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Investigating how height affects time taken for a falling object to reach ground level.

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Introduction

Physics Coursework 2003:

Investigating How Height Affects Time Taken for A Falling Object to Reach Ground Level.

Introduction:        In this investigation, how height will affect the time taken for a steel ball bearing to reach the ground will be investigated.

It is was Isaac Newton that first discovered gravity and wrote laws defining it. His Second Law of Motion states that the Resultant Force on an object (F) is equal to the Mass of the body (m) times its acceleration (a), or image01.png.

The weight (W) of a body is the force of gravity acting on it, which gives it acceleration (g) if it is falling freely close to the earth’s surface. If the body was to have a mass (m) Newton’s 2nd Law of Motion could calculate its weight. Given that image02.png and image12.png Newton’s Law becomes image18.png.

In April of 2003, in a method similar to that, which will be conducted in this investigation, the acceleration of gravity was concluded to be 9.81image21.png.

Using the knowledge mentioned above, several equation of motion have been created.

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Middle

0.082

0.3

0.247

0.061

0.2

0.202

0.041

0.1

0.143

0.020

0.0

0.000

0.000

This is what the expected graph of Height vs. time should look like:

image00.png

        Height (m)

                                Time (secs)

The following page shows what the expected graph for Height vs. time2 should look like. It is a straight line passing through the origin, thus proving the prediction image17.png.

The expected gradient, m, should be equal to ½ g, or, 4.905ms-2. It is actually 4.926ms-2, which is only 0.021 ms-2 out or 0.428%. This is probably due to the rounding of decimal places when drawing the graph and human error in plotting the points (i.e. not exactly accurate to 3 decimal places.)


Apparatus & Diagram:

Safety: As there is a very minimal risk in this investigation, no safety measures need to be taken.

It is planned to drop the ball from a height of 1m and decrease in intervals of 0.1m. At each height 5 readings will be recorded and then the mean result will be calculated. This makes the results more reliable (and better for use in calculation like working out g or the mass of the steel ball.)

The Results will be recorded in a table like this:

Height (cm)

Time taken for ball to reach ground (seconds)

Mean Result

Mean Result2

1st

2nd

3rd

4th

5th

100

90

80

70

60

50

40

30

20

10

00

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Conclusion

image20.png.

Note: The factor that affected the acceleration was g, (which, on earth, is image22.png) is the mass of the planet, for Earth this is constant.

The results of the investigation are consistent with the prediction. The relationship of image17.png was proved in the similarity of the graphs on page 4 & 8, they had almost the exact same gradient, only 0.072ms-2 in difference (or 1.462%) it was also very similar to the mathematical prediction of the gradient (½g) again only 0.051 ms-2 out.

Evaluation:In this investigation, all results are held to be very reliable. When the data was being collected, sophisticated technology was used which measured time accurately and reliably to the nearest thousandth of a second. All recorded results were in very close proximity of each other, so that 0.006seconds was the maximum difference observed.

There were no anomalies observed. All points on the graph on page 8 are not only close to the line of best fit, they are actually on it.

The results in this investigation are believed to be very reliable; as a result no changes need to be made to the procedure.

Physics Coursework October 2003                Andrew Lavery S2F

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