 

[iloveannaw]

wouldn't that mean the tension in the string was also infinite? btw the actual question was to find tensions T_1 and T_2.

 

[shyta]

No. Tension is a force, do not confuse it with resultant force!
In a way, it is true that the acceleration of the string is infinity as well.

You should be considering either of the mass blocks as a FBD

 

[iloveannaw]

are you sure? if we look at m_1: it must have the same acceleration as m_2 and pulley_2.

If acceleration of pulley_2 was infinite then the acceleration of m_1 would also be inf. and so would the force acting on it (in other words the tension), since m_1 != 0. Since we are dealing with a massless string the tension is constant throughout. This means the tension at any part of the string would be infinite.

 

[shyta]

The more mass an object has, the slower the acceleration when subjected to the same force.
No doubt the pulley will experience infinite acceleration, but do not simply equate this to be the same as m1's acceleration.
There are many other factors to consider such as how the pulley is attached to the block? If it is rigidly attached, then there would be a retarding force by m2 on the pulley, during the fall, if the acceleration of the pulley is faster than that of the block, but then again, the faster acceleration of the pulley does not affect m2's acceleration either because it's massless to start with rememeber?

Don't confuse yourself, work it out like i said. consider a fbd on m1 and m2.

 

[iloveannaw]

sorry had to go to a lecture,

yeah, i should have said that the very first thing i did was to draw free body diagrams and try to work out the sum of the forces in the relevant directions for the bodies involved.

thanks for your help so far but I would prefer a straight answer to my original question. I don't know how the pulley is attached to the block, I imagine it is a chain or another piece of string.

 

[Cilabitaon]

I don't think there's any big deal about how the objects are connected, it's a simple problem. I do have a problem with your diagram, however; to me it seems that m_1 is attached directly to the massless string, whereas m_2 is not even connected to the string, only to the pulley(in turn - connected to the string).

Isn't the question simply asking what would happen if m_2 were to suddenly become massless?

If so;
1. What happens to each block if m_2 &gt; m_1 (as stated)?

2. What happens when m_2 &lt; m_1

 

[ehild]

How does this affect the acceleration of the blocks (which I would expect to have same acceleration - ideal string etc.)?

The accelerations of the blocks are not the same.
The net force F on the massless pulley (m=0) must be zero at arbitrary acceleration as F=ma=0.

ehild