Gravity is a force of attraction between any two masses. This force is unusual as it is the only force discovered that has no repulsive effect unlike for example, magnetism which can attract and repel other masses.
The Earth is surrounded by a gravitational field which exerts a force on any mass in it. In terms of this experiment the ball is attracted towards the earth as it falls.
I read that experiments done in the past have shown that at a particular place all bodies falling freely under gravity in a vacuum or where air resistance is negligible have the same constant acceleration irrespective of their masses. This is why for this experiment the mass of the ball is irrelevant as long as it remains constant throughout the experiment. This is due to the fact that acceleration due to gravity is a constant for all objects irrespective of mass where air resistance is negligible.
If we wish to find the acceleration due to gravity we only need to know the displacement of the ball and the time taken for it to fall that distance.
This value is taken as 9.8m/s/s; that is to say that the velocity of any body travelling downwards will increase by 9.8m/s every second neglecting the effect of air resistance.
As a result, my initial prediction is that the time taken for the ball to hit the plate will increase as the distance increases and as a result the acceleration will increase.
This prediction is based upon the evidence found in the textbook mentioned above but also through initial examination of the data.
For this experiment my partner and I decided to attach the metal plate switch at 20cm intervals from 20-200cm so a wider range of results could be calculated. We wished also to see if we could obtain the terminal velocity of an object in free fall i.e. the speed at which it will stop accelerating but the distance between the ball and the switch was not great enough.
The final graph I will plot will be the displacement of the ball bearing over the time taken to open the switch squared.
The two values should show positive correlation as if we arrange the equation from the textbook:
S=ut + 1/2at²
s/t² = u/t + ½ a
s/t = u/t + ½ a
We know that intital velocity is Zero so:
s/t² = ½ a
This rather conveniently allows us to find the acceleration due to gravity by simply doubling the gradient.
g = 2( s/t²)
We see now how it is possible to obtain a value for g as I have data on both the displacement of the ball bearing and the time taken for it to fall that distance.
An initial graph without reference to the data should be virtually straight line taking experimental error into account, perhaps looking roughly so:
I have shown here the time squared for an object to fall over 50cm. I have taken g to be 10 which I have read is an approximate value. We see here that the time taken to fall increases proportionally to the displacement. I believe this will be true for the actual data also but need to plot this also.
The highlighted result is the one I see as anomalous; I will explain later the major sources for error in the experiment.
We see that the graph is almost a straight line showing that my initial prediction was correct in that the time squared had a positive correlation with the distance travelled.
Let us presume now that we do not know that g is 9.8m/s/s and work it out based upon data on the graph.
We know from my previous rearrangement of the equation in the textbook that the acceleration is the gradient doubled.
To work out the gradient we must divide the change (delta) of they Y axis by the change of the X axis.
When plotting the gradient it is wide to take it over the widest range possible to take all results into account. As a result I have decided to take the results from the extreme points of both the displacement and time. This is why I took the displacement over two metres instead of one – to obtain a wider range of results.
The data is taken from 20-200 cm. This is 180cm. However the modern convention is to measure length in metres which gives us a change of 1.8 m.
The change along the X-axis is equal to 0.4-0.033 which comes to 0.367
If we divide 1.8 by 0.367 the result comes to 4.905 which we know is half the acceleration.
If we double this value we find that (barring experimental error) the acceleration of the ball was 9.809 m/s/s which if we round up to 9.81m/s/s we find that it is very close to the conventional value for g.
This does not leave us much room for experimental error as the variance between the value I obtained and the value stated in any textbook is 0.1m/s/s. However I believe there were sources of error for this experiment in general which I will now outline irrespective of the fact that they did not affect my own.
The most significant factor when measuring g is that air resistance will act upon the ball. Explaining Physics tells us that we can neglect this factor as the ball itself is very dense. However, air must provide some resistance to the ball falling and could conceivably affect an experiment especially as air resistance isn’t the same from one moment to the next for example, someone could open a window and cause an air current to act upon the ball.
The only real remedy for this factor is to perform the experiment in a vacuum.
A less likely factor to affect the experiment is the fact that the ball may display residual magnetic properties through repeatedly being attached to the electromagnet. The atoms within the ball could well have been ordered to make the ball itself be attracted to the electromagnet after the switch was thrown.
Even if current was no longer flowing through the wires around the core, a weak magnetic field may have been apparent in the ball causing it to be attracted towards the iron core due to previous use.
While iron is magnetically ‘soft’ and would probably not have magnetic properties once the switch was opened the ball is made of steel which can retain magnetic properties.
A solution for this problem would be to demagnetise the steel ball by either using a demagnetising tool or by simply heating it up by placing it in a naked flame for several seconds.
One improvement I would have like to make to the experiment concerned the metal plate switch. I realised that it took a certain amount of time to actually break the contact between the plate itself and the rest of the circuit which could affect the overall time recorded by the Digital voltmeter.
I believe it would be more efficient for a light sensor and a laser to replace the plate switch so the ball could fall uninterrupted and the time recorded would be more accurate. This is due to the fact that breaking a light beam can occur almost instantaneously while a metal plate is more difficult to move.
If I had more time I would have liked to increase the distance over which the ball fell. This would not only provide a more accurate value for g but would also allow me to calculate the terminal velocity of a given mass.
Ideally it would be interesting to see how the gravitational field of the earth varied in different locations, perhaps by obtaining data on the acceleration of the ball in various geographical locations. It would then be possible to see how g can vary due to the fact that the mass of the earth is not a constant all across the surface.