How am I going to conduct the experiment?
Set-up:
Below you can see my car with the card stuck on top of it using the plasticine, the card is exactly 5cm wide which is vital when we work out the speed the car is travelling.
This is a diagram of my experiment:
Measurements
Measuring the speed:
To measure the speed we have to use a simple equation triangle:
S = Speed D = Distance T = Time
As you can see, speed equals the distance divided by the time. I can apply this formula to my experiment, for each time the car is rolled down the slope we have to work out the speed it is travelling at. To do this we simply divide the distance (this is the length of the piece of card on top of my car) by the time is takes for that piece of card to go through the light gate (the Electric Timer tells us the time in seconds).
Example:
S = D / T
S = 5 cm / 0.2 sec
S = 25 m/s
We have to work out the speed for each trip the car makes and measure the distance it travels before it comes to a complete stop.
The electronic timer is set to its most accurate of settings, 10,000th of a sec so all my results will have 4 decimal places.
Measuring the distance:
To measure the stopping distance of the vehicle I will use a metre rule stuck to my work surface / desk. This will be measured in centimetres to one decimal place. I am measuring the stopping distance the car travels from when it is in the middle of the light gate to the front of the car when it comes to a complete stop.
The set-up to measure the stopping distance of the car is something like this:
(from above)
In total I have 10 blocks each of equal height, which gives me 10 different heights to release the car from. At each of these heights I will take 3 different readings. Each height will have 6 readings in total, the 3 different speeds and the 3 different stopping distances, it is possible for us to workout the average speed and distance for each height thus giving us an average speed and distance for each height. My simple results table would, therefore look
something like this:
(Remember 1 block is 1 cm high)
A Fair Test?
There are a few variables in this test that need to be controlled / kept the same, we need to use the same:
- Car, (this means there will be the same amount of friction acting on the desk each time as every car would have different amounts of friction acting on it as it moves.
- Work Surface / Desk, (this is varnished wood, with dents and holes in its surface)
- Light Gate,
- Electronic Timer
- Ramp,
- Blocks.
If we were to change any of these then we would make the test unfair.
Safety
There are few dangers in this experiment, the only real danger that I can foresee is the main electricity that is used to power the light gate and electronic timer but the room is fitted with a RCD that would isolate the circuit in the room if anything was to go wrong, thus making the room safe. We also need to ensure that all un-used plugs are turned off and no food or drink should be allowed in the room and all books and bags should be off the floor and away from the experiment area.
Looking deeper into my prediction and the experiment
My car is being rolled down the same slope at different heights many times and each time is perfectly feasible for us to get a different stopping distance; this is because of the forces of friction and gravity that are acting on the car. As the car goes down the slope and then rolls along the work surface its Kinetic energy is converted to sound and heat.
Kinetic Energy
Car decelerates
Heat and Sound Energy
The following formula that is vital to my experiment works out the kinetic energy an object has:
KE = ½ Mass x Velocity x Velocity (KE = Kinetic Energy)
I said before that the KE of my car is being converted into Heat and Sound Energy (this is called Work.) The change of energy from one from to another is called work and the formula for this work done is:
Work Done = Force x Distance
Wd = F x d
Force = F = Frictional Force Distance = d = Stopping Distance
For the car to stop the Kinetic energy, (½ M x V x V,) has to be converted to heat and sound at the desk surface and inside the workings of the car; therefore Work done is the same as the Kinetic Energy:
Kinetic Energy = Work Done
½ M x V2 = F x d
In this equation there are certain things that do not change throughout the experiment:
- The mass of the car
- The ½ that we use
- The friction
We can therefore remove this that leaves us with this new equation:
D = V 2
The equals sign is replaced with a proportional sign, .
We now have a new prediction:
The stopping distance is proportional to the velocity squared.
This means if we double the speed then we also have to double the velocity squared; that is increasing the velocity by a factor of four. However this means that you have to increase the distance by a factor of four aswell. This means if you travel twice as fast as before then the distance must also increase by a factor of four to dissipate the extra Kinetic Energy that is being exerted by the model car.
