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Determination of the Acceleration due to Gravity on the Earth’s Surface

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Introduction

PLAN

Determination of the Acceleration due to Gravity on the Earth’s Surface

I will be investigating the acceleration due to gravity on the Earth’s surface using an experiment based on this effect. The acceleration due to gravity is constant for all objects, as it is defined by the strength of the gravitational field strength of the object, and not the mass of the object it is pulling.

Therefore, in a vacuum, all objects will accelerate at the same rate due to gravity. This only applies in a vacuum, as air resistance plays a significant role as a frictional force. The Earth’s acceleration due to gravity (also referred to as Standard Gravity, or simply g) is 9.80616ms2 (according tohttp://medical-dictionary.thefreedictionary.com/Standard+gravity), or 9.81ms-2 to three significant figures.

The weight of an object is its downwards force, which is given by the equation:

F = mg

Where F is the downwards force, or weight; m is the mass of the object; and g is the gravitational field strength of the body attracting it (this is simply g on Earth; standard gravity).

When forces are taken into account, frictional forces play a part in determining the resultant force. The downwards force of the body is constant, as the mass does not change as the body falls. However, air resistance increases with velocity, in the case of freefall under gravity.

...read more.

Middle

n/a

18.6

0.1

1.86

4.4

26.5

0.1

2.65

7.9

39.5

0.1

3.95

13

47.5

0.1

4.75

8.25

54.0

0.1

5.40

6.25

My results give an average acceleration of 7.96ms-2, which is quite satisfactory considering the effects of friction and air resistance. In the actual run, however, I will use a 200g mass, as this should further reduce the effects of these frictional forces. Therefore, the acceleration given should be closer to g.

Accuracy and Reliability

To improve the accuracy of my results, I will use a mechanical timer, which will remove human error from this process. Also, I will measure the dot-to-dot distance with a metre ruler with millimetre increments, to increase the accuracy of that process. This should give an error of ±1mm.

The time increments, height of the drop and the gravitational field strength are all constant, so the accuracy of the readings should be fairly high.

To improve reliability, I will repeat the experiment three times. The same scenario will used in each, keeping height, gravity, and time increments the same. If there are no anomalous results, then my results should be quite reliable.

Equipment

  • A.C Power supply
  • 200g mass
  • Clamp stand
  • Ticker tape timer
  • Ticker tape
  • Sellotape
  • Metre ruler
  • Connecting wires

Risk Assessment

Risk

Cautionary Procedure

Risk of electric shock if connecting wires are unsafe or bare

Check to ensure that electrical equipment is kept in safe condition

Masses dropping from height

Be aware, and raise awareness of others, that there are suspended masses

Sources Used

  • Sang, D., Gibbs, K. & Hutchings, R. (ed.) 2004, Physics 1,
  • Cambridge University Press, Cambridge, UK
  • Wikipedia 2007, Standard gravity, viewed 27 March 2007,
  • < http://en.wikipedia.org/wiki/Standard_gravity>
  • Wikipedia 2007, Pendulum, viewed 27 March 2007,
  • < http://en.wikipedia.org/wiki/Pendulum>
  • Saunders 2007, Standard gravity - definition of Standard gravity in the Medical dictionary - by the Free Online Medical Dictionary, Thesaurus and Encyclopedia., viewed 27 March 2007,
  • <http://medical-dictionary.thefreedictionary.com/Standard+gravity>

Results

First Run

Distance

(x10-2m)

Time

(s)

Speed

(ms-1)

Acceleration

(ms-2)

6.30

0.1

0.63

n/a

16.2

0.1

1.62

9.90

24.5

0.1

2.45

8.30

34.7

0.1

3.47

10.2

43.2

0.1

4.32

8.70

54.8

0.1

5.48

11.6

...read more.

Conclusion

1 – F2

        = 0.128N

Therefore, there must have been a 0.128N friction opposing the motion of the mass.

Evaluation

There were several flaws and limitations of the experiment, when it came to the actual procedure.

The tape may have run through the timer at an angle, which would have affected the vertical fall of the mass, and therefore, the distance between the dots. This would have changed the value for g that resulted.

The timer may also have been irregularly marking the tape, which would severely negate the accuracy and reliability of my results. This would have made the timing inconsistent, and the time is crucial to calculating the value of the acceleration. There was no way of knowing which dots may or may not have been anomalous, so this compounded the problem.

The tape may have had kinks or small rips in it, which would have altered its path and added to friction. This would change the position or regularity of the dots on the tape.

The reliability of the results is questionable, as the latter two graphs showed an acceleration of within 0.07ms-2 of each other, but the first graph shows a reading of 8.4ms-2,which is a whole 1ms-2 out from the others. This made a definite difference to the average value of standard gravity.

Percentage error        = (highest result – lowest result)        x 100

                                     Average result

                        = 1.07                x 100

                           9.17

                        = 11.7% error

This is a fairly large percentage error.

The error bars on my graphs, blue for maximum and black for minimum, also show how wide the possible error for my results is.

...read more.

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