Free+Fall+Lab+JN

= __**Free Falling Lab: Bombs Away**__ = Navin Raj and Jimmy Ferrara Period 2 09/27/2010


 * Objective:** What is the acceleration of a falling body due to gravity? -->**Theoretical Value:** g=9.8 m/s 2
 * Materials:** spark timer, ticker tape, masking tape, mass, meterstick, clamp


 * Hypothesis:** We can say that acceleration due to gravity is the amount an objects speed changes as it falls because of the force gravity has while pushing down on the object in question. We hypothesize this because of our knowledge of velocity over time and the fact that it increases if enough force is pushing behind it. Also, the theoretical constant value of acceleration due to gravity is 9.8m/s 2 , meaning it will constantly increase at this interval. This would mean that as the object falls from the top, the dots on the tape would constantly be spread farther apart due to the increase in speed.


 * Procedure:**
 * 1) Attach the spark timer to a flat surface off the ground (in this case a cabinet), using a clamp.
 * 2) Tape the mass to the ticker tape using masking tape, being careful to make sure the tape is flat.
 * 3) Set the spark timer to 60Hz.
 * 4) Loop the tape up-through the spark timer so that one end is on the backside of the cabinet, and the mass is on the front.
 * 5) Pull the mass to the top of the timer and let go of the mass.
 * 6) Tape both ends of the ticker tape to a table and measure each dot over however much time it took.
 * 7) Input data onto a chart and graph.


 * Data:**

=__Data Table of Free Fall__=

= =
 * Dot Number || Time (s) || Position (m) ||
 * 0.0 || 0.0000 || 0.00 ||
 * 1.0 || 0.0167 || 1.13 ||
 * 2.0 || 0.0333 || 2.10 ||
 * 3.0 || 0.0500 || 3.35 ||
 * 4.0 || 0.0667 || 4.72 ||
 * 5.0 || 0.0833 || 6.49 ||
 * 6.0 || 0.1000 || 8.51 ||
 * 7.0 || 0.1167 || 10.63 ||
 * 8.0 || 0.1333 || 13.05 ||
 * 9.0 || 0.1500 || 15.45 ||
 * 10.0 || 0.1667 || 18.29 ||
 * 11.0 || 0.1833 || 21.48 ||
 * 12.0 || 0.2000 || 24.62 ||
 * 13.0 || 0.2167 || 28.24 ||
 * 14.0 || 0.2333 || 32.00 ||
 * 15.0 || 0.2500 || 36.01 ||
 * 16.0 || 0.2667 || 40.11 ||
 * 17.0 || 0.2833 || 44.73 ||
 * 18.0 || 0.3000 || 49.45 ||
 * 19.0 || 0.3167 || 54.48 ||
 * 20.0 || 0.3333 || 59.65 ||
 * 21.0 || 0.3500 || 64.99 ||
 * 22.0 || 0.3667 || 70.80 ||
 * 23.0 || 0.3833 || 76.40 ||
 * 24.0 || 0.4000 || 82.44 ||
 * 25.0 || 0.4167 || 88.98 ||
 * 26.0 || 0.4333 || 95.89 ||
 * 27.0 || 0.4500 || 102.95 ||
 * 28.0 || 0.4667 || 110.04 ||
 * 29.0 || 0.4833 || 117.44 ||
 * 30.0 || 0.5000 || 125.11 ||
 * 31.0 || 0.5167 || 132.99 ||
 * 32.0 || 0.5333 || 141.14 ||
 * 33.0 || 0.5500 || 149.38 ||
 * 34.0 || 0.5667 || 158.24 ||
 * 35.0 || 0.5833 || 167.04 ||
 * 36.0 || 0.6000 || 176.34 ||
 * 37.0 || 0.6167 || 185.44 ||

=__Graph of Free Fall__=

**Calculations:**

Trendline: y=426.66x 2 +37.058x, R 2 =1 y=Ax 2 +Bx <-- equation of trendline
 * **Acceleration:**


 * d=Bt+At 2 <-- sub in t for x
 * d=V i t+1/2at 2 <-- most similar equation
 * y=d, A=1/2a <-- equivalent values

426.66 cm/s 2 = 1/2a a= 853.32cm/s 2 __**//a= 8.5332﻿m/s//** **//2//** __ experimental acceleration= 8.5332m/s 2

Percent Error= __|Experimental Value-Theoretical Value|__ Theoretical Value X100 Theoretical Value ds;lfakdjsfakljd X100
 * **Percent Error:**

Percent Error= __|8.5332-9.8|__ dalsfjlkdfjadls;ffdsaj 9.8 kjfd X100

__**//Percent Error= 12.9%//**__


 * Discussion Questions:**

Yes, because the polynomial fit used only had a R2 value of about 1. The polynomial fit makes sense because as gravity acted on the mass, it increased in speed. The graph matches the ideal graph of a position-time graph for increasing speed away, which is correct because the ticker tape is being pulled away from the timer.
 * 1. Does the shape of your graph agree with the expected graph? Why or why not?**

We found that our acceleration due to gravity was 853.32cm/s 2, while the class average turned out to be 848.65cm/s 2 ﻿. In order to compare this to the class average, it was necessary to find the percent difference. To do this, we subtracted our results from the class average. We then used the absolute value of that answer and divided it by the class average. The final step was to multiply it by 100 to get a percentage.
 * 2. How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)**

4.67/848.65= .00550 .00550X100= .550% difference
 * 853.32-848.65|= |4.67|=

Thus, we can see that our result was but .550% away from the class average. Which is very close, meaning that our answer is a relatively common answer.

Yes, because the slope of the line is very smooth and increases very steadily.
 * 3. Did the object accelerate uniformly? How do you know?**

The velocity-time graph of this object would be a linear line with a positive, increasing slope. slope should be? This is because the distance covered over a certain amount of time increases over time. The starting point of the velocity-time graph would be at zero, since initial velocity is zero. It would just increase positively from there. The slope of the graph would be positive because the acceleration is positive.
 * 4. What should the velocity-time graph of this object look like?**

y=426.66x, the v-t graph will be a positively sloping line starting from zero. slope should be "g" not 1/2 a
 * 5. Write down the expected equation of the line from this v-t graph (use specific information from your x-t graph).**

The acceleration due to gravity might be higher or lower than it theoretically should be because of human error. A perfect drop depends on how perfect the free fall is. For instance, if you hesitate while dropping or glide the tape down with your hand, then the acceleration due to gravity might be lower than it should be. It is also important for the mass to hit the ground straight-on. If it is hindered by the tape, for example, then the free fall will be altered and the acceleration due to gravity will be less than it should be. On the contrary, if one puts extra force behind the drop, causing initial velocity to be above 0, then the acceleration due to gravity would be higher than it should be. In our case, it is very likely the acceleration due to gravity is lower because we had a notebook barrier between the ground and the mass in order to protect the mass from breaking off. Thus, it did not hit perfectly straight.
 * 6. What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?**

conclusion?