# Tension Problem in a pulley system

• jen333
In summary, the conversation is discussing a question about a vertical/horizontal pulley system. The question involves determining the tension in a string attached to a 2.0kg mass on a smooth table and a 5.0kg mass hanging off the pulley. The formula for finding the net acceleration and the tension force is discussed and diagrams are suggested as helpful tools. The conversation ends with the suggestion to use the equation for finding the net acceleration.
jen333

I have a question that relates to a vertical/horizontal pulley system:
i'll try drawing the diagram, hopefully someone can understand!

O-------------|2.0kg|
|
|
|
|
|
|mass=5.0Kg|

alright, i guess i should explain that ^^^ if it clarifies the diagram a bit. alright, so there's a mass of 2.0kg on a surface attached to a string which attaches to a pulley (shown by "O") on the edge of the surface. This string is also connected to a 5.0kg mass which is shown in the diagram to simply be hanging off the pulley.

So the question is: A 2.0kg mass, placed on a smooth level table, is attached by a light string passing over the edge of a table. Determine the tension in the string. (the answer given is 14N)

i've found that the total mass of the two are 7.0kg, and is aware that the tension is the same on both the strings. however, what formula would i use to execute this question. would multiplying each mass by 9.81 assist? if the diagram is difficult to understand, please respond so i can further clarify it!

ps) if anyone knows how to add in diagrams, etc. other than using keyboard letters and symbols, that would be great!

Last edited:
First, find out all the forces acting on the 2 mass. Which force you think is the force that accelerates the 2 mass?
Then find out the net acceleration. (the 2 mass have the same acceleration).
And finally, find out the tension of the string. (Nore that only the tension will accelerate the 2.0 kg mass).
Viet Dao,

i still feel lost. alright, yes, tension due to the 5.0kg mass and gravity creates tension to acclerate the mass. the forces that are working on the masses are obviously tension, force gravity, normal force on the 2.0kg mass. and since the surface is "frictionless", friction is not in this problem.

Okay, so there are 2 forces acting on the first mass: P1, and T1. Can you find out its acceleration? Let's call it a1.
Then find out the acceleration of mass 2. Call it a2.
Now you have a1 = a2. Remember that:
$$\frac{a}{b} = \frac{c}{d} = \frac{a + c}{b + d}$$
And you will find out the acceleration of the net. a1 = a2 = a(net). So you now a2, and can you find out the magnitude of the tension force?
Or you can use the equation:
$$a_{net} = \frac{\sum F_{external}}{\sum m}$$
There are 3 external forces here: P1, P2, N2. And you have $\vec{P_{2}} + \vec{N_{2}} = \vec{0}$
Hope it help,
Viet Dao,

## 1. What is tension in a pulley system?

Tension in a pulley system is the force applied to the rope or belt that is used to support or move an object. It is the force that is transmitted through the rope or belt and is responsible for keeping the object in place or in motion.

## 2. How is tension calculated in a pulley system?

Tension in a pulley system can be calculated using the formula T = (m1 + m2) * g, where T is the tension, m1 and m2 are the masses of the objects, and g is the acceleration due to gravity (9.8 m/s²). This formula assumes that the rope or belt is massless and there is no friction in the system.

## 3. What factors affect tension in a pulley system?

The tension in a pulley system is affected by various factors, such as the mass of the objects being supported or moved, the angle of the rope or belt, the number of pulleys, and the friction in the system. These factors determine the amount of force needed to keep the objects in place or in motion.

## 4. How does tension change in a pulley system with multiple pulleys?

In a pulley system with multiple pulleys, the tension in the rope or belt changes depending on the arrangement of the pulleys. As the rope or belt passes through each pulley, the tension is divided among the different segments. The more pulleys there are, the less tension is required to support or move the objects.

## 5. What are some common problems with tension in a pulley system?

Some common problems with tension in a pulley system include rope or belt slippage, uneven distribution of tension, and excessive friction. These issues can lead to inaccurate tension calculations and can cause the system to malfunction. Regular maintenance and proper setup can help prevent these problems.

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