The collected data will be presented graphically to find a value for gravity, this can be done by using an equation for constant acceleration, where
x = displacement, u = initial velocity, a = acceleration, t = time
x = ut + at²
It is assumed that there was no air resistance during the ball’s descent, therefore
a = g , the constant of gravitational acceleration.
The ball falls from rest so u = 0
The equation has been modified to now give
x = gt²
This can be compared to the equation of a straight line graph, y = m x + c.
x = g t² + 0
y = m x + c
Where m = gradient of graph
c = intercept
y = vertical axis – displacement
x = horizontal axis – time
GRAPH
The gradient of the graph is found by dividing displacement by time and represents g. The acceleration of gravity can be obtained by multiplying the gradient by 2.
Change in ΔΥ = gradient = g
Change in ΔΧ
A line of best fit was plotted on the graph, which made it possible to calculate the gradient.
Gradient = ΔΥ = d - d
ΔΧ t - t
ΔΥ = 0.494 – 0.10 = 0.394m
ΔΧ = 0.10 – 0.02 = 0.08s
0.394
0.08 = 4.925
Acceleration of gravity = gradient x 2
4.925 x 2 = 9.85 ms²
CONCLUSION
From my findings it appears that the experiment has proven to be quite accurate in determining a result for the acceleration of gravity in free fall. The textbook value is 9.81ms² and I obtained 9.825ms², which is very close.
The process of finding this value was made easier by converting the results into a graph, where the advantages outweigh those of calculating each set of results, one being time consumption.
The use of a graph with a line of best fit enables you to see relationships between the results, constants, and the possibility of predicting the behaviour of results, showing new values. Instantaneously the line of best fit can reveal results that are inaccurate. A graph is easier to understand and make sense of results.
I think my result is good, however the fact that my result is above
9.81 ms² means the ball was travelling faster than the usual acceleration of gravity, which is quite strange. It would have been more expected for the ball to travel slower.
Plotting a line of worst fit against the line of best fit, and working out the difference between the two results for the acceleration of gravity would give the result a ±error.
There are theories that could explain the reasons why errors have occurred in the experiment.
One error which comes to mind to make the acceleration seem faster or slower is the measurement of the distance. Inaccurate results seemed to occur at the top of my graph where the distances were greater; perhaps this shows a relationship between distance and accuracy of measurements.
Due to the curved surface of the ball it hard to see where the ball coincides with the ruler, even with the aid of a set square, and this could cause the distance measured to be greater or smaller than it actually is.
One way to avoid this error could be to measure the distance between the electromagnet and the trapdoor and then subtract the diameter of the ball (which could have been measured before hand).
It may be worth doing an extra reading for each height to try and gain an even better average time. You would imagine that the readings for one height would be the same, yet this only happened once, all the other readings were different. The fact that it is not due to the measurement makes you question why this has happened.
Air resistance could be a factor, but again, you would imagine the air resistance to be the same as the same ball is used for each reading. If however, air resistance was occurring, a slightly different sized ball could used to repeat the experiment and see if it makes a difference.
One theory that could explain the differences in the results is retained magnetism. When the power is cut off to the electromagnet, a small amount of magnetism is retained. This is lost gradually over a very short period of time. Thus holding the ball up for a very short amount of time, not enough to visually notice but perhaps enough to make a difference and cause a slight error.
Another method for the experiment that would prevent some of these errors occurring is to use a multiflash photograph, which involves the use of a stroboscope. The release of the ball triggers a camera to photograph the ball at each flash.
