Measuring g in more than one way

The greatest error for the experiment was contained within this problem. Allowing for an effect on the result of the measurement.

To calculate this error i evaluated the maximum amount a miss-drop could alter the distance read.

 

Therefore error = (82+42)1/2  - 8= 901/2 – 8 = 9.48683 – 8 = 1.49 (3.s.f) or 8 + or – 9.3125%

Or 10.7703 – 10 = 0.770 (3.s.f) therefore + or – 3.85%

In the averages this results in

9.73 + or – 0.957  (3.s.f) for mask size 8cm

9.84 + or – 0.391 (3.s.f) for mask size 10cm

This clearly shows that there is a lower uncertainty in the larger mask size.

The results average at 9.785 + or – 0.674, showing a fairly large uncertainty within the experiment. To reduce this uncertainty i could have made the mask bigger, attached the cardboard to a system which would keep it upright during its descent or reduced the width I cut into the cardboard (in this case 4cm)

Experiment 2:

For this experiment I needed

• A pendulum
• 1 x stand
• 1 x boss
• A stopwatch

Method:

I set up the pendulum by attaching a spherical weight to the end of a piece of string of length L and attaching this to the boss on the stand. I then would start the pendulum and measure the time for 10 oscillations. This is to reduce the uncertainty introduced by the stopwatch and human error. Then using the equation below I calculated the value of g. T, time period = time for 10 oscillations/10. After i had taken 6 measurements to ensure accuracy I would change the length of the string to see the effect on my results.

 

Whereby slope = T2/L

Results:

This table shows that this method is very accurate with only 1 of 4 values being wrong correct to 2 significant figures.  The results however average out overall at 9.862544134 or 9.9 to 2.s.f. The greatest uncertainty in this experiment was held in the human error introduced by the stopwatch. However I reduced this uncertainty by measuring 10 oscillations and dividing the resulting time by 10 to get T. For this reason I reduced the uncertainty from 0.215 seconds (Average reaction time of a human) to 0.0215 seconds. Due to this the error introduced due to human error in timing is at the most 0.34% ((100/Av time for 10cm 6.336666) x 0.0215 = 0.339)

This means that the greatest error introduced would be through my assumption that the pendulum was a simple pendulum. Meaning that it was a ball of no mass held from a light, inextensible string, with no effects of air resistance or friction. These assumptions would introduce a fair uncertainty to this experiment, however the greatest uncertainty was introduced within the length of string the weight was suspended by. Due to the design of pendulum I used I could only change the length of the string to a degree of 2cm. This means the average uncertainty within this measurement was 25cm (average L) + or – 1 or 25cm + or – 4%. This means my final uncertainty for the second experiment was 9.86 + or – 4%

I could have reduced that uncertainty by creating a compound pendulum and using the modified equation for a compound pendulum, however there are many more factors to be considered when a compound pendulum is involved.

Conclusion:

What I have found is that both methods are fairly accurate in their final values of g, with the first experiment being closer to my assumed value of g, and the second containing less uncertainty in its results. I can conclude that both are suitable methods for confirming the value of g to a fair degree of accuracy.

Other Methods considered:

I also considered performing the first experiment, but with two light gates and a metal ball. The problem with this however was that it would have been hard to ensure that the diameter of the sphere would pass through the light gates. For this reason I chose to adapt the experiment using a piece of cardboard with a mask to reduce the uncertainties.

I also considered the traditional method of measuring g, before QED’s were created, by using what was called an “Atwood’s Machine” involving a pulley with weights on either side and measuring the time taken for one weight to hit the ground. This again introduced human error in the timing of this period and, unlike when using a pendulum, it would be difficult to reduce that uncertainty.

Sources:

1.        http://www.physics.mun.ca/~cdeacon/labs/simonfraser.pdf

2.        http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html

3.        http://en.wikipedia.org/wiki/Acceleration_due_to_gravity

4.        http://en.wikipedia.org/wiki/Reaction_time