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

AI Thread Summary
The discussion centers on calculating the tension in a rope during non-uniform circular motion while considering air resistance. The user is attempting to apply Newton's second law and an rtz coordinate system but is confused about the roles of gravitational force (mg) and drag force in the calculations. Clarifications suggest that at different positions in the circular path, mg affects tension differently—added at the bottom and subtracted at the top—but its relevance at the horizontal position is questioned. The importance of drawing a free body diagram to visualize the forces acting on the object is emphasized, along with the need to account for air resistance in the calculations. Overall, the focus is on understanding how to set up the problem correctly to find the net force acting on the object.
fenstera6
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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?
 
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They are only asking for the force when it is moving straight upward. They are not asking you to solve the entire problem.
 
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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.
I read
Air resistance is not negligible.
:nb)
 
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:
I read :nb)
Thanks. My eyes are getting worse.
 
I got the "not" the third time I read it!
 
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