Variables……
Independent:
Mass is the only variable that I am changing. Therefore, in my experiment even though the mass is changing the size of the object will be kept the same in order to measure the depth of the crater, because if the size changes different width will be formed. The different masses of the object that I will be using are
- No weight (2.7gram)
- 5ml of water (5 gram)
- 10ml of water (10 gram)
- 15ml of water (15 gram)
- 20ml of water (20 gram)
Mass will be measured in kilograms. To change the mass I will be using syringes and injects the amount of water that I want into the ball.
Dependent:
The dependant variable is the variable dependant on others to produce a result and also what I am trying to find out about. The the dependent variable in my experiment will be the depth of crater that is formed each time I drop the ball, and the time taken for it to reach the surface of the powder. The depth of the crater will be measured in millimetre, and the time taken will be measured in seconds.
Controlled:
The most important controlled variables are the Height and the directed surface; these two things will need to be kept constant throughout the experiment this is to ensure these variables compliment and help produce accurate results when varying masses. In order to keep the height and the directed surface the same, the wood shown on method step two is shown in order to drop it from the same place, and also in order to dropped it at the directed surface, where the container is place also need to be kept the same, this is because if the height of the dropping object increases the gravitational potential energy would also increase. Moreover, the same brand of ping pong balls needs to be used, since different brands of ping pong balls have different sizes. Also try to keep the same person dropping the ball, and same person recording the stopwatch and keep the same stopwatch. This is because, different person might drop the ball in different ways, and same as the stop watch, and this might affect the result. In addition, every time the ball is dropped, the powder needs to be resurface because if the surface is not flat or the same, the result might get affected. In order to do this, every time when a drop is done, the container needs to be shaken to flatten the surface in order to produce a smooth surface.
When the ball has been dropped it must be treated the same every time it needs to be really carefully removed from the crater every time, without affecting the depth. The angle at which I drop the object will also affect the size of the crater. To make it a fair test I will have to drop the object from the same angle ever time. Which I will drop the ball from 90 degrees above the surface of the powder.
Results……
Mass of balls measured in gram (x10-3kg)
Depth of crater using string measured Centimeter by ruler (x10-2m)
Descriptions of Each ball in detailed:
Ball 1 (x10-2m)
- The first reading shows that this reading is quite reliable since that the results in each trial are very close to each other.
UNCERTAINTIES of BALL 1 -Depth of crater measured in ruler (*10-2m):
- From the table above, the differences compared to calculated average isn’t that much difference, and I think that the in ball 1, the measurement of the depth of the crater are quite close to each other.
Ball 2 (x10-2m):
- In this reading, there is one number that is quite different from the others, even though the results in the second reading seem to be close enough. 2.50cm deep of crater shows that it might be an outlier in this row of data, because 2.3 and 2.1 appeared more than twice, but 2.5 only appeared once.
UNCERTAINTIES of BALL 2 -Depth of crater measured in ruler (*10-2m):
Ball 3 (x10-2m):
- This result seem to be a little different from the previous readings, the minimum number is 2.3cm and the maximum is 2.7cm, and the gap between them is 0.4cm which is quite a lot, and it could have affected the number in the average, by lowering down.
UNCERTAINTIES of BALL 3-Depth of crater measured in ruler (*10-2m):
Ball 4 (x10-2m):
- I think that the highlighted number has lower the average down, since every number is above 2.5cm except for the 2.4
UNCERTAINTIES of BALL 4-Depth of crater measured in ruler (*10-2m):
Ball 5 (x10-2m):
- In this reading, we can clearly see that 3.2 is a little different from the 2.9 and 3.0 because both of them are repeated, therefore it’s hard to say whether or not the 3.2 is an anomaly or not, because I think that the number is quite reasonable, since 3.0 is the average it will be ok to have a 3.2 there
UNCERTAINTIES of BALL 5-Depth of crater measured in ruler (*10-2m):
As you can see on this graph, it clearly gives an evidence of what is on my prediction. As the mass increases, the depth of the crater increases, and I think that there is an interesting point that I found from the graph:
As you can see that, this is the increases of the depth of crater each time the masses of the balls are increased. From the table above, you can see that the in the first time it increases the most, because it starts from no water and then increase 5grams, but then as u can see, the normal average increase weight will be around 0.36cm, but from the third ball which is 1.56cm to fourth ball 2.64 it did not increase as much as I thought it would be, and the number is a lot lower than the average amount. This shows one of the weaknesses in our experiment, that we could have done more weights to see what will happen whether or not that the increasing rate will still be around 0.36cm.
Time of the dropping objects measured by stop watch in seconds (s)
The reason of having such a big number of uncertainties in time is because we are using stop watch. It increases the level of uncertainties, because by using stop watch, it creates many human error, because there might have some problem with eye sight when the ball reached the surface and the time we actually click to stop the stop watch. Also when a person is dropping the ball, it would also be a little different from the person who starts the stopwatch.
