Demonstration of the gravitational

acceleration value

Methods used to calculate “g”

• Wireless dynamic sensor system (WDSS);

• Position sensor;

• Curve fitting.

WDSS

The Wireless Dynamcs Sensor System allows you to take data from a three-axis

accelerometer, a force sensor, and an altimeter, using a Bluetooth wireless

connections to your computer. It is the perfect tool for dozens of physics and

physical sciences experiments. We used it to measure the gravitational acceleration.

WDSS specifications:• Dimensions: 12.1 cm x 5.3 cm x 3.9 cm• Mass: about 200 g depending on battery

type used and attachments

Accelerometers• Range: -60 to +60 m/s2

• Accuracy: +/- 0.5 m/s2 (+/- 0.05 g)

Experiment description

The experiment consists in dropping

the WDSS from about 2.20 meters in a box to

reduce the impact. The WDSS measures

automatically the acceleration. Then we

connect it to the computer which

process the data.

Position sensor

The position sensor uses

ultrasound to study the body motion.It reports only the

position of the nearest object

which produces the most intense echo.

- Ultrasound frequency: 40 KHz- Resolution: 1 mm- Accurency: ± 2 mm- Range: 0.15 m / 6 m

Technical characteristics

Data

Time (s)

Position (m)

Speed (m/s)

Acceleration (m/s^2)

0,80 0,267 0,118 3,413

0,85 0,273 0,341 5,792

0,90 0,295 0,713 7,853

0,95 0,341 1,168 9,060

1,00 0,411 1,645 9,613

1,05 0,505 2,142 9,787

1,10 0,626 2,634 9,729

1,15 0,769 3,111 9,716

1,20 0,936 3,601 9,689

1,25 1,129 4,096 9,014

1,30 1,347 4,570 5,857

1,35 1,585 4,909 -3,027

1,40 1,850 4,752 -20,439

1,45 2,149 2,889 -36,522

1,50 2,188 0,136 -33,731

1,55 2,085 -1,221 -15,918

1,60 2,002 -1,246 -0,291

1,65 1,950 -0,821 7,181

1,70 1,922 -0,327 9,361

Acceleration and position graphs

Speed graph

Acceleration and position graphs

Speed graph

Curve fitting

We dropped a ball from a given height and we filmed it. Then we used a software

(Logger Pro) which draws the position of the ball on a graph frame by frame and

processes speed, time and position related to the given height.

Using the curve fitting, the process of constructing a curve, or mathematical

function, that has the best fit to a series of data points, we calculated the best approximation of the gravitational

acceleration.

Data

Time (s) Y (m) Speed Y (m/s)1,872 2,689 -1,4401,905 2,646 -1,5891,940 2,580 -1,6801,975 2,531 -1,8552,010 2,455 -2,1992,045 2,379 -2,6122,078 2,286 -3,2602,113 2,144 -3,6152,148 2,025 -3,7672,183 1,894 -4,2022,218 1,731 -4,6542,252 1,567 -4,9082,287 1,398 -5,2002,322 1,202 -5,4302,357 1,012 -5,5112,390 0,826 -5,6012,425 0,636 -5,8412,460 0,413 -6,127

Conclusions

To sum up:

In all three methods the results are approximately similar to the standard

value of “g” (9,81m/s2). The errors in the last experiments are due to the material of

the ball (sponge) because of the friction with the air.