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Gold3nlily

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## Homework Statement

Fig. 6-53 shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.012 kg, the string has length L = 0.86 m and negligible mass, and the bob follows a circular path of circumference 0.52 m. What are (a) the tension in the string and (b) the period of the motion?

Image:

http://edugen.wiley.com/edugen/courses/crs4957/art/qb/qu/c06/fig06_43.gif

## Homework Equations

Y: Tcos@-mg=m(0)

Y: Tcos@=mg

X: Tsin@=(mv^2)/r

C=2pi*r

r=C/(2pi)

Period = (2pi*r)/v

## The Attempt at a Solution

First I solved for the radius and angle:

r=C/(2pi) = 0.52/(2pi) = 0.08276

sin@=r/Length = 0.08276/0.86

@ = sin^-1 (0.08276/0.86)

@=5.52 degrees

Then I solved for tension:

Tcos@=mg

T=mg/cos@ = (0.012*9.8)/cos(5.52)

T=0.118N (this was the correct answer)

Now I cannot solve for the period.

This is what I have tried:

Period = (2pi*r)/v

Period = (0.52)/v

…need to solve for V

Tsin@=(mv^2)/r

V=((r*Tsin@)/m)^(1/2)

V=((0.08276*0.86sin5.52)/0.012)^(1/2)

V=0.755

Period = (0.52)/ 0.755

Period = 0.688 (this was incorrect)

What did I do wrong?

P.s.- my first test is the Wednesday so hopefully someone can help me really understand this problem soon. (Also, i didn't wait till the last minute this homework just came up yesterday...)

Thank you so much in advance for helping me.