Tension in a string of mass

In summary: When the pulley is locked: What's the acceleration of the masses?The masses are at a constant velocity and they experience an acceleration of 9.8m/s2.
  • #1
chaoseverlasting
1,050
3

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?
 
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  • #2
A picture of the problem would be nice.
 
  • #3
Here's the diagram
 

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  • #4
chaoseverlasting said:
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?
 
  • #5
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?
 
  • #6
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?
 
  • #7
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?
 
  • #8
chaoseverlasting said:
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?
 

1. What is tension in a string of mass?

Tension in a string of mass refers to the pulling force exerted by the string on the objects it is attached to. It is a measure of how stretched the string is and is typically measured in newtons (N).

2. How does the mass of an object affect the tension in a string?

The mass of an object does not directly affect the tension in a string. However, a heavier object will require a greater force to accelerate it, which in turn can increase the tension in the string.

3. What factors can affect the tension in a string?

The tension in a string can be affected by factors such as the force applied to the string, the properties of the string (e.g. its material, length, and thickness), and the mass and acceleration of the objects attached to the string.

4. Why is tension important in physics?

Tension is important in physics because it is a fundamental force that allows objects to move and interact with each other. It plays a crucial role in many physical concepts, including gravity, friction, and elasticity.

5. How can tension be calculated in a string of mass?

The tension in a string can be calculated using the formula T=mg, where T is the tension (in N), m is the mass of the object (in kg), and g is the acceleration due to gravity (9.8 m/s² on Earth). Alternatively, the tension can also be calculated using the equation F=ma, where F is the force applied to the string (in N) and a is the acceleration of the object (in m/s²).

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