How Does Unlocking the Pulley Affect String Tension?

[chaoseverlasting]

Homework Statement

Two masses of 4kg and 6kg are hanging from a pulley which is hung by a string. Initially the system is locked (the pulley is not allowed to rotate), and then it is released. Find the ratio of tension in the string holding the pulley before and after release.

The Attempt at a Solution

How the heck will the tension change? Wont it be the same?

 

[radou]

A picture of the problem would be nice.

 

[chaoseverlasting]

Here's the diagram

 

[Doc Al]

How the heck will the tension change? Wont it be the same?

Consider the forces acting on each mass and apply Newton's 2nd law. What's different between the "locked" and "free to fall" cases?

Hint: Imagine holding a string that's tied to a rock. What's the tension in the string? Now let go of the string. Is the tension in the string the same?

 

[chaoseverlasting]

No, tension wouldn't be same. Am I supposed to take friction into consideration here? Even so, how would the tension in the upper string change? There's no extra force acting on it. The tension in the strings holding up the masses will change, but in the one holding the whole system, where's the change?

 

[Doc Al]

Ignoring the weight of the pulley itself (consider it massless), how does the tension in the string at the top relate to the tension in the string attached to the masses?

 

[chaoseverlasting]

That tension is equal to the sum of the tension in the strings attached to the masses. T=2T' where T' is the tension in the string holding the masses. But T' is a constant. Its one string, and tension in it is uniform. How does it change?

 

[Doc Al]

That tension is equal to the sum of the tension in the strings attached to the masses. T=2T' where T' is the tension in the string holding the masses.

Correct!

But T' is a constant. Its one string, and tension in it is uniform. How does it change?

The tension is uniform throughout the string, but unlocking the pulley makes a huge difference. Remember my example of the rock on a string? If the rock is allowed to fall, the string tension will change. Similarly, if the masses are allowed to fall--by unlocking the pulley--the string tension will change.

When the pulley is locked: What's the acceleration of the masses?
What about when the pulley is unlocked?