Velocity…..
To calculate the Speed from the time given:
Example:
Ball 1:
V=distance/time
V=2.05(m)/ 1.21(s)
V= 1.70ms-1
- Velocity will be calculated to show whether or not when the masses of the ball increases the velocity will be faster.
Therefore, something that I’ve found was that,
V2=2as
Velocity2=2*acceleration*displacement
V2= 2 (9.81)(2.05)
V=2 (9.81)(2.05)
V=6.34ms-1
Kinetic Energy= 1/2*m*v2
Example of ball 1:
KE=1/2* 2.7(x10-3kg)*v2
V2=1/2* 2.7(x10-3kg)
V=2*2.7(x10-3kg)
V=0.073ms-1
Another method:
Gpe=ke
Mgh=1/2mv2
2*g*h=V2
6.34ms-1=V
Velocity should be this, if there aren’t any factors such as air resistance, human error, collision..Etc. And from these two equations it shows that mass in gravitational potential energy and kinetic energy canceled each other out, which means that no matter how heavy the balls are it won’t change the speed of velocity. Therefore, the following tables show that, because of the varieties of factors that could affect the time taken to reach the surface of the powder that is why the velocity changes.
Calculation of uncertainties:
A table to show the time taken for the object to drop by using stopwatch in seconds:
Average velocity:
V=distance/time
V=2.05/1.21
V=1.69ms-1
Minimum velocity:
V=distance/time
V=2.05/0.71
V=2.89 ms-1
Maximum velocity:
V=distance/time
V=2.05/1.71
V=1.20 ms-1
This shows that, the uncertainties are more likely to be larger, because as the amount of uncertainties increases, as we can see on minimum velocity it increases, which means that it gets closer to the expected velocity 6.34 ms-1. Also, this shows that the time that I stop the stopwatch is slower than what it is suppose to be.
Another example: (ball 5)
Average velocity:
V=distance/time
V=2.05/0.75
V=2.73 ms-1
Minimum velocity:
V=distance/time
V=2.05/0.25
V=8.50 ms-1
Maximum velocity:
V=distance/time
V=2.05/1.25
V=1.64 ms-1
The expected time for the stopwatch timing:
2.05/ time = 6.34 ms-1
2.05/6.34=time
Time=0.32
0.32 seconds is what the time it supposed to be around of, if there isn’t any factors affecting the speed.
A table to show the changes in Speed as the mass changes(ms-1):
Description of Highlighted numbers:
The highlighted bits are the outliers that I’ve got. I think that for the 1.68gram one is quite acceptable, therefore for the 1.64ms-1 one, it is 0.1 ms-1 compare to the maximum I’ve gotten.
- Compared to the average I’ve calculated, I think that these two numbers are out of the range, and this might be due to the difficulties in controlling the stopwatch, or measurement from the ruler.
- I think that these two is an outlier, but it doesn’t seem to affect the result, as it shows in the average, because when one of the lower number pulled the average down, the other one pulled it up.
- These two numbers are totally out of the average; this shows that there are many problems in the measurement of the time with stopwatch, which causes lots of anomalies to appear.
- In this data, there isn’t any number that is repeated or even very close, which shows that there might be a need of repeating more times if I could redo the experiment again.
Minimum and Maximum velocity:
Example calculation:
V= distance/ time
V= 2.05/ (time taken)
Minimum velocity in Ball 4 and 5 are the closest to the expected velocity 6.34ms-1; this means that as the mass increases the velocity does increase in this case when there are friction, collision and problems with human error. This also means that the minimum time taken, the faster it is, the more time it takes, the slower the speed. The calculated time for both minimum and maximum is calculated straight from the minimum time and maximum time from the average. Therefore, if we just use the average time taken velocity and make a table of maximum and minimum the result is different:
This is different from the calculated one because in the calculated velocity, when there is it in the maximum time, the time is higher, so when 2.05 divided higher number, the number turns out will be smaller. But also when using the calculated one, it is more closer to the expected velocity when using the minimum time taken.
In this table it does fit in with what I have predicted. In my hypothesis, I thought that no matter what the weight is, the final velocity and speed would be the same. When we look at the graph above it shows that as the mass of the ball increases, the speed increases. And to find out the final velocity, and to prove that the result I’ve got is reliable I did an extra experiment with ticker timer:
(Will be continue in conclusion)
The red line= minimum time taken= high velocity
Green= Maximum time taken- Slower velocity
Blue=Measured from experiment= Average
Kinetic Energy……
Expected amount of Kinetic Energy:
KE=1/2MV2
Ke=1/2(2.7 x10-3kg)(6.34)2
KE= 0.054 joules
The amount of Energy in that it has when the ball is dropped from the height of 2.05m is really little. This is because, the mass of a table tennis ball is really light, so when the ball is dropped not much of the energy is created compared to when it is heavy object. Which means that as the mass of the object increases the speed increases, and the amount of energy also increases. And we can see this from the equation:
Ke= 1/2mv2
If mass increases, kinetic energy would be increased.
