Amanda+and+Spencer

**Names:** Amanda Donaldson and Spencer Edelman **Class Period:** 2 **Date Completed:** 9/27/10 **Date Due:** 9/28/10
 * Acceleration Due to Gravity – Free Fall Lab**

__Objective:__ What is acceleration due to gravity?

__Materials:__ spark timer/tape, mass, ruler __Hypothesis:__ The acceleration due to gravity will equal 9.81 m/s2, which can be calculated with a ticker-tape. __Procedure:__ __Data:__ units in headings __Calculations:__ Trendline: y = 434.47 x2 + 4.6755x y=A x2 + Bx d = (A) t2 + (B) d = B + (A) t2 d = vit + ½ a t2 d = 4.6755x + 434.47 x2 434.47 = ½ a 868.94 cm/s2 = a  // Should be around 981 cm/s2; however, the ticker tape timer may have slowed it down. // Constant = 9.81 m/s2 = 981 cm/s2 (|868.94 – 981| / 981) (100) = 11.423% error
 * 1) Clamp spark timer to cabinet door and plug it in.
 * 2) Select “60 Hertz” on the spark timer.
 * 3) Get a piece of ticker tape, a little longer than a meter.
 * 4) Start to thread the tape through the timer.
 * 5) Connect a mass to the end of the ticker tape. Our mass is 100 grams.
 * 6) Pull the tape back up so that the mass is at the end of the ticker timer.
 * 7) Turn on the spark timer, while simultaneously releasing the mass/ticker tape.
 * 8) Turn spark timer off and remove mass from tape.
 * 9) Secure tape to table.
 * 10) With meter stick measure distance of the dots and put collected data in table.
 * 11) Create a position-time graph.
 * 12) Find the trendline (polynomial).
 * 13) Find the equation and the R2 value of the trendline.
 * 14) Calculate the acceleration with the equation of the trendline.
 * 15) Calculate the percent error.

__Discussion Questions:__ 1. Does the shape of your graph agree with the expected graph? Why or why not? Overall, yes our graph does agree with the expected graph. The object began with a 0 slope due to the fact it started at rest; overtime, this polynomial graph shows that the velocity increased. The increase in position related to time, provides us with the capability to determine acceleration.

2. How do your results compare to that of the class? (Use percent difference to discuss quantitatively.) Our results are fairly accurate in relationship to the outcomes of the other groups in the class. Our experimental value of "g" is 868.94 cm/s2. The class average of the experimental value of "g" is around 848.65. If you find the absolute value of the difference between our value of "g" and the class average, divide that by the class average, and multiply by 100, you will find the percent difference which allows you to compare the results. Here's what it looks like: ( |868.94-848.65| / 848.65 ) X 100 = 2.39%. This value proves that our results in comparison to the class average, is very close!

3. Did the object accelerate uniformly? How do you know? In this lab, there was a free-falling object with a mass that were affected by gravity. With a free-falling object, gravity is a constant. The value of acceleration due to gravity is g = 9.81 m/s2. Therefore, yes, the object in free-fall was accelerating at a uniform/constant pace throughout its' drop. How do you know? Smooth curve, fits quadratic well.

4. What should the velocity-time graph of this object look like? The velocity-time graph should be a linear line with a positive slope, including a y-intercept at 0, since initial velocity is 0. As the mass accelerates, the velocity increases, becoming larger. Acceleration should be a constant number. Because acceleration is the slop of a velocity-time graph, the graph should be a straight line, with the same slope at any two points.

5. Write down the expected equation of the line from this v-t graph (use specific information from your x-t graph). Velocity is equivalent to the derivative of a position-time graph. Since our equation for the position-time graph is f(x)

434.47x2 + 4.6755x, f'(x) = 868.94x+ 4.6755. F'(x) = the equation for the velocity-time graph. good
6. What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be? Acceleration due to gravity could be higher than the actual constant 9.81m/s2. If there was a greater force pulling on the mass than just gravity, acceleration would be greater. If there is any type of mass attached to the free-falling object, this could slow down the mass, causing acceleration to be lower than it should be.

Conclusion: Our experiment was successful, although our calculations were not exactly the constant we were hoping to get. Because of other factors, such as the way the mass was dropped, the tape attached to the end, and the tape rubbing against the cabinet, there was a greater resistance, causing the free fall to be lower than the expected value. We only got 11.423 percent error, which shows the experiment was very successful. Summarize (recap) actual results (numeric). If we were to redo this experiment, we could be more careful with the way the tape came through the machine, and also repeat this step a few times. After we could take the average between each point, which should be closer to the constant 9.81m/s2. Overall, our experiment proved our hypothesis to be correct, and we accomplished our goal. e