Aaron Scherer
Joshua Jesser
Matias Silvestre
Tony Terjeson

PRO-JECT MAGIC

Background

In free fall, all objects will accelerate at the same rate regardless of size, mass, or

shape. This was proven by several scientists. The most common experiment to prove this is

where two objects of the same shape but different masses are dropped from the same height and

then both hit the ground at the same time. In Galileo’s experiment, he used inclined planes to

slow down the acceleration to measure the elapsed time more accurately. The ball was allowed

to roll a previously measured distance down a ramp, and the time was recorded. Galileo showed

that the motion on an incline plane had a constant acceleration which was dependent only on the

angle of the plane, and not the mass. Unfortunately, Galileo couldn’t prove that free fall motion

behaved the same way. In fact it is possible to describe a free fall motion as an inclined plane

motion with an angle of 90. Using Newton’s laws we can prove Galileo’s theory. We can split

the gravitational force acting on the rolling balls into two vectors: one horizontal and one vertical

(Rubin). Although it is commonly belief that Galileo did an experiment where he dropped two

objects of different masses from the same height, it was first performed by a scientist named

Simon Stevin in 1586 (Drake 20). These studies were used in the early 1600’s in order to

calculate the trajectory of cannonballs shot from a cannon (Stern). It was proven once again on

the surface of the moon by David Scott, when he dropped a hammer and a feather at the same

time and they fell at the same rate (Stern). The net force at which an object falls divided by its

mass will be the same for all objects as this equals their acceleration (The Physics Classroom).

Our experiment will also be closely related to drag as this is one of the most important

variables in our experiment. Both mass and shape affect drag; shape can affect how much drag

and mass affects how much of an effect drag has on the object (Benson). Different shapes

have what they call drag coefficients, which are used in our calculations to solve for different

variables such as terminal velocity (Benson). We will try to keep our variables constant, besides

that of the mass, in order to make our results more valid.

Statement of the Problem

The purpose of this experiment is to determine the relationship of a ping pong balls mass

and the rate at which it falls. We will also determine the force at which it falls at and its velocity.

Hypothesis

I believe that ping pong balls with a greater mass will accelerate faster and have a greater

velocity at the bottom of its fall. I believe this will happen because wind resistance will have less

of an effect on the ping pong balls as they fall. We will measure acceleration in meters per

second per second and velocity in meters per second. The control variables will include where

we throw the ping pong balls off the cliff, the distance at which it falls, weather, and size of ping

Method: Materials and Procedure

First, we gathered our materials need for this experiment. We needed 15 Ping

Pong balls, a cup of water, a syringe, ruler, and a video camera. We then found an area that had

very little wind and was about 40-50 feet high (Tualatin High Bleachers). Before going to that

area, we set up our experiment. We set aside three ping pong balls to be used as our control.

They would have no water in them. Using the syringe, we filled three ping pong balls up with 7

ML of water, three with 14 ML, three with 21 ML, and finally three with 28 ML (basically full).

We took into account that the ping pong ball weighed about 2.7 grams initially, so we added that

to our final weight of the five different measurements. We then went to the TuHS bleachers and

filmed the dropping of each ping pong ball. After that we took that film into Logger Pro to

analyze when the ball reached terminal velocity. Since our video was recorded in 1080P, 60 FPS,

we could have a better analysis in Logger Pro. We could tell when the ball was at terminal

velocity because the speed of the ball would level off. Once we found the terminal velocity, we

still needed to find the drag. We used the formula F=pv2CA. F is the force of drag in Newtons, p

is the mass, v is the terminal velocity, C is the drag coefficient, and A is the reference area. We

then discovered that the drag coefficient of a sphere was 0.47. The reference area was found by

taking the radius of the ping pong ball (at its widest place), squaring that, and multiplying it by

pi; in other words, the reference area was the equivalent of the area of the largest cross-section of

the ping pong ball. Now all we needed was to plug in our values for terminal velocity (v) (which

we previously recorded in our experiment) to find the drag.

Diagram

Results

The top three lines are velocities with an average under them while the next three lines are the forces of drag with an average under them.

Data file: Text .:. Excel

Conclusion

We conducted our experiment in order to see the effect that mass has on the terminal

velocity of a falling ping pong ball. Furthermore, we wanted to see the effect that terminal

velocity had on the drag the ping pong ball experienced while falling. After conducting the

experiment and looking at our results, I think it is easy to see that our results were conclusive.

All of our graphs ended up as exponential or logarithmic showing that our data followed a trend.

When we matched the mass of the ping pong balls against the terminal velocity that the ping

pong balls fell with, we saw a logarithmic trend. As the mass got higher, the velocity got higher

at the start, but eventually the velocity leveled off. This is due to the fact that at a certain point,

the ping pong ball is getting close to the speed it would fall if it was in a vacuum, meaning there

is no drag on the ping pong ball. In our experiment, the velocity of the ping pong ball seemed to

approach a limit of just over 13 meters per second. This is because the combined force of the

ping pong ball’s mass and gravity was greater than the force of drag on the ping pong ball. In our

trials where the ping pong balls had a greater mass, the ping pong balls fell as if they were not

affected by drag, even though the force of drag was still rising. In our next graph, we tried

velocity versus drag. This time we saw exponential growth in our data. At first glance, the five

data points seemed to have a linear relationship. If our data was linear, then there would be a

point at which the ping pong ball had some velocity but no drag. It is only possible for there to

be an absence of drag if the ping pong ball was dropped in a vacuum, which it was not.

Therefore, the graph must be exponential in order for there to be drag at all velocities.

Bibliography

Benson, Tom. “The Drag Equation.” Grc.nasa.gov. 2010.
<www.grc.nasa.gov/WWW/K-12/airplane/drageq.html>

-NASA website about drag and equations relating to it.

Benson, Tom. “Terminal Velocity.” Grc.nasa.gov. 2011.
<www.grc.nasa.gov/WWW/K-12/airplane/termv.html>

-NASA website about terminal Velocity and equations relating to it

Drake, Stillman. Galileo at Work: His Scientific Biography.

The Physics Classroom. “Newton’s Second Law of Motion.” 2011.
<http://www.physicsclassroom.com/class/newtlaws/u2lthreee.cfm>

-Website relating to Newton's second law of motion

Rubin, Julian. “The Falling Bodies Experiment.” Following the Path of Discovery. 2011.
<http://www.juliantrubin.com/bigten/galileofallingbodies.html>

-Stuffs pertaining to Galileo. yeah.

Stern, David. “The way things fall.” From Stargazers to Starships. 2004.
< http://www-istp.gsfc.nasa.gov/stargaze/Sfall.htm>