Circular Motion with Tension and Finding Angle

In summary, the question asks for the measure of angle θ in a scenario where 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. The solution involves breaking down the forces at work and creating a free body diagram and graph. The answer can be found by using the x and y components equations and considering whether the angle is measured from vertical or horizontal. The final answer will depend on the value used for g, the number of significant figures specified, and whether the answer is expected in degrees or radians.
  • #1
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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.

FullSizeRender(2).jpg
 
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  • #2
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?
 
  • #3
Haruspex,
Thank you for your response. Here is the image associated with the problem.
FullSizeRender(3).jpg
 
  • #4
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)
 
  • #5
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!
 

What is circular motion with tension and how is it different from regular circular motion?

Circular motion with tension refers to the motion of an object moving in a circular path while also experiencing tension from a string or rope. This is different from regular circular motion, which does not involve any external forces acting on the object.

How is the tension in a string related to the mass and speed of the object in circular motion?

The tension in a string is directly proportional to the mass of the object and the square of its speed. This means that as the mass or speed of the object increases, the tension in the string will also increase.

How can the angle between the string and the horizontal be calculated in circular motion with tension?

The angle can be calculated using the formula: θ = tan^-1 (v^2/rg), where v is the speed of the object, r is the radius of the circular path, and g is the acceleration due to gravity.

What happens to the angle between the string and the horizontal when the speed of the object increases?

As the speed of the object increases, the angle between the string and the horizontal will also increase. This is because the tension in the string increases, causing the string to pull at a greater angle.

Can the tension in the string ever be greater than the weight of the object in circular motion with tension?

Yes, it is possible for the tension in the string to be greater than the weight of the object in circular motion with tension. This can occur when the object is moving at a high speed and the tension in the string is also high, causing the string to pull at a steeper angle.

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