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Shoot for Your Grade!
Nolan Richter
Physics Department
Academy for Math Engineering and Science
October 7, 2014
Abstract:
Starting with a ramp and a small marble; calculations were made to predict how far
the marble would land after falling off of a table which was .917 meters tall, and
getting the marble to land on the 50 point bull’s eye. The experiment was
conducted in the Physics Lab. Where the marble landed depended on the ramp that
each group was given.
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I. INTRODUCTION:
In order to successfully conduct this experiment; we needed to know how to
use the different equations of motion. Students will be interested in where
the marble lands on the bull’s eye because we are using this for a real life
situation and it also determines a large part of the grade. Because of this, it is
crucial to find the time, velocity, and acceleration to help us find where to
place the bull’s eye.
II. THEORY:
In order to find where to place the bull’s eye, we would need to find the
velocity, time for the marble to travel along the 50cm of the flat part of the
track, and the time it would take the marble to travel from the top of the
counter to the ground. When these things are solved, we will have a good
estimate to where the marble will land.
III. EXPERIMENTAL DETAILS:
A ramp was given to each group and they each had a different length and
height. After we were given the ramp, we decided how long we wanted the
ramp to be flat in order to decide where to place the marble before letting it
drop. We decided that we wanted to use 50cm of the ramp which we would
let the marble drop at the top of the 50cm mark. We used time trials to figure
out how long it would take the marble to travel the 50cm until I caught it
right as it was coming over the edge. We also knew that the distance from
the top of the table to where the ground was is approximately 0.917 meters
and that gravity would pull it down at 9.8 meters per second squared. In
order for us to get our estimate on where the marble would hit the ground,
we used the equations:
o V= distance/time along the 50cm of the track to get velocity
o Yf= yi+ viyt + ½ ay(t)^2 to find the time it would take the marble to
travel from the top of the counter to the ground.
o Xf= xi + vixt + ½ ax(t)^2 to find where the marble will hit the ground.
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IV.
RESULTS:
In order to find out where the marble will land; we calculated the height of the
table and the length of the flat part of the track.
We timed how long it took from the marble to begin on the straight part of the
track until it fell over the edge of the table; which turned out to be .432 seconds on
average.
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V.
DISCUSSION:
Ramps were given out to each group randomly, and all ramps were different
lengths and heights. Each group had the option to choose where on the ramp
to place their marble. Our group chose to place ours 50cm up and completed
several time trials to find the average time it took for the marble to travel the
50cm of track. After finding the time, we used the equation of velocity to
solve for our velocity. Velocity = .50m/1.05sec = 0.473m/s. We then used
the height of the table (0.917m tall) and divided by the force of gravity
(9.8m/s^2) to get the time it would take the marble to travel from the top of
the table to the ground, which was found to be 0.432sec. After finding this,
we were finally able to solve for the distance to which the marble would
land on the ground. We multiplied the velocity of 0.473m/s and the time of
0.432sec together to get an estimate of .24m (24.0cm) away from the table!
VI.
CONCLUSION:
For this experiment, we predicted that the marble would land approximately
20.4cm (.24m) away from the base of the table. When our prediction was
tested, our marble did land within the 50 point bull’s eye region on the
target. The marble may not have landed on exactly .024m away, but it did
come extremely close. Close enough to where it landed where we hoped it
would land. Our experiment for Shoot for Your Grade was a major success!
VII.
REFERENCES:
Lab notes courtesy of Tarun Sunkaraneni