Period of a Pendulum on an Arm

[KonigGeist]

Homework Statement

The “Giant Swing” at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 6.17 m long, the upper end of the cable being fastened to the arm at a point 3.77 m from the central shaft. Find the time of one revolution of the swing if the cable supporting a seat makes an angle of 32.7 degrees with the vertical.

Give your answer in seconds to the second decimal place.
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Homework Equations

a = 4$$\Pi$$²R/T²

The Attempt at a Solution

Calculate the x component of the swing chain:
x = Lsin($$\Theta$$)
x = 6.17sin(32.7)
x = 3.33

Solve a = 4($$\Pi$$)²R/T² for T:
a = 4$$Pi$$²$$Theta$$/T²
tan($$Theta$$) = 4$$Pi$$²$$Theta$$/T²
T = 2$$Pi$$$$sqrt{Lcos(Theta)/g}$$

I've calculated T using both the combined radius of the chain and arm, and using the chain and adding the arm. Am I going about this the right way? Does this equation even apply here?

 

[anathema]

Thank you for your post. Your approach to solving this problem is correct, however, the equation you have used is not the most appropriate for this scenario. The equation you have used, a = 4\Pi2R/T2, is used to calculate the acceleration of an object in uniform circular motion. In this case, we are looking for the time of one revolution of the swing, which can be found using the formula T = 2\Pi\sqrt{L/g}, where L is the length of the swing's cable and g is the acceleration due to gravity (9.8 m/s^2).

Using this equation and the given values, we can calculate the time for one revolution of the swing:

T = 2\Pi\sqrt{6.17/9.8}
T = 2.49 seconds

I hope this helps. Let me know if you have any further questions.