# Find tension of rope. Frictionless system.

• JohnKSmith
In summary: The only thing I would suggest is to make sure you are keeping track of the direction of the forces and the signs when setting up your equations. In summary, the conversation discusses a problem involving a frictionless table and pulley, with the goal of finding the tension in a rope. The solution involves setting up equations for the forces on both blocks and solving for the tension using the acceleration calculated from the equations. The correct answer is around 58.8N, which may be reached by double checking the signs in the equations.
JohnKSmith

## Homework Statement

This image: http://i52.tinypic.com/35i0j1k.jpg, assume the table surface and pulley to be frictionless. Please ignore the given a=1.96 in the photo as I will show how I reached that further below.

F=ma

## The Attempt at a Solution

Well, my stab at the problem was like this, for the 12kg block we had it at rest on the vertical so I left it out as Fn+12g=0. I assumed the clockwise spin of the pulley to be positive so the horizontal of the 12g block's equation looked like
T-0=12a ∴T=12a
and I found the hanging block's equation to be 3g-T=3a so I take the T I found for the top block into this equation to find
3g-(12a)=3a
3g=15a
a=1.96 as the acceleration in meters per second squared.
With this acceleration I took it and placed it into the very first equation T=12a of the block resting on the table to deduce rope tension to be 23.5N assuming three significant digits.

Is this method the correct way to find the tension of a rope as seen in the given image above? I was told the answer is actually somewhere around 58.8N and I don't see the logic to reaching that conclusion. Comments, corrections, and explanations welcome.

Your method and solution looks good!

## 1. What is tension?

Tension is a force that is exerted by a string, rope, or any other type of flexible material when it is pulled tight from both ends.

## 2. What is a frictionless system?

A frictionless system is a theoretical concept in which there is no resistance or friction between two surfaces. This means that there is no loss of energy due to friction in the system.

## 3. How do you find the tension of a rope in a frictionless system?

To find the tension of a rope in a frictionless system, you can use Newton's laws of motion. You will need to know the mass of the object being pulled by the rope, the acceleration of the object, and the angle at which the rope is being pulled. Using these values, you can calculate the tension of the rope using the equation Tension = Mass x Acceleration x Cosine (angle).

## 4. Can tension exist in a frictionless system?

Yes, tension can still exist in a frictionless system. Even though there is no friction, there can still be a force exerted by the rope on the object being pulled, which is known as tension.

## 5. How does tension affect the motion of an object in a frictionless system?

Tension is one of the forces that can affect the motion of an object in a frictionless system. If the tension is greater than the force of gravity, the object will accelerate in the direction of the tension. If the tension is equal to the force of gravity, the object will maintain a constant velocity. And if the tension is less than the force of gravity, the object will decelerate and eventually come to a stop.

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