What is the angle between the string and the vertical?

AI Thread Summary
To find the angle between the string and the vertical for a mass of 3.900 kg revolving in a horizontal circle with a tangential speed of 3.247 m/s, the centripetal force must be analyzed. The relationship involves both vertical and horizontal forces, where the tension in the string provides the necessary centripetal force. The equation sin(theta) = r/L is used, with r derived from the centripetal force equation Fc = mv^2/r. The weight of the mass contributes to the vertical component, while the tension provides the horizontal component, leading to the conclusion that Fc equals the horizontal component of the weight. Ultimately, the problem requires careful consideration of both force components to solve for the angle theta.
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"A mass of 3.900 kg is suspended from a 1.450 m long string. It revolves in a horizontal circle.
The tangential speed of the mass is 3.247 m/s. Calculate the angle between the string and the vertical (in degrees)."

Here is a diagram, labelling angle theta I'm supposed to solve for: http://capaserv.physics.mun.ca/msuphysicslib/Graphics/Gtype11/prob03_pendulum.gif

I've deduced so far that: sin(theta) = opp/hyp

In this case, opp = radius and hyp = length of string (L) or (1.450 m)

So sin(theta) = r/L

In turn, r can be solved by means of Fc = mv^2/r, as r = mv^2/Fc

so sin(theta) = mv^2/FcL

M is given, V is given, and L is given. Fc I'm sort of puzzled on, since I can't use the MV^2/R equation again. Any clues?
 
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Hint: What provides the centripetal force?
Hint: Consider both vertical and horizontal forces acting on the mass.
 
Okay, I think I'm getting somewhere. Would it be right to say the Fc is equal to the x-factor of the weight of the mass on the string? I could say this therefore:

Fc = mgsin(theta)

and then

sin(theta) = mv^2/mgsin(theta)L

which would cancel mass, giving me:

sin(theta) = v^2/gsin(theta)L

would that be right? or is mass even significant in this problem?
 
Not right. For one thing, the weight of the mass acts down--it has no horizontal component.

Try this: Identify all the forces acting on the mass. (There are two forces.) Then consider horizontal and vertical components.
 
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