Solved: Conical Pendulum: Calculating Tension & Period

In summary: Period_and_tension_analysis In summary, the tension in the string is 0.118 N, and the period is 0.688 seconds.
  • #1
Gold3nlily
42
0

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.
 
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  • #2
I believe the period of a conical pendulum is 2*Pi*sqrt(L*cos(theta)/g). Google period conical pendulum for explanation
 
  • #3
RTW69 said:
I believe the period of a conical pendulum is 2*Pi*sqrt(L*cos(theta)/g). Google period conical pendulum for explanation

You're right. Thank you. <3

I found explanation here:
http://en.wikipedia.org/wiki/Conical_pendulum
 

Related to Solved: Conical Pendulum: Calculating Tension & Period

What is a conical pendulum?

A conical pendulum is a type of pendulum where the weight is attached to a string or rod that is suspended from a fixed point, causing it to move in a circular motion instead of a back and forth motion like a traditional pendulum.

How do you calculate the tension in a conical pendulum?

The tension in a conical pendulum can be calculated using the formula T = (m*v^2)/r, where T is the tension, m is the mass of the weight, v is the velocity of the weight, and r is the radius of the circular motion.

What factors affect the period of a conical pendulum?

The period of a conical pendulum is affected by the length of the string or rod, the mass of the weight, and the angle of the string or rod with respect to the horizontal plane.

Why is the tension in a conical pendulum greater than the weight of the hanging mass?

The tension in a conical pendulum is greater than the weight of the hanging mass because the weight must provide both the centripetal force to keep the mass in circular motion and the gravitational force to counteract the tension in the string or rod.

How can the period of a conical pendulum be increased?

The period of a conical pendulum can be increased by either increasing the length of the string or rod, decreasing the mass of the weight, or decreasing the angle of the string or rod with respect to the horizontal plane.

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