Conditions for pulleys and strings

[andyrk]

So that the the string doesn't break or move on its own due to unbalanced forces..

 

[voko]

The string actually does move: either with the pulley, if it is not skidding, or on top if it. Don't see a problem here.

Likewise, a difference in tension doses not necessarily break a string. Take a string, and hold it firmly in the middle. Then pull at one end. Clearly, the tension will be very great on one side of the string, and zero on the other. Yet it may stay intact.

 

[andyrk]

Yes the string won't break until it has reached its tensile strength..So what conclusion do we reach from here Voko about a massless pulley and its effects if it is not massless? Also, about the string being inextensible, why should it be inextensible, even if it behaves as a spring, what happens then?

 

[voko]

You should reach a conclusion here, not 'we'. Last time I checked, you had incorrect FBDs. Perhaps you should correct them.

 

[andyrk]

So the conclusion that I reach is that for massive pulley to rotate the tensions should be different in the string so that the string will move upon the pulley by itself or break if tensile strength is reached. If the tensions are equal over the massive pulley then the pulley doesn't move and the string simply skids upon the pulley. I don't know about an in extensible string. If you could lay your thoughts upon it I would be really grateful.

 

[voko]

I really don't see how you ended up with those conclusions. They are not conclusions, they are speculations at best, because you failed to back them up with a thorough FBD analysis.

Solve this: two masses a and b are hanging on a string though a pulley, which is a uniform thin ring of mass c and radius d. The string is massless and inextensible; static friction between the pulley and the string is very great. The pulley rotates about its axis without any friction.

 

[andyrk]

Why can't the tension remain same around the pulley even though it has mass? Ok the pulley needs to rotate so tensions are different, then how does a massless pulley rotate? The tensions are taken same even then it does rotate, then how is that?

 

[voko]

Why should the tensions be the same?

Regarding your question about the operation of massless pulleys: solve the problem above. Then see what happens with tensions as the pulley's mass goes to zero.