I am swinging a ball around in a horizontal circle with a radius of 0.60 m a) What is its vertical component of acceleration? _____ m/s^2 b) At what constant speed must it travel so that the horizontal component of its acceleration is 3.5 m/s^2 v = _____ m/s
Answers
Answer:
The Physics of Swinging a Mass on a String for Fun
With a specific setup, you can control the tension in the string.
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FABRIZIO BENSCH/GETTY IMAGES
Occasionally there are physics lab demonstrations that I think are pretty awesome but that my students just think are "meh." This is one of those cases. The basic idea in this demo, which I used in my class at Southeastern Louisiana University, is to swing a mass around in a horizontal circle. But wait! There's a cooler part: By running the string through a vertical tube and attaching it to another mass, we can control the tension in the string. It's loads of fun.
What am I talking about? Maybe this will help.
Yes. That is me. I have a confused look on my face because I have to concentrate to keep the swinging length constant. Maybe this is why the students dislike this lab. Oh well. There are a few important features of this swinging mass. Let me draw a diagram.
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If you want to swing the mass around with a lower angular velocity, the string will need to be longer. If you want a shorter string, the mass will have to spin around faster. This is the only way to make it work since the tension in the string is constant. Why is the tension constant?
Consider the mass hanging down at the bottom of the tube (I have labeled this M2). Since this mass is just hanging there (and not spinning in a circle) then it is in equilibrium with an acceleration of zero meters per second squared. Since the acceleration (in the y-direction) is zero, then the net force must be zero Newtons. There are only two forces in the vertical direction, the downward gravitational force with a magnitude of M2g (where g = 9.8 N/kg) and the upward tension (T). That means the tension has to have a value of M2g—no matter how you are swinging the other mass.
What about that angle that the string makes as the mass moves around in a circle (labeled as θ above)? How does this angle change as you swing at different speeds? Let me start with a force diagram for mass m1.
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Although this mass is moving in a circle, it's just a horizontal circle. There is no motion and no acceleration in the vertical direction. This means the net force in the y-direction must be zero. Looking at the tension, the component of tension in the y-direction depends on the magnitude of the tension (which I already know) and the angle (which I don't). I can write this as the following equation.
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