Why massless rope is required for making these two forces eq

In summary, if a person applies a force on a rope and that rope is pulling another body which is attached to it, the force applied by the person on the rope will be equal to the force applied by the rope on the body if two conditions are met: 1. The rope cannot increase in length due to the force, and 2. The rope is massless. This is because, according to Newton's second law, the net force on the rope is equal to its mass multiplied by its acceleration, and if the forces on both ends are equal and opposite, then either the rope must be massless or have zero acceleration.
  • #1
Tahmeed
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I am pulling a rope and that rope is pulling another body which is attached to rope. The force applied by me on the rope will be equal to the force applied by rope on that body if 1. The rope can't increase in length due to force, or 2. if the rope is massless.

I understand the reason behind first condition, but why there is that second condition?? what happens if it's massless??
 
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  • #2
The first condition is not correct. You can have unequal forces even if the rope is unstretchable.

Newton's second law applies. f = ma. The net force on the rope is equal to the mass of the rope multiplied by its acceleration. If the forces on the ends are equal and opposite then it follows that either:

1. The rope is massless.
2. The rope has zero acceleration.
 
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Related to Why massless rope is required for making these two forces eq

1. Why is a massless rope required for making two forces equal?

A massless rope is required because the weight of the rope itself would add an additional force to the system, making it impossible to achieve equilibrium between the two forces. In order for the forces to be truly equal, the rope must have no weight or mass.

2. Can't a rope with a very small mass be used instead?

No, even a rope with a small mass would still add a force to the system, however small it may be. In physics, the concept of a massless object is used as an idealization to simplify equations and calculations. In reality, all objects have some mass, but for the purposes of solving problems, we can assume the rope is massless.

3. What if the rope is very thin and has a negligible weight?

Even if the rope is thin and has a very small weight, it would still add a force to the system. In physics, we consider the weight of an object to be its mass multiplied by the acceleration due to gravity. Therefore, even a thin rope would still have a weight and add a force to the system.

4. Are there any real-life examples of a massless rope?

No, there are no objects in the real world that can truly be considered massless. However, in situations where the mass of an object is negligible compared to other forces, we can use the concept of a massless object to simplify calculations. This is often seen in mechanics problems involving pulleys and ropes.

5. Is the concept of a massless rope only applicable to equal forces?

No, the concept of a massless rope can be applied to any situation where the weight or mass of the rope is negligible compared to other forces. This includes situations where the forces are not equal. As long as the mass of the rope is insignificant, we can treat it as if it is massless for the purposes of solving problems.

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