Then we can deduce ‘g’ from equation:
g = 2h/ t2 or g = 2△h/ △t ( from the gradient of height-time graph)
In this case, I will vary the height( h ) of dropping between the range 0.1 to 0.7 m , and increase by 0.05m each time. Additionally, I as G = mg, I will keep the ball mass by using the same ball each time, therefore the mass of the ball are the same and will not affect the result. For getting an accurate result, I will do the experiment 3 times to get an average value. These all enable me to get reliable results and plot a nice graph to deduce the acceleration( g ) .
I will also use another two methods to get ‘g’, and compare them to find out which method is the best to use to get the most reliable results.
The other two methods are:
Using a ticker-timer
When weight is falling down, it pulls a tape through a ticker-timer. The spacing dots on the tape increases steadily and showing that the weight is accelerating. A dot is made every 0.02s with the timer, and as the dots space out, the distance travelled by the tape increases with each 0.02s. this distance can be measured by using the equation:
Velocity = displacement / time
The velocity can also be calculated. This can in turn be used to calculate the acceleration of the mass and the tape by using the equation:
Acceleration( g ) = change in velocity / time
Using a light gate
A weight can be attacked to a card ‘inter-put’. The card can bread the light beam twice as the weight falls. The computer can then calculate the velocity of the weight twice as it falls, and hence find the acceleration.
Equipment
A free fall adaptor
Receptor pad
Clamp stand
Electronic timer
Metric stick
A steel ball
Method
- set up apparatus like the diagram
- measures the height(h) from the bottom of the ball to the receptor pad
- release the ball
- record the time taken from the timer
- reset the timer and measure it of fall from the height between 0.1 to 0.7m and each time increase by 0.05m
- repeat the experiment at least 3 times
- calculate the average of results and plot a graph which is height against time
Result table
Conclusion
In this experiment, I carried out 12 different height in the range of 0.1m to 0.7m for the free fall experiment. I took three reading for each height and took an average for each the times. Then I divided these values by 3 to get the average reading for the time.
Average = t1 + t2 + t3 / 3
This would influence the accuracy of my results.
To calculate the acceleration due to gravity ‘g’ is acquired by measuring the time and height through a free fall ball and use following equation:
S = ut + 1/2 at2
S = height( h ) / displacement
U = initial velocity of free fall ball
In this case, u = 0 ms-2 as it started from the rest
a = acceleration / acceleration due to gravity ‘g’
t = time travelled for free fall ball
because: u = 0 ms-2
therefore: h = 1/2 gt2
so : g = 2h/ t2
where: g = acceleration due to gravity(ms-2 )
h = the distance for the ball travelling from the rest to the receptor pad( m )
t = time taken to fall( s )
From this equation, we can see the ‘g’ can be determined by measuring the time( t) and the height( h ). Therefore we can determine the g by simply dropping the steel ball from a measured height and measuring the time it is taken to reach the pad.
After this, I plotted a graph with height against time2 and rearranged the formula to find out the gradient of the line.
In order to find out the gradient, I drew the line of best fit which nearly goes through all the points on the graph. The line of best fit shows a positive correlation which shows that the height is directly proportional to the time2 . i.e. if the height was doubled, the time would be doubled.
Therefore, the gradient of the line which is the acceleration due to gravity can be calculated by using the formula:
g = 2△h/ △t2
△h = 0.32m – 0.17m = 0.15m
△t2 = 0.068s2 – 0.036 s2= 0.032 s2
So:
g = 2△h/ △t2
= 2 x 0.15m / 0.032 s2
= 9.375 ms-2
Therefore: g = 9.375 ms-2
The vale of acceleration due to gravity is 9.375 ms-2 , this is not very accurate compare to the actual value 9.81ms-2 . There is 0.435 ms-2 differences between them.
Evaluation
I think I did this experiment quite well and the results seem to be fairly accurate and reliable.
Because the variable in this experiment is the height of free fall ball travelled and the mass of the steel ball are the constant through out the experiment. The intervals between the heights were increased by 0.05m each time. This will help me to identify a clear pattern in my results.
