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

[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 ma_r = (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?

 

[Chestermiller]

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 !$\$

 

[haruspex]

I'm trying to solve this problem using an rtz coordinate system, and Newtons second law. I know that ma_r = (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.

 

[BvU]

It says to ignore that.

I read

Air resistance is not negligible.

 

[hutchphd]

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.

 

[haruspex]

I read

Thanks. My eyes are getting worse.

 

[hutchphd]

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