27 August 2014 - Free Fall Lab and the Determination of g; Errors and Uncertainty

Free Fall Lab 

     Purpose: To examine the validity of the statement: In the absence of all other external forces 

except gravity, a falling body will accelerate at 9.8 m/s^2. 


The first step was to prepare the necessary equipment:
     1. A meterstick: to measure position
     2. A free-falling object
     3. Heavy tripod base with leveling screws    
     4. An electromagnet to release the object
     5. Tape and a spark generator: To mark the position as the object fell
     6. Computer: To calculate the data

    

     The picture above depicts a spark generator attached to a sturdy column with two wires, where a 

object is dropped from an electromagnet at the top. During the fall of the object the spark generator 

makes intervals on a spark-sensitive tape that records a permanent record of the fall. 

     

Above is a picture of multiple lengths of spark-sensitive tape.

     The picture above shows our length of spark-senstive tape. On this tape we marked 15 points out

and measured the total distance.


     We the proceeded to use Excel to create a chart where from the known time and distance came

up with five columns. These columns consisted of time, distance, the change of position in

between two points, the mid-interval time, and the mid-interval speed.

Time  (s)	Distance  (cm)	∆x (cm)	Mid-interval Time (s)	Mid-interval Speed (cm/s)
0	0	2.7	0.008333333	162
0.016666667	2.7	2.9	0.025	174
0.033333333	5.6	3.3	0.041666667	198
0.05	8.9	3.5	0.058333333	210
0.066666667	12.4	3.7	0.075	222
0.083333333	16.1	4	0.091666667	240
0.1	20.1	4.3	0.108333333	258
0.116666667	24.4	4.5	0.125	270
0.133333333	28.9	4.9	0.141666667	294
0.15	33.8	5	0.158333333	300
0.166666667	38.8	5.5	0.175	330
0.183333333	44.3	5.6	0.191666667	336
0.2	49.9	5.9	0.208333333	354
0.216666667	55.8	6.2	0.225	372
0.233333333	62	-	0.241666667	-

     In Excel we used formulas to come up with the change in distance, mid-interval velocity, and mid-

interval time.  From that information we graphed a chart of mid-interval velocity over mid-interval

time graph and as a result came up with the mid-interval acceleration as our slope. We also graphed a

position over time chart and came up with velocity as our slope. Both graphs are see below.

Graph of Mid-interval Velocity (cm/s) Over Mid-Interval Time (s)

Graph of Position (cm) Over Time (s)

      In class we combined the data that we got with the data of the other groups so that we would be 

able to find any deviation in our data results and find out any uncertainty that we had in the 

experiment. 

Group	g	Deviation	Abs Deviation	Deviation^2
1	961	5.711111111	5.711111111	32.61679012
2	936	-19.28888889	19.28888889	372.0612346
3	975	19.71111111	19.71111111	388.5279012
4	969.6	14.31111111	14.31111111	204.8079012
5	939	-16.28888889	16.28888889	265.3279012
6	975	19.71111111	19.71111111	388.5279012
7	949	-6.288888889	6.288888889	39.55012346
8	930	-25.28888889	25.28888889	639.5279012
9	963	7.711111111	7.711111111	59.46123457
Average:	955.2888889		14.92345679	16.29726933

     We found that as a class we had an absolute deviation of 0.149 m/s^2 of a fall due to gravity. As 

seen in the graph above.

Summary

     In class we attempted to validate the statement that with no other forces except gravity an object 

falls at a rate of 9.8 m/s^2. We dropped a object from an electromagnet that established a current 

between two wires on a column creating marks on a spark tape. From these marks we found the 

distance between 15 points and with the help of Excel the distance in between each of those points, 

the mid-interval time in between each point and the mid-interval speed. After this had been 

accomplished as a class we took down the all the groups information and averaged them out. We then 

found the average deviation of the classes' experiments from that average that we found for the 

groups cm/s^2 of gravity.