And if Velocity increased, kinetic energy would double, because velocity is squared.
Graph:
This graph shows that the amount of Kinetic energy it has when the ball is dropped with different masses. And as a result we can find that, as the masses of the ball increases they are more kinetic energy used.
Conclusion……
As I predicted, my graphs and results show the more the mass the deeper the size of the crater. This is due to the potential energy being bigger as the mass increases. All of the potential energy is converted into kinetic energy when the ball reaches the surface, resulting in a larger crater. If the crater is larger, the diameter (depth) is bigger.
Also, something that was additional in this experiment to look at was the speed of the ball dropping from the same height while changing the mass. What I’ve found out was that as the masses of the ball increases, the speed of the ball also increases, and also I predicted that, if there isn’t anything friction, collision, air resistance or human error happening while the ball is dropped the velocity will be the same. Which I found out that the speed of the ball when it is dropped from a height of 2.05meters without any factors affecting the speed, the v= 6.34ms-1, when there is no mass taking amount, because the formula is V=2as, square root of 2* acceleration * displacement.
And also I did an additional testing with ticker timer to show that the results I got was right,
What I have found out from this was that, the one without weight which I repeated 3 times, it shows that they are almost the same. But when we compared to the one that is added on weight, and as we repeated 3 times we can see that they are all close enough too, and it is not exactly the same due to the uncertainties we could get from the stopwatch. Comparing both two stripes, it does show that the one with the weight is faster because the gap between each dots are wider. I think that the results are quite different, because there are some factors that are affecting the velocity, such as air resistance, and also when we inject water inside the ball as the ball is a liquid, when the ball is falling down it is unbalanced because of the water inside.
And also as what I have mentioned before, there is a small pattern of increasing rate in the crater’s diameter (depth),
I assume that as the mass increases in a constant rate, 5ml each time, the pattern of the increasing rate could be a little similar, therefore, there is an anomaly in this table, which from 2.56 to 2.64, which is ball 3 to 4, it seems to only increased a little bit. But this could be made by human error, because some water might have been leaking out from the whole of injection while the ball is dropping, or by the time we repeated to the fifth trial, the amount of water inside the ball might have been less than in the first trial. Therefore, it would be more accurate if I had increased the independent variables.
Evaluation:
I think that the investigation went quite well, with my experiments my results followed a pattern which agreed with my prediction, giving me a clear conclusion. On the other hand, there is this unpredicted result coming out from my experiment, it is the Ticker Timer graph, and also the recorded time on the table shown in the result section shows that as the mass increases the time gets slower. The minority of results that didn’t fit the trend may have been due to the accidental force placed on the ball when dropped, because it is really hard to control the force when dropping the ball. And also when the ball is dropped there are friction, air resistance, collisions, human error and all sorts of factors that could affect the time taken.
Also inaccurate readings might cause the some anomalies on the data, for example using ruler for measuring the string. By using a centimeter ruler, it is not as clear as using a millimeter ruler in this experiment, because when we measure the string, the length of the string is more likely to fall in between 2 lines, so many uncertainties are shown.
- When the ball is dropped some of the starch might get stuck on the bottom of the ball, and it has a little impact on the measurement of depth.
- Also, by using a soft string, it is hard to measure and it made the uncertainties bigger, because soft strings bent every time when we are trying to measure the depth.
- The scale for meter ruler was not sensitive enough. This leads to results being in accurate due to the results being hard to get right. However, this inaccuracy is a systematic error because it would affect all the results.
- Also, by using powder,
If I repeated the experiment again, I would change the angle in which the ball is dropped, to see what affects it has on the size of the crater, because changing the angle would simulate more realistically of what happen in reality, because things don’t normally drop straight down from 90 degree.
In this experiment I could have been improved in a few areas. Most noticeably area is in the measuring of the depth of the crater itself. A ruler, I believe is not the most accurate of measuring devices.
- The second matter in which the experiment could have been improved is that the surface of the powder was difficult to assure that the surface was even. This could have had an effect on the results.
- I could have repeated the experiment more than five time to get a better average, and increase the independent variables to see if there is a pattern between the rate of increasing the mass of the ball and the depth of the crater it has.
- And also, it would have been better, if we used light gate to measure the time, because by using stopwatch it creates a large number of uncertainties, because of human error, and by using light gate, it has less error compared to when using stopwatch.
