Measurement Of Free-Fall Acceleration Essay, Research Paper

Measurement of Free-Fall Acceleration

Introduction

Galileo Galilei ( 1564-1642 ) , the adult male foremost accredited with the right impression of free-fall with unvarying acceleration, stated that & # 8220 ; if one were to take wholly the opposition of the medium, all stuffs would fall with equal speed. & # 8221 ; Today, this statement holds true for all objects in free-fall near the Earth s surface. The intent of this experiment is to verify Galileo s averment that acceleration is changeless. In add-on, the magnitude of acceleration will be calculated.

Theory

By definition, acceleration is the rate of alteration of speed with regard to clip. Instantaneous acceleration is the derived function of speed with regard to clip.

a ( T ) = dv / dt.

Average acceleration is the alteration in speed during a clip interval, Dt, divided by the length of that interval,

aave = Dv / Dt.

In this experiment, mean acceleration of gravitation will be determined by mensurating the alteration in place of a falling object at on a regular basis timed intervals. With this, mean speeds for these intervals will be calculated. A graph of the mean speeds versus clip should give a consecutive line whose incline is the acceleration of gravitation ( g ) .

Apparatus

To find the acceleration of gravitation the Behr setup will be used. The device consists of two perpendicular conducting wires, a thin strip of paper held between them, and a metal-girdled weight designed to fall between the wires along the length of the paper strip. A spark timer transmits a high electromotive force electric pulsation to the wires about 60 times a 2nd. Every clip a pulsation is transmitted, two chief flickers flow through the system. One flicker passes from one wire to the metal girdle around the weight. The 2nd flicker causes a little burn in the paper, taging the location of the weight at that blink of an eye.

Procedure

Bend on the electromagnetic power supply and suspend the weight from the terminal of it. Confirm that the weight falls swimmingly into the cup at the base of the setup when the electromagnet switch is turned off. Run this trial tally about three or four times before you continue. Next, draw a fresh strip of paper from the base of the device and clamp it in topographic point. Turn on the electromagnet, and suspend the weight at the terminal of the magnet. Keep down the flicker switch, and so instantly turn off the eleectromagnet power supply. The weight should fall down to the base of the setup, doing flickers to go through between the two wires and itself. Turn off the power to the flicker timer and inspect the paper strip. A series of Burnss should be seeable along the length of the paper. Remove the paper strip from the setup and instantly tag the musca volitanss with a pen or pencil to see them more clearly.

Datas and Consequences

The undermentioned tabular array

shows the informations calculated for the experiment. The musca volitanss found on the paper strip are shown as ( N ) . The distance of the metal girdle along the strip is denoted by ( ten ) . Speed is ( V ) and acceleration is ( a ) . The estimated clip ( Dt ) for this trial was 60.2 ten 0.7s-1.

Calculations of distance, speed, and acceleration of metal girdle.

n x N ( centimeter ) xn+1 & # 8211 ; x n ( centimeter ) xn+1 & # 8211 ; x n / Dt = V N ( cm/s ) vn+1 & # 8211 ; v n ( cm/s ) vn+1 & # 8211 ; v n / Dt = a ( cm/s2 )

1 0.00

2 0.70 0.70 ten.02 42.1 tens 2

3 1.43 0.73 ten.04 43.9 ten 3 1.8 ten 5 108 tens 302

4 2.43 1.00 ten.04 60.2 ten 3 16.3 ten 6 981 tens 373

5 3.72 1.29 ten.04 77.7 ten 3 17.5 ten 6 1054 ten 373

6 5.27 1.55 ten.04 93.3 ten 3 15.6 ten 6 939 tens 372

7 7.07 1.80 ten.04 108.4 ten 4 15.1 ten 7 909 tens 432

8 9.16 2.09 ten.04 125.8 ten 4 17.4 ten 8 1047 ten 494

9 11.5 2.32 ten.04 139.7 ten 4 13.9 ten 8 837 tens 491

10 14.1 2.61 ten.04 157.1 ten 4 17.4 ten 8 1047 ten 494

11 17.0 2.90 ten.04 174.6 ten 4 17.5 ten 8 1054 ten 494

12 20.1 3.15 ten.04 189.6 ten 5 15.0 ten 9 903 tens 552

13 23.6 3.45 ten.04 207.7 ten 5 18.1 ten 10 1090 ten 615

14 27.2 3.65 ten.04 219.7 ten 5 12.0 ten 10 722 tens 610

15 31.2 3.98 ten.04 239.6 ten 5 19.9 ten 10 1198 ten 616

16 35.4 4.20 ten.04 252.8 ten 5 13.2 ten 10 795 tens 611

17 39.9 4.52 ten.04 272.1 ten 6 19.3 ten 11 1162 ten 676

18 44.7 4.72 ten.04 284.1 ten 6 12.0 ten 12 722 tens 731

19 49.7 5.00 ten.04 301.0 ten 6 16.9 ten 12 1017 ten 734

20 55.0 5.33 ten.04 320.9 ten 6 19.9 ten 12 1198 ten 736

21 60.6 5.60 ten.04 337.1 ten 6 16.2 ten 12 975 tens 734

22 66.5 5.87 ten.04 353.4 ten 7 16.3 ten 13 981 tens 794

23 72.5 6.07 ten.04 365.4 ten 7 12.0 ten 14 722 tens 851

24 78.9 6.35 ten.04 382.3 ten 7 16.9 ten 14 1017 ten 855

25 85.8 6.68 ten.04 402.1 ten 7 19.8 ten 14 1192 ten 857

26 92.7 6.93 ten.04 417.2 ten 7 15.1 ten 14 909 tens 853

27 99.9 7.15 ten.04 430.4 ten 7 13.2 ten 14 795 tens 852

28 107.4 7.46 ten.04 449.1 ten 8 18.7 ten 15 1126 ten 916

29 115.0 7.74 ten.04 465.9 ten 8 16.8 ten 16 1011 ten 975

30 123.1 8.01 ten.04 482.2 ten 8 16.3 ten 16 981 tens 975

31 131.1 8.20 ten.04 493.6 ten 8 11.4 ten 16 686 tens 971

32 139.9 8.55 ten.04 515.0 ten 8 21.4 ten 16 1288 ten 978

33 148.7 8.80 ten.04 530.0 ten 9 15.0 ten 18 903 ten 1034

African American Vernacular English = 9.47 x.69 m/s2 s = 9.47 x.78 m/s2 incline ( m ) of graph = 8.9

Decisions

The mean value of acceleration for each clip interval is closer to the desired value of 9.8 m/s2 than the deliberate incline of the velocity-time graph. The norm of uncertainnesss for the deliberate accelerations is a better as pick of uncertainness because it provides a narrower field of uncertainness than does standard divergence. In decision, the deliberate value of 9.47 ten.69 m/s2 for acceleration is acceptable.

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