Circular Motion with Tension and Finding Angle

AI Thread Summary
A 0.020-kg mass attached to a 1.2-m string moves in a horizontal circle with a tension of 0.200 N, prompting the calculation of angle θ. The forces involved include tension and weight, leading to equations based on the components of these forces. Initial calculations yield θ=11.2 degrees, but the ambiguity regarding whether the angle is measured from vertical or horizontal complicates the solution. Further discussion suggests possible variations in gravitational acceleration and the need for significant figures, with one participant noting a reference answer of 24.6 degrees. The conversation highlights the importance of clarity in problem statements and the potential for differing interpretations in physics problems.
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Homework Statement


A 0.020-kg mass is attached to a 1.2-m string and moves in a horizontal circle with a constant speed. The tension in the string is measured at 0.200 N. What is the measure of angle θ?

Homework Equations


∑F=ma, a=v^2/r

The Attempt at a Solution


I broke down the forces at work, being T (tension) and W (weight). I made a free body diagram, then drew a graph. I came up with the x components as -Tsinθ=ma, and y components as Tcosθ-W=0. After plugging in for T and m*g (from W) in the y component equation, I came up with θ=11.2, but this is not correct.

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The question as posted does not indicate whether the angle is to be measured from vertical or from horizontal. I assume there is some diagram which makes it clear it is to the vertical.
I agree with your answer in degrees. Are you sure the question does not want the answer in radians?
 
Haruspex,
Thank you for your response. Here is the image associated with the problem.
FullSizeRender(3).jpg
 
Then I see only four possibilities:
- you were expected to use a slightly different value of g; the answer will be somewhat sensitive to this, .980 giving 11.5 degrees e.g.
- for the same reason, you should only specify two sig figs.
- the answer should be in radians
- the book is wrong (maybe in the question statement)
 
Haruspex, thank you. I'll have to do some digging, but it gives the answer as 24.6 degrees. So I'll try to get to the bottom of it. Thanks again!
 
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