A Rolling Marble Gathers No Moss

A Rolling Marble Gathers No Moss: 

The Ramp Lab

Procedure:

Procedure:

1) Decide on 3 different types of ramps with varying arrangements to test (see picture)

 2) For each ramp type release the marble from the edge of the tallest book 

4) Start timer as the marble exits the ramp and begins rolling across the table

5) stop timer as the marble reaches 1.5 meters

6) Repeat twice for each Ramp Type/Height

Synopsis of the Procedure:

Our group decided our three ramp types (pictured) and combined two tables to make space for our ramp. We chose one marble to consistently use, as well as establishing where the ramp would always end. After setting up the ramp, we placed the meter sticks for the total of 2 meters, with the intention of only measuring 1.5 meters. We started with Ramp Type 1 Height 1, and proceeded to do two trials for each height of each Ramp Type. I would release the marble at the edge of the highest textbook, the marble would roll down the ramp, my partner Garrett would start the stopwatch as the marble began rolling onto the table, Garrett would stop the stopwatch as the marble passed 1.5 meters, and our other partner Allison would then write down the data. We repeated this process for the entirety of the trials with the same materials.

What do these graphs tell us?

When looking at these graphs it becomes very apparent that the height of the graph is far more important than its form. Across every type of ramp, there is a noticeable increase in speed for each height. The location of the points on these graphs tell us that height of a ramp and speed at the end of a ramp are directly related. It could also be assumed that there is a not a connection between length of ramp and speed at the bottom of a ramp. There appears to be very little evidence of a connection between the two, and if there is one, it is probably

negligible. It should be noted there is a break in this pattern between Ramp 1 Height 2 and Ramp 1 Height 3 where it appears that their averages are the same. However,  it is debatable as to whether this discrepancy actually roots from a possible mis-click on the timer or another form of human error. Disregarding this once instance, it appears from the data and the graphs that their is a strong link between height of a ramp and the speed at the bottom of the ramp.

Speed	Height	Ramp Type
1.03	2	1
1.05	2	1
1.46	3	1
1.29	3	1
1.42	4	1
1.39	4	1
1.05	2	2
1.17	2	2
1.43	3	2
1.17	3	2
1.46	4	2
1.53	4	2
1.1	2	3
1.06	2	3
1.24	3	3
1.24	3	3
1.74	4	3
1.53	4	3
0	0	N/A

An Exponentially Important Graph

With an exponential trendline in place, it becomes incredibly visible that ramp height and the speed at the bottom of the ramp are exponentially related. What this means is that as ramp height gets higher and higher, regardless of the length of the ramp, the speed of the marble will increase even more. A drop down the curve of King-Da-Ka at Six Flags and a roll down an equally tall, but longer, ramp will yield the same speed (although I am sure the wait time to get on King-Da-Ka and the time it takes to slide down an incredibly long ramp would be about the same). By the end of the longer ramp, you will generate the same amount of speed as King-Da-Ka because, as proven in this lab (and disregarding all friction/other slowing factors), length of ramp is not important, height is.

A Straight Line: Speed Squared

Speed squared, the diagonal line, what does that mean and why is it important? Before we look at speed squared, lets first investigate the relationship between another similar phenomenon, radius squared and its relationship to a circle's area. The graphical pattern between radius and area of a circle is an exponential curve, but more importantly, when the radius is squared, it becomes a diagonal line with a constant; a constant that roughly equals 3.14, and is commonly abbreviated with the symbol π. Following the formula for a line (y=mx+b), with a y-intercept of zero, the equation of the graph of radius squared to area becomes A=πr^2+0, or more commonly known as A=πr^2. When we take this approach to the graph of speed squared, in a world of perfectly accurate statistics and data on a high school lab, we should get H=9.8s^2+0, or H=9.8s^2. Just like radius squared, this number is not random, 9.8 m/s^2 is the approximate value of earths gravitational pull, the force that would act on a marble rolling down a ramp. The relationship between speed at the bottom of ramp squared and height of the ramp are connected by the gravitational force, forming a perfect diagonal line.