# Tension in rope for non-uniform circular motion with air resistance

• fenstera6
In summary: I think your question is whether mg (or mg+drag) affects the tension.The answer is yes, mg affects the tension.
fenstera6
Homework Statement
A 4.4-cm-diameter, 24 g plastic ball is attached to a 1.2-m-long string and swung in a vertical circle. The ball’s speed is 6.1 m/s at the point where it is moving straight up. What is the magnitude of the net force on the ball? Air resistance is not negligible.
Relevant Equations
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I'm trying to solve this problem using an rtz coordinate system, and Newtons second law. I know that mar = (m(v)2)/r. I'm failing to understand how mg and the drag force affects the solution and how I would set it up. I know if it was at the bottom of the circle that mg would be added to the tension force, and if it was at the top it would be subtracted, is it irrelevant at the sideways position?

They are only asking for the force when it is moving straight upward. They are not asking you to solve the entire problem.

BvU
Hello @fenstera6 ,
: welcome: !

Personally, I 'm not familiar with an rtz coordinate system. I do know about cylindrical coordinate systems (##\rho,\ \phi, \ z##).

In your exercise, the net force on the ball is asked. So the thing to do is to set up a free body diagram showing the acting forces. ##mg## is definitely one of them. So is the tension in the string, for which you have an expression. And the third is the drag force. Three forces, three expressions.
I can't think of any others; can you ? Straightforward vector addition !##\ ##

fenstera6 said:
I'm trying to solve this problem using an rtz coordinate system, and Newtons second law. I know that mar = (m(v)2)/r. I'm failing to understand how mg and the drag force affects the solution and how I would set it up. I know if it was at the bottom of the circle that mg would be added to the tension force, and if it was at the top it would be subtracted, is it irrelevant at the sideways position?
Not sure why you mention drag. It says to ignore that.
I think your question is whether mg (or mg+drag) affects the tension.
The horizontal acceleration is still v2/r, and the tension is the only horizontal force.

haruspex said:
It says to ignore that.
Air resistance is not negligible.

You need to know the drag force. Presumably you have been told how to calculate this from the size of the ball and its speed. Then draw a vector diagram of the three forces on the ball at that position (yes draw a free body diagram) and do the vector addition.

BvU said:
Thanks. My eyes are getting worse.

I got the "not" the third time I read it!

## What is non-uniform circular motion?

Non-uniform circular motion is when an object moves in a circular path at a varying speed. This means that the object is not moving at a constant speed, but instead is accelerating or decelerating as it moves along the circular path.

## How does air resistance affect tension in a rope for non-uniform circular motion?

Air resistance, also known as drag, is a force that acts in the opposite direction to an object's motion. In non-uniform circular motion, air resistance can cause the object to slow down, which in turn affects the tension in the rope. The greater the air resistance, the more tension is required to maintain the circular motion.

## What factors affect the tension in a rope for non-uniform circular motion with air resistance?

The tension in a rope for non-uniform circular motion with air resistance is affected by several factors, including the speed of the object, the mass of the object, the radius of the circular path, and the density of the air. These factors all play a role in determining the amount of air resistance and therefore the amount of tension required to maintain the circular motion.

## How can the tension in a rope be calculated for non-uniform circular motion with air resistance?

The tension in a rope for non-uniform circular motion with air resistance can be calculated using the equation T = mv^2/r + mg + Fd, where T is the tension, m is the mass of the object, v is the speed, r is the radius of the circular path, g is the acceleration due to gravity, and Fd is the force of air resistance. This equation takes into account all the factors that affect the tension in the rope.

## What are some real-world applications of non-uniform circular motion with air resistance?

Non-uniform circular motion with air resistance is a common occurrence in many real-world scenarios, such as a roller coaster moving along a track, a car turning around a curve, or a satellite orbiting the Earth. Understanding the principles of tension in a rope for non-uniform circular motion with air resistance is important in designing and analyzing these types of movements and ensuring their safety and efficiency.

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