How is tension in a string affected by moment of inertia?

In summary, the tension in the string for block 1 (causes counter clockwise torque) will act against the acceleration of block 2 (causes clockwise torque). But block 1 still moves TO THE RIGHT, when the only force acting on it is the tension in the string, which supposedly acts TO THE LEFT against the acceleration of block 2.
  • #1
Luke0034
26
1

Homework Statement



I'm in need of a more conceptual answer, rather than numerical.

Say you have a block on a horizontal frictionless table (block 1). Then you have a string tied to block one and strung over a pulley that is at the right end of the table (the pulley has mass). On the other end of the pulley, there is another block hanging there connected by the same string (block 2). So the tension in the string will be different for block 1 and block 2.

I'm trying to figure out a way to find the acceleration of the system. I know that gravity will act on block 2 and cause it to accelerate downwards. So block 2 will cause a clockwise torque on the pulley. I'm confused about block 1. How would you find the tension in the string for block 1? Since there's no friction, shouldn't block 1 not resist the force that block 2 is providing?

I found a source online that says the tension in the string for block 1 (causes counter clockwise torque) will act against the acceleration of block 2 (causes clockwise torque). But here's my question: If the tension in the string for block 1 is resisting the acceleration of block 2, then why does block 1 still move TO THE RIGHT, when the only force acting on it is the tension in the string, which supposedly acts TO THE LEFT against the acceleration of block 2.

Homework Equations



(T2 * R) - (T1 * R) = 1/2MRR * (a/R)
  • So in this equation you can see that tension for block one acts against the tension for block 2.

mg - T2 = m2 * a
  • One of the equations to find the acceleration of system

T1 = m1a
  • So here it says that the tension in the string for block 1 equals the force applied to block 1. So why does block 1 move to the right when it's tension is supposedly acting to the left?
  • T1 acts to the left (counter clockwise torque) and T2 acts to the right (clockwise torque)... so why does block one move to the right, when the only force acting on block one is T1 (which acts to the left)?

The Attempt at a Solution



Again, not numerical, just conceptual explanation would be great. Thanks in advance!
 
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  • #2
Luke0034 said:
shouldn't block 1 not resist the force that block 2 is providing?
It has inertia, which means it resists acceleration.
Luke0034 said:
why does block 1 still move TO THE RIGHT, when the only force acting on it is the tension in the string, which supposedly acts TO THE LEFT
Tension (likewise compression) is better thought of as pairs of opposing forces. Pick a small element of the string. The tension provides a force to the right on the right hand of the element and a force to the left on the left.
See section 2 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/
 
  • #3
haruspex said:
It has inertia, which means it resists acceleration.

Tension (likewise compression) is better thought of as pairs of opposing forces. Pick a small element of the string. The tension provides a force to the right on the right hand of the element and a force to the left on the left.
See section 2 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/

Wow, that was actually really easy to understand. Thanks for the simple straightforward explanation, you're the GOAT.
 

FAQ: How is tension in a string affected by moment of inertia?

1. How does the moment of inertia affect the tension in a string?

The moment of inertia of a string is directly proportional to the tension in the string. This means that as the moment of inertia increases, so does the tension in the string. This is because a higher moment of inertia indicates a larger resistance to change in rotational motion, resulting in a greater force needed to maintain tension in the string.

2. Does the length of the string affect its moment of inertia and tension?

Yes, the length of a string does affect its moment of inertia and tension. The longer the string, the higher the moment of inertia and tension will be. This is because a longer string requires more force to maintain tension and has a larger resistance to change in rotational motion.

3. How does the mass of the string impact the moment of inertia and tension?

The mass of the string does not directly affect the moment of inertia and tension. However, a string with a larger mass will have a higher tension due to the increased force needed to support the weight of the string itself. The moment of inertia may also be affected if the mass is distributed unevenly along the length of the string.

4. What role does the shape of an object have on its moment of inertia and tension in a string?

The shape of an object can greatly impact its moment of inertia and tension in a string. Objects with a larger radius of gyration (distance from the axis of rotation to the center of mass) will have a higher moment of inertia and require more tension in the string to maintain rotational motion. Additionally, the shape of an object can affect its distribution of mass, which can also impact the moment of inertia and tension.

5. How does the tension in a string change when the moment of inertia is increased?

As mentioned earlier, the tension in a string will increase when the moment of inertia is increased. This is due to the relationship between moment of inertia and tension - as one increases, the other will also increase. Therefore, increasing the moment of inertia will require a greater force to maintain tension in the string.

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