**Abstract**

The objective of this lab experiment is to determine the tensile strength required for flying pig leashes, which could allow pigs to fly in a circular path that keeps them safe from injury. In our method, we attached the sticky side of the leash of a toy flying pig to the ceiling, making sure the pig is suspended in the air. After the materials setup, we measured the length of the leash in meters and found the radius of the circle the pig makes while flying in meters and mass in grams. To calculate the time it takes for the pig to circulate around one full circle in seconds, we activated the pig to spin around in a circular motion. Lastly, we calculate the force of tension of the leash on the pig as it is circulating, showing that the string must be quite strong in order to hold up such a heavy pig. We also calculated other variables: calculations and numerical results are listed in the table and subsequent sections in this report.

**Background information**

Bernie Sprute is a world-renowned pig farmer. His cutting-edge work has led him to farm the flying pig, which is shown to have more world health benefits than farming Earth-bound pigs. Therefore, in order to set up his experiments with flying pigs, Sprute needs to determine the tensile strength required for flying pig leashes, which can allow the pigs to fly in a circular fashion that keeps them safe from harm. Recently, Mr. Sprute partnered with PrettyGoodPhysics and received an NSF grant to help calculate the tensile strength of the leash of the flying pig.

Therefore, the objective of this lab experiment is to calculate, from finding other variables, what is the tensile strength required for durable flying pig leashes. To answer this question, in this lab investigation, we attached the sticky side of the leash of a toy flying pig to the ceiling, making sure the pig is suspended in the air. After the materials setup, we measured the length of the leash in meters using a meterstick and found the radius of the circle the pig makes while flying in meters with a meter stick and mass in grams using a small scale. To measure the time it takes for the pig to circulate around one full circle in seconds, we activated the pig to spin around in a circular motion and utilized a smartphone stopwatch. Lastly, we calculated the force of tension of the leash on the pig as it is circulating, showing that the string must be quite strong in order to hold up such a heavy pig. Tension is basically the force that is transmitted when a string/rope is attached to something and is directed along its length to pull on objects [1]. So, calculating tension is useful for trying to test the flying pig leash’s strength, flexibility, how much it’s pulling on the flying pig, etc.

We also calculated other variables besides the force of tension, such as tangential velocity, net radial acceleration, net radial force, angle of the leash to the vertical, rotational kinetic energy, rotational inertia (I), and angular velocity (w). I predict that these variables can be purely calculated by mathematical formulas, but I do expect there will be some errors such as due to human error, air resistance, etc.

**Materials and Methods**

Below is the step-by-step process we used to conduct our experiment:

We used the adhesive on one side of the leash to attach it to the ceiling, with the pig hanging in midair straight down. We used a small scale to measure the mass of the pig and the meter-stick to measure the length of the leash and the up and down height from the ceiling to the pig in this step.

We activated the pig’s wings by pressing the button on the side of it and pushing the pig a little bit so that it could start moving around in a circle, like a ceiling fan.

As it was spinning, we marked two opposite ends of the circle it formed with our fingers, then used the meter-stick to measure the diameter of that circle. We divided this diameter by two to find the radius of the circle.

As the pig was spinning, we marked a spot on the circle in midair so we could, with a stopwatch, calculate the time it took for it to spin around one full circle, 360 degrees.

After the experiment, we used formulas to calculate the variables listed above.

Results of the variables above are either measured using a physical device or calculated using a mathematical formula.

**Results**

From the results calculation table 2 above, it looks like the tensile strength of the string is quite strong, the pig has a high amount of rotational kinetic energy, and the pig was moving in a circle extremely fast for a small toy pig. We have successfully determined the tensile strength of the leash for the toy pig, though I did not expect it to be this large of a number.

**Discussion**

The purpose of this experiment was to calculate the tensile strength required for flying pig leashes, which can allow the pigs to fly in a circular path that keeps them safe from injury. This also requires the measurements and calculations of several different variables. In this experiment, we set up the flying pig to move in a circular motion.

Numerical results involving using the tension force (T) formula resulted in 3870 N for the pig’s leash, which is unexpectedly a high number. Because the string of the pig was slanting as the pig traveled in circles, we utilized the sine of the angle to the vertical direction and Ty (tension force in the y direction) to calculate the resulting net T. We also calculated the angle of the leash to the vertical direction, which was 23.063 degrees, which is expected as we observed the string slanting more downwards halfway below the horizontal as the pig was flying (meaning the angle had to be less than 45 degrees).

Our experimental design does adequately address the objective of this research, which is to calculate tensile strength and find other variables. Because we utilised tools such as meter-sticks and stopwatches, we were able to achieve somewhat precise results. There were faulty assumptions that may have impacted our results, such as ignoring air resistance as the pig was flying. We assumed the pig would be flying in circles forever at the same speed, which is not true because, after a few minutes, the pig started to slow down and stop.

Therefore, our results prompt a new question: Would tensile strength and/or other variables such as rotational kinetic energy be a larger or smaller number if we factor in air resistance?

Experiments are not 100% accurate or precise, as there always exist sources of error and uncertainties. We may have gotten several inaccurate values for some of the variables calculated, which can be due to our experimental method having a few sources of error/uncertainties. Due to human reaction or reflexes, we may have pressed the stopwatch start and stop buttons approximately 0.1 seconds too early or late, the precision of the meter sticks only going up to 2 significant figures (whole numbers), etc. To decrease the amount of uncertainty, we can utilise meter sticks that have tick marks that go to the tenth decimal place to more accurately record the string’s height. In addition, we could have used a more accurate measurement for the diameter of the circle the flying pig made in motion, as we only used our fingers to mark two opposite edges of the circle. Perhaps we could have done this several times in several trials to more accurately record the diameter and radius of the circle.

**Conclusion:**

After conducting this circular motion experiment and evaluating the variables listed above, we verified that the tensile strength of the pig’s leash is 3870 N, which is the most optimal strength that will keep the pig in motion and keep it from injury.

**Cited Sources**

[1] https://www.vedantu.com/physics/tension-force

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