How to calculate a trapeze/ pendulum's arc distance

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In summary, the conversation discusses the understanding of a pendulum's motion and the attempt to determine the motion of a trapeze on the moon. The equations involved include KE, PE, T, Fc, and Ft, and the attempt at a solution involves drawing a free body diagram and using conservation of energy. The amplitude of a pendulum's swing is determined by its initial speed and conservation of energy.
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katkinson
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Homework Statement



This is an update to an earlier post. Since then, I now understand that a pendulum stops when its tension force= mg sin(theta)--because then centripetal force will=0, so velocity will be 0. However, now I am trying to determine how a trapeze would work on the moon.

Homework Equations



KE=1/2 mv^2
PE= mgh
T=2π√(L/g)
Fc=mv^2/r
Ft=Fc-mg sin(theta)
KE (initial) + PE (initial) = KE (final) + PE (final)

The Attempt at a Solution



Drawing a free body diagram, I determined that when an object peaks during its swing the following is true: Because the object is stopped, Fc=0. Because Fc=0 and the radius and mass are supposedly constant, velocity must=0. (That also means that it is 100% PE). Because Ft - mg sin (theta) = 0, then Ft= mg sin (theta). I am trying to determine what sin (theta) is, because then I can determine the length of the swing on the moon. However, I do not know how to determine Ft so I thought I would try using the other method while using T=2π√(L/g). However, I do not know how I can use the time to determine the length of the arc

Thanks so much
 
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The amplitude (length of swing) depends on how fast the pendulum was pushed to begin with, i.e., its speed when it is at the lowest point. That, and conservation of energy, result in a particular amplitude.
 
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Related to How to calculate a trapeze/ pendulum's arc distance

Q1: What is a trapeze/ pendulum's arc distance?

The arc distance of a trapeze or pendulum is the length of the curved line that it traces as it swings back and forth.

Q2: How do I measure a trapeze/ pendulum's arc distance?

To measure the arc distance of a trapeze or pendulum, you will need to measure the length of the curved line from one end to the other. This can be done with a ruler or measuring tape.

Q3: What is the formula for calculating a trapeze/ pendulum's arc distance?

The formula for calculating a trapeze or pendulum's arc distance is: arc distance = (length of the string or rod) × (angle of swing in radians).

Q4: How do I convert degrees to radians for the arc distance formula?

To convert degrees to radians, you can use the formula: radians = (π/180) × (degrees). Alternatively, you can use an online converter or a scientific calculator to make the conversion.

Q5: Can I calculate the arc distance of a trapeze/ pendulum without knowing the angle of swing?

Yes, it is possible to calculate the arc distance without knowing the angle of swing. However, you will need to know the length of the string or rod and the time it takes for the trapeze or pendulum to complete one full swing. You can then use the formula: arc distance = (length of string or rod) × (π/2) × (time for one swing in seconds).

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