Why Does a Pulley System Show Different Tensions for Different Masses?

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In summary, the conversation is about a homework problem involving two unequal masses and a rope wrapped around a pulley. The question is asking for the tension in the rope holding the lighter and heavier blocks. The solution manual provides different answers, leading to confusion about whether tension is always the same in the same rope. The response explains that tension would be the same if the rope and pulley were ideal, but the presence of mass and friction can affect the tension.
  • #1
Psi
I am working out a homework problem in which two unequal masses are on either end of a rope, which is wrapped around a pulley. The problem asks what the tension is in the part of the rope holding "(a) the lighter block, and (b) the heavier block". The solution manual reports different answers for these parts, but I thought tension was always the same in the same rope...?

Am I right? If not, could you explain what is happening in this problem?

Thanks a lot!

--Psi
 
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  • #2
Originally posted by Psi
The solution manual reports different answers for these parts, but I thought tension was always the same in the same rope...?
Tension would be the same if the rope were massless and the pulley were massless and frictionless. Consider that the rope exerts torque on the pulley.
 
  • #3


Hello Psi,

Thank you for reaching out about this tension problem. It is understandable that you are confused about the different answers reported in the solution manual. While it is true that tension is always the same in the same rope, it is important to consider the different forces acting on the rope in this particular scenario.

In this problem, the two unequal masses are exerting different forces on the rope due to gravity. The heavier block exerts a greater downward force on the rope, while the lighter block exerts a smaller downward force. This means that the tension in the rope will be different in each section, as the tension is equal to the force applied on the rope.

To better understand this, let's think about the forces acting on the rope. On one side, we have the tension force pulling the rope upwards, and on the other side, we have the weight of the heavier block pulling the rope downwards. In order for the rope to remain in equilibrium, the tension force must be equal to the weight of the block. This means that the tension in the section of the rope holding the heavier block will be greater than the tension in the section holding the lighter block.

I hope this explanation helps clarify the concept of tension in this problem. It is important to always consider the different forces acting on an object when determining the tension in a rope. Please let me know if you have any further questions or concerns.


 

FAQ: Why Does a Pulley System Show Different Tensions for Different Masses?

What is the "Yet Another Tension Problem"?

The "Yet Another Tension Problem" is a hypothetical problem in the field of materials science that explores the behavior of materials under tensile stress.

Why is the "Yet Another Tension Problem" important?

Understanding the behavior of materials under tensile stress is crucial for the development of new materials and technologies. The "Yet Another Tension Problem" helps scientists gain insight into the properties of different materials and how they respond to tension.

How is the "Yet Another Tension Problem" studied?

The "Yet Another Tension Problem" can be studied through experiments, computer simulations, and mathematical models. Scientists use various techniques to measure and analyze the behavior of materials under tension, such as strain gauges and stress-strain curves.

What are the potential applications of the "Yet Another Tension Problem"?

The insights gained from studying the "Yet Another Tension Problem" can be applied to various fields, such as engineering, construction, and manufacturing. This knowledge can help in developing stronger and more durable materials for use in different industries.

What are some challenges in solving the "Yet Another Tension Problem"?

One of the main challenges in solving the "Yet Another Tension Problem" is the complexity of materials and their behavior under different conditions. Additionally, there may be limitations in experimental techniques or computer simulations, which can make it difficult to fully understand and predict the behavior of materials under tension.

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