Find Angle Theta for Mass Revolving in Horizontal Circle

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AI Thread Summary
To find the angle theta for a mass revolving in a horizontal circle, the problem involves analyzing the forces acting on the mass, including tension and weight. The tension has both vertical and horizontal components, which can be resolved using trigonometric functions. The vertical component of tension balances the weight of the mass, while the horizontal component provides the necessary centripetal force for circular motion. Setting up equations based on Newton's second law for both the vertical and horizontal directions will help solve for theta. Understanding these relationships is crucial for deriving the correct equations and ultimately finding the angle.
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Homework Statement


A mass m = 5.500 kg is suspended from a string of length L = 1.570 m. It revolves in a horizontal circle (see Figure). The tangential speed of the mass is 2.874 m/s. What is the angle theta between the string and the vertical?
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Homework Equations



a = v2/r

The Attempt at a Solution



I am totally stumped. I don't want anyone to give me an answer; all I want is a hint so I can get started on this problem (I assume I'll have to use sin / cos somewhere in the formula). Thanks in advance.
 
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Start by drawing a free body diagram for the mass and resolve the forces in the radial and +z direction, +z pointing upwards.
 
I believe the Tension and weight forces cancel with respect to the y direction, that means there is a centripetal force towards the center of the circle in the x direction and since the mass is tilted along an angle theta, then the tension also has an x component. I guess I'm stuck again, maybe that's because its getting late; I'm not sleeping until I solve this problem :P
 
Radarithm said:
I believe the Tension and weight forces cancel with respect to the y direction, that means there is a centripetal force towards the center of the circle in the x direction and since the mass is tilted along an angle theta, then the tension also has an x component. I guess I'm stuck again, maybe that's because its getting late; I'm not sleeping until I solve this problem :P
What equations did you get for the two directions?
 
CAF123 said:
What equations did you get for the two directions?

Still didn't get any. I have no idea how to get θ.
Any tips? :confused:
I did get this though (and I'm pretty sure its wrong): Fnet = Tx + Fcentripetal cos θ × m(v2/r)
 
Radarithm said:
Still didn't get any. I have no idea how to get θ.
Any tips? :confused:
I did get this though (and I'm pretty sure its wrong): Fnet = Tx + Fcentripetal cos θ × m(v2/r)
It is dimensionally inconsistent, so just by looking at it, it must be incorrect.

There is a component of tension in the vertical direction. What is this in terms of θ? What other force acts in the vertical direction? Write Newtons second law for this direction.

There is also a component of tension in the horizontal direction. What is this in terms of θ? This force component is providing the centripetal force required for the mass to revolve. So you may equate this to the general expression for a centripetal force.

This will give you two equations. What you said was correct in #3, now you have to translate those ideas into equations.
 

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