Jason Crasnick

Ryan Connolly

Lindsey Franklin

PROCEDURE:

For our procedure, we began by setting up a track for our cart to roll down. We then attached a motion sensor to the end of this track to determine the velocities for all of our trials. For the surface area trials, we attached cardboard (of different areas) to the outside of our cart to simulate different surface areas of different parachutes. For the mass trials, we added three different weights to simulate different masses of different divers. While this was probably not the best experiment, we figured that it would adequately test the variables of mass and surface area as they pertain to terminal velocity. However, we soon learned that our experiment lacked the realistic simulation of skydiving that it needed to be accurate in the real world of skydiving.

 RELATIONSHIP IDENTIFICATION:

Before our experiment, we hoped that we would see that as more surface area was applied, the terminal velocity would go down. Because terminal velocity is reached when the force of gravity equals air resistance, both these equations help decide terminal velocity. The air resistance can be calculated by multiplying the atmospheric pressure (the density of the air), velocity (squared), surface area, and the drag coefficient (which is established by the shape of the diver) by one-half :

As a result of this equation, a diver will fall much faster in a tuck position than if he or she kept a spread eagle position; due to the increase of surface area in the spread eagle position, the air resistance will affect the diver more. It was this principle that was the basis of our experiment, because we knew that changing the surface area would change the terminal velocity of our cart.

For the mass, we hoped that as mass was added, the terminal velocity would increase. Newton’s Second law states that force is directly proportional to mass and acceleration:

This law is used to find the force of gravity. And, because the constant acceleration of gravity is equal to -9.8 m/s², the force of gravity can be calculated by multiplying the mass of the diver by the acceleration of gravity constant. Because of this, we figured that by changing the mass, we would change the force of gravity, and thus the terminal velocity.

However, because the differences in mass and surface area were not enough to effect our experiment as they do in the real world of skydiving, our data did not support our hypothesis the way that we would have liked.

RELATIONSHIP EXAMPLES:

We obtained data through velocity vs. time graphs and position vs. time graphs of each different variable.

• The large surface area graphs (position vs. time on top):

• The medium surface area graphs:

• The small surface area graphs:

The large mass graphs:

The small mass graphs:

This data is very unreliable, however, for the following reasons.

ERRORS:

We experienced many errors while experimenting. First of all, we began with a 2 meter track, at about a thirty degree angle, and worked our way from there. As a thirty-degree angle proved to be too high, and the cart did not reach terminal velocity, as a result of the short track and steep angle. Thus, we began to lower the track, testing it each time, yet were still unable to reach terminal velocity. To revise our experiment, we began by trying a very flat slope for our track. However, the cart, even with the maximum amount of surface area that we have, still accelerated to the very end of the track. So, we unhooked everything, and attached a new track, this one twice the size of the original. With this new track, we began with a slightly steeper slope, hoping that the length of the track would compensate for the slope and we would perhaps be able to reach terminal velocity. This was not the case, however, and we had to lessen the slope once more, to an almost flat angle. Furthermore, we experimented with "pushing" the cart to make it reach terminal velocity before it hit the end of the track, as the cart was still not reaching proper terminal velocity. Because we could not gauge our pushes, our data could have come out incorrect. We also should have done an experiment using actual parachute and diver models, instead of simply testing the general physics principles of which skydiving is based. Our surface areas and masses did not differ enough to make any substantial change in the data (as seen in the graphs), and so our data did not support our hypothesis. Because our experiment did not simulate the actual process of skydiving as much as it should have, it did not promote the most accurate and "real life" results.