Flying Pigs Practical

Determining Period of a Pendulum

From the equation to the right we can determine the period of a pendulum from simply knowing which planet we are on and measuring the length of the pendulum.

Can we do the same, with flying pigs? (YES)

Bernie Sprute is a world-renowned pig farmer. His cutting edge work has led him to farm the flying pig. The benefits of farming flying pigs so obviously out-weighs farming Earth-bound pigs that we will leave that discussion for another time.

Bernie wants to determine two quantities:

Given a leash of length, l, how long will it take the pigs to fly one complete circle (T).
Using the same leash, what will be the tension in the leash flying at the speed of v_T?

Mr. Sprute needs to determine the tensile strength required for flying pig leashes. These leashes will allow pigs the freedom to fly in a circular fashion and yet keep them safe from harm. Mr. Sprute has asked us at ACS-AD to help him with this investigation.

Given only a meterstick and the knowledge that we are on the planet Earth, determine the period of your flying object.

Outline of experimentation

Observe your flying object (pig or plane)
1. Draw a sketch of the scenario. Use the diagram as a guide.
2. Include any measurements you will need to take.
3. Include any calculations you may need to make.
Create a Free Body Diagram of the forces acting on your flying.
1. Which angle will you be measuring? How will you measure this angle?
2. Does the flying object accelerate in the following directions:
  1. Vertical direction?
  2. Horizontal (radial) direction?

Complete the following Table of Forces

3. From your FBD, describe how the net forces (horizontal and vertical) were determined.

4. From the sum of the horizontal and vertical forces, show the following relationship exists:

5. Rearrange the equation above in terms of v (tangential velocity)

6. Combine the following equations express T (Period) in terms of R, g, θ, and any other physical constants needed.

Resources that may Help With Calculations

Calculations to complete

Calculate angular speed, ω
Calculate tangential velocity, Vt
Calculate the centripetal acceleration, ac
Calculate the centripetal force, Fc
Calculate the tension in the string, FT
For each of the above calculations, create a generalized equation in terms of g, θ, m, r, t, and any additional physical constants, as necessary.
Write a brief summary of the procedure that you used to determine the variables above.
Explain how knowledge of the physics of circular motion would be important for designing the swing ride pictured below for safety.

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