Sammy+and+Dylan


 * Objective:** To find the acceleration of an object due to gravity.


 * Hypothesis:** With our knowledge of association between velocity position and time, we hypothesized that we could find the acceleration due to gravity. Because velocity increases from the instant we dropped the weight, the spaces between dots on the ticker tape will increase as time passes and then the spaces will steadily become equal as the final velocity is reached. We used the data points collected from ticker tape to create a graph of position vs time of an object in free fall. Using the equation y=Ax^2+Bx, we are able to calculate acceleration, initial velocity, and acceleration due to gravity.

Procedure: 1.) Attatch the spark timer to the top of the cabinet. 2.) Tape the object to the ticker tape. 3.) Set the spark timer to 60 hertz. 4.) Turn on the spark timer and drop the object simultaneously. 5.) Measure the distance of each dot from the starting point 6.) Create a graph of distance vs time using this data.

Materials: Tape Spark Timer Ticker Tape Meter Stick Cabinet Door Clamp Object to tape to ticker tape

Calculations: This goes after the data and graph. A=acceleration T=time D=distance a=acceleration due to gravity

y=Ax^2+Bx D=At^2+Bt D=Vit + (1/2)at^2

y=4.3282t^2+.0577t Vi=.0577 m/s^2 4.3282=1/2a=A 8.6564=a

Data:   Discussion Questions: 1.) The graph we created corresponds to the expected graph. This is showed by our r^2 and our line of best fit. Since the r^2 value is very close to one, we know that a high percentage of the data points fit the trend of the line. Our line shows the trend of an exponential function (second degree polynomail) and this is what the equation is. We were able to use our line to calculate acceleration, initial velocity, and acceleration due to gravity. It is clear that our data points are very relative to the line of best fit. 2.) The class average for gravity is 848.649 cm/s^2. We calculated 865.64 for gravity cm/s^2. We took our calculation, and subtracted the classes average from it, and then we divided the difference by the class's average. This gave us 2.002%. Because this number is so low, we know that we have a low percent error. This means that our data is very similar to the rest of the students in the class. This makes me even more confident that our data is close to perfect. 3.) Did the object accelerate uniformly? How do you know? The lab involved an object affected by gravity. When the object is free-falling, one must use the gravity as a constant. The value of gravity is always 9.81 the the acceleration is constant as well as the object was dropped.
 * Points || Time in Seconds || Distance in meters ||
 * 0 || 0.00000 || 0 ||
 * 1 || 0.01667 || 0.0035 ||
 * 2 || 0.03333 || 0.0075 ||
 * 3 || 0.05000 || 0.014 ||
 * 4 || 0.06667 || 0.0215 ||
 * 5 || 0.08333 || 0.033 ||
 * 6 || 0.10000 || 0.045 ||
 * 7 || 0.11667 || 0.0625 ||
 * 8 || 0.13333 || 0.08 ||
 * 9 || 0.15000 || 0.1015 ||
 * 10 || 0.16667 || 0.1255 ||
 * 11 || 0.18333 ||  ||
 * 12 || 0.20000 || 0.1805 ||
 * 13 || 0.21667 || 0.212 ||
 * 14 || 0.23333 || 0.2455 ||
 * 15 || 0.25000 || 0.2825 ||
 * 16 || 0.26667 || 0.321 ||
 * 17 || 0.28333 || 0.363 ||
 * 18 || 0.30000 || 0.4065 ||
 * 19 || 0.31667 || 0.4535 ||
 * 20 || 0.33333 || 0.5055 ||
 * 21 || 0.35000 || 0.5575 ||
 * 22 || 0.36667 || 0.6125 ||
 * 23 || 0.38333 || 0.6703 ||
 * 24 || 0.40000 || 0.73 ||
 * 25 || 0.41667 || 0.7891 ||
 * 26 || 0.43333 || 0.84 ||
 * 27 || 0.45000 || 0.889 ||
 * 28 || 0.46667 || 0.9435 ||

4.) What should the velocity-time graph of this object look like? The velocity-time graph should be a linear line. The linear line would have a positive and constant slope because the slope is acceleration.

5.) Write down the expected equation of the line from this v-t graph (use specific information from your x-t graph). y=8.6564x+.0577

6.) What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be? If there was a greater force pulling or pushing the object down, then the acceleration due to gravity could be higher than it was in the experiment. If there is something interfering with the free falling object, the acceleration due to gravity could slow down.    Conclusion: The point of this lab was to find the acceleration due to gravity using the ticker tape. Our hypothesis stated that the spaces between dots on the ticker tape will increase as time passes because of the increasing velocity during the free fall. We put our results into a chart and then we created a graph with this data. This data created the equation y=4.3282x 2 + .0577x. We realized that our A value represents 1/2 of acceleration. Our A value was 4.3282 which made our acceleration 8.65 cm/s2. This result reflects our hypothesis because 8.65 is very similar to the known value of acceleration due to gravity, 9.81. Our percent error was 11.82%. Our experimental value came out to be slightly less the theoretical value for acceleration due to gravity. This error most likely occurred because of human error. When we dropped the weight, we let the tape run through our fingers to make sure it wouldn't know into something or anything of that sort. This had to effect the acceleration slightly. Another error is concerning the B value. The B value should be equal to 0 because in all free fall situations, initial velocity is 0. Our B is equal to .0577. While this isn't so far off, it could be corrected by having quicker reflexes and dropped the weight immediately when we were supposed to. 