EMILY+AND+ELENA

=Free Fall Lab Report:= Elena Solis and Emily Van Malden Period 2 Date Started: 9/27/10 Due Date:9/28/10


 * Purpose/ Objective:** to find what the acceleration is due to gravity.


 * Hypothesis:** Using what we know about the relationship between position, velocity and acceleration graphs, we hypothesize that we can calculate acceleration due to gravity. We can use the ticker-tape to create a position time graph of the object's free-fall. Then from this graph slope, we can calculate the velocity graph and using the same methods, the acceleration. From past courses, we have learned that the acceleration due to gravity is 981 cm/s 2 and so this is our goal.

1. Clamp the spark timer to the top of the cabinet. 2. Make sure the spark timer is set to 60 hertz. 3. Use tape to attach the spark tape to the object. 4. Put the tape through the timer so that the end without the object in on the other side of the cabinet. 5.Turn on spark timer. 6. Drop the object. 7. Tape the tape to the table and measure the distances each dot it from the start. 8 Record data and use it to make a graph and determine what gravity is.
 * Procedure:**

1. Spark timer 2. Clamp 3. Meter stick 4. Tape (ticker and masking) 5. Object to drop
 * Materials:**

Calculating gravity due to acceleration:
 * Calculations:** **Goes AFTER data and graph.**

D=vit+.5at2 D=Bt+At2 A=.5a D=1.8312x+389.94x2 A=.5a 389.94=.5a a=779.88 cm/s2 Percent Error:
 * 779.88-981|/981=20.5% error


 * Data:**


 * || Time s || Position cm ||
 * 0 || 0.00000 || 0 ||
 * 1 || 0.01667 || 0.25 ||
 * 2 || 0.03333 || 0.65 ||
 * 3 || 0.05000 || 1.23 ||
 * 4 || 0.06667 || 2.04 ||
 * 5 || 0.08333 || 3.12 ||
 * 6 || 0.10000 || 4.41 ||
 * 7 || 0.11667 || 5.86 ||
 * 8 || 0.13333 || 7.46 ||
 * 9 || 0.15000 || 9.31 ||
 * 10 || 0.16667 || 11.47 ||
 * 11 || 0.18333 || 13.7 ||
 * 12 || 0.20000 || 16.22 ||
 * 13 || 0.21667 || 18.91 ||
 * 14 || 0.23333 || 20.85 ||
 * 15 || 0.25000 || 24.99 ||
 * 16 || 0.26667 || 28.44 ||
 * 17 || 0.28333 || 32.01 ||
 * 18 || 0.30000 || 35.79 ||
 * 19 || 0.31667 || 39.85 ||
 * 20 || 0.33333 || 43.97 ||
 * 21 || 0.35000 || 48.38 ||
 * 22 || 0.36667 || 52.95 ||
 * 23 || 0.38333 || 57.8 ||
 * 24 || 0.40000 || 62.79 ||
 * 25 || 0.41667 || 68.11 ||
 * 26 || 0.43333 || 73.51 ||
 * 27 || 0.45000 || 79.28 ||
 * 29 || 0.48333 || 91.32 ||
 * 30 || 0.50000 || 97.99 ||
 * 31 || 0.51667 || 105.11 ||
 * 32 || 0.53333 || 111.95 ||
 * 33 || 0.55000 || 119.25 ||
 * 34 || 0.56667 || 126.65 ||
 * 35 || 0.58333 || 133.98 ||
 * 36 || 0.60000 || 142.05 ||



1.Our graph agrees with the expected graph. We know this because when we calculated the r2 we got .9999 degrees, which is very close to 1 so we know that we are accurate. Our line is polynomial and it matches the polynomial equation Ax2+Bx so we know that it agrees. Our graph started off with a velocity and zero and than accelerated as time passes and the object dropped. We could then use our line to calculate the acceleration, which can be seen in the calculations above.
 * Discussion:**

2. For acceleration we using the calculations above determined that the acceleration was 779.88 cm/s squared. The class average was 926.39 cm/s squared. To see how our data matched with the class we took subtracted the absolute value of our acceleration (779.88 cm/s squared) by the class's (926.39) and then divided that number by the class average. We got 15.8% difference. Since this number is not too big we know that our data fits in with what the class collected. Also by just looking at the chart of the class averages we can see that our data is not too high or too low but near the middle although ours is towards the lesser side. The reasons for this difference is the error of our lab and the error in the other lab groups which is disscussed in the conclusion

3. The object accelerated uniformly because it is increasing exponentially. We know this because of our graph. The position is increasing with larger intervals between each point over a period of time. Therefore we can conclude that the velocity is also increasing at this rate because velocity is distance divided by time and we can also conclude that the acceleration is also increasing.

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The velocity-time graph of this object should be a straight line with a constant positive slope. Initial velocity is zero, so the y-intercept should be 0. Then slowly as the object gains speed and distance from the original starting point, the velocity increases. Since acceleration should theoretically be a constant, then the velocity should increase at a constant rate, giving us a straight line, whose y-values (velocity) is steadily increasing. =====

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If our position-time graph's equation is 389.94x 2 + 1.8312x, then our velocity's slope should be the derivative of that or 779.88x + 1.8312. This makes sense when we check: the slope of our velocity equation should equal our acceleration due to gravity. 779.84 = 779.84. =====

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Acceleration due to gravity can be manipulated very easily in real life situations so that it's actual value is far from the theoretical one. If there is a lot of resistance (either air resistance from lighter, thinner parts more likely to catch a breeze or friction caused by the ticker tape running over the cabinet top or through our hands), then the acceleration due to gravity would decrease. If there was some force that caused the object to fall faster then it normally should, like some force bent on pulling the mass straight down or some “grease” to make the ticker tape run through the machine quicker with less friction, then the acceleration due to gravity would be faster then normal. =====

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In this experiment, my partner and I set out to determine the acceleration of a free-falling object due to gravity. Prior knowledge led us to predict that the acceleration of a free-falling object was 9.81 meters per second squared (981 cm/s2). Our hypothesis was correct. Even though our own results were low compared to that, the class average (848.65 cm/s2) was very close to the theoretical values. Use percent difference, percent error to discuss results. =====

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Overall, we calculated that our free-fall graph had about 20.5% percent error. The main sources of error came from the way we dropped the object and from our data collection. For the drop, we made sure the object's path was clear but there was probably some resistance from our hands when we guiding it into the spark timer as the object fell. In our data collection, we saw that we were missing one interval in the middle of our tape this affected our graph and our calculations. This missed interval probably occurred because we were not holding the tape close enough for the spark to make a mark. Also, the tape may have caught some air resistance as it fell down, slowing the objects acceleration slightly. Unlikely To improve our lab we could create something to hold the tape steady vertically so it does not have any resistance that would affect our data. =====