However the results in my experiment certainly contain errors. This may because of mistakes. i.e. reading an instrument incorrectly or recording the wrong number. Errors may also occur because of the limit of precision of equipment involved.
There are two variables measured in the experiment, they are height and time. So all the errors in the finding out g come from the error of measuring of height and time. I think the error in the measurement of height and time dependent on the equipment used.
A meter rule was used to measure the height, its finest measurement is down to +/- 0.005m , the maximum percentage error generated by the 1-meter-rule with the data of 3%.
0.005m / 0.15m = 0.03 = 3%
A electronic timer was used to measure the time, its figure was down to 1 mill-second which gives the maximum percentage error generated by the timer with the data of 15.6%.
0.005s / 0.0321/2 = 0.028 = 2.8%
Therefore the total maximum percentage error is :
3% + 2.8% = 5.8%
g = 9.375 +/- 5.8% ms-2
The percentage error value of 5.8% is unsatisfactory. This high percentage error indicates experimental errors. The percentage difference for the experiment can be calculated as:
% different = the actual value – the value measured / the actual value x 100%
Therefore:
% different = 9.81 ms-2 – 9.375 ms-2 / 9.81 ms-2 x 100%
= +/- 4.43%
However the average time was calculated. This error in the measurement of time will be about 0.02s. it is more important to reduce the fractional error in the measurement of time than to reduce the fractional error in the measurement of height because the error in the measurement of time was doubled as square of time.
The error of measuring time could be the time delay of the receptor pad to the electronic timer, although the time recorded was done using a circuit and a receptor pad, there is always a delay from the time that the ball bearing starting to free fall and the time that the timer starts. However this delay is very minimal.
The most significant factor when measuring g is that air resistance which act upon the ball. In fact we can neglect this factor as we were doing this experiment inside, there is nearly no air resistance act on the ball. However, air must provide some resistance to the ball falling and could conceivably affect an experiment. The only real remedy for this factor is to perform the experiment in a vacuum.
Also, different location may affect the value of g. This is because in different places, object may have slightly different value of attraction from the earth, therefore different acceleration due to gravity. To avoid this problem, it would be better to do the whole experiment in the same place.
In order to improve the experimental procedures, I think it is better to use an apparatus with a higher degree of accuracy. Such as a meter rule with the scale of millimetres standing out more , so that the measurement would be more accurate. Additionally, to reduce the error of measurement for time, I can improve on this by implementing better techniques and equipments.
Except by using an electronic timer, I also used a ticker timer and a light gate to find out g .
From the method of using a ticker timer, I got a tape after experiment and I stick every five-dot- tape on the graph paper, then I drew the line of best fit through the mid-point of the tape. The line of best fit is drawn by velocity against time, hence, I can find out the g by calculating the gradient of the line.
Gradient of the line(g) = velocity / time
g = △V / △ t
= 1.16-0.4 / 0.25-0.1
= 5.07 ms-2
There is a big difference between the actual value 9.18 ms-2 and the measured value 5.07 ms-2 . That is means there is a big error in this experiment. The experiment itself is flawed, as friction on the tape passing through the timer, and air resistance would both decrease the acceleration of the tape. Therefore this would result in a lower value for g .
Another method is done by suing a light gate. In this case, this method gave me the most accurate value : g = 9.82 ms-2 , because this value is calculate from the computer and this is the easiest way to get the value of g .
However this method may give random errors, as there is no way of regulating the angle or tilt that the card is at when it passes through the light beam. This has an effect on the reading given, as the length of the card interrupt will change due to this tilt. The tilt of the card could increase the g value also means that this experiment may produce unreliable and inaccurate results.
Consequently, I think the best way to determine g is by suing an electronic time.
Overall, I think my experiment went quite well and the results I got for g is reliable and accurate. If I had more time, I would like to increase the height of which ball fell, I think this would give me a more accurate value of g. Ideally, I think it would be interesting to see how g change in different location.