It is possible to draw a graph of the distance against the velocity squared it would look something like this:
Analysing and considering evidence
I have now obtained my evidence with precision and skill, it is clear and concise and is a good set of data to work from. These are my results:
Anomalous Readings:
In all experiments you have unexplainable anomalies and this experiment is no different; I have highlighted my anomalous readings in yellow. Such readings are inevitable in such a large-scale experiment and it is upto me to notice them and omit these from any averaging.
Explaining my table:
- No. of Blocks – this is simply the amount of blocks that the ramp is resting on.
- Run No. – This is tell me which run I am on at that particular height (I did 3 runs at each height, as this is a nice easy number to work from and it makes things reasonably simple with out being to simple.
-
Time – This is the time the card on the car takes to travel through the light gate, measured to one 10,000th of a second.
- Length of card – this is the width of the car; this is needed to work out the speed of the model car.
- Velocity or Speed – this is a simple calculation, the distance divided by the time or s=d/t.
- Average Velocity - this is simply the velocities at that height divided by three (for the number of runs.)
- Distance – this is the distance the car travels along the work surface / desk.
- Average Distance – this the average of my three distances for each block height.
-
Average Velocity2 – this is the average velocity squared.
(Note: I used the formula function in Microsoft Excel to do all my calculations.)
Analysing my Results
My results show simply that as the number of blocks increase so does the speed to a certain point but then all of a sudden the speeds start to decrease and I wonder why they do so?
I can see that there are several reasons for this:
- The car travels so fast but then reaches and optimum speed and it can travel no faster.
- The car is somehow limited in its speed.
- There is a physical obstruction when it reaches a certain speed.
We will never know truly why my results do this but it is interesting why they do so; personally I think it is because after they reached a certain speed going down the ramp as they left it and crossed over onto the desk they hit it and this would have slowed them down noticeably and stopped them from travelling any faster.
It is possible to plot the speed of my vehicle against the distance is travels on a scatter diagram and we can also add a best-fit line:
Considering my results
From my data I can draw several conclusions, firstly that as my speed increases so does my stopping distances; this therefore proves my first prediction: (see below for a detailed explanation)
The faster the model car is travelling the greater the stopping distance of the car will be.
I can see that I have proved this prediction; the faster the model car is travelling the greater the stopping distance of the car will be. I think it is easier if I use the averages of the stopping distances and speeds to show you:
As you can see at the average velocity increases so does the stopping distance, this is a common and expected trend throughout my results. I say expected because it is, as the speed of the car increases the more kinetic energy it has to be converted into heat and sound. This increase in energy makes the car go faster as it speeds down the ramp and onto the bench.
Whilst I am looking at predictions I shall look at my second, more complicated one:
If you double the speed then you quadruple the stopping distance.
Is slightly more difficult for me to explain but I think it would be easier to use my graph and a diagram very much like the one I used previously in the planning part of my coursework. I shall simply lift results from my graph and double them and investigate the relationship between them and the quadrupled stopping distance:
(I shall use my best-fit line to do this)
If I was to double 20m/s (metres per sec) I would get 40m/s according to my prediction the speed doubled is distance quadrupled, so if I was to quadruple my distance for 20m/s I would get the stopping distance for 40 m/s. If I was to actually do this I would get these results:
Speed x 2 = distance x 4
Therefore: (20 x 2) = (19 x 4)
40m/s = 76cm
According to my results it travelled 70cm. As you can see these results are not exactly the same, but are very similar; there is one main reason why I think they are so similar but not identical.
- Human error – worked off my own best fit line, which may not have been entirely accurate and my reading off the graph may not have been entirely accurate.
If I was to do this experiment on a much larger scale to a much higher degree of accuracy and efficiency I think I would find that the relationship would be much stronger as in the diagram in my plan which is related to much more accurate data.
I can actually draw a graph of the distance squared against the stopping distance very much like I did in my plan when I was looking at my Highway Code data:
As you can see from my results they are not as perfect as the Highway Code data but I did not expect them to be. The best-fit lines starts off in a straight line like I anticipated but it then levels out, as I noted from my results earlier. So to conclude, there is a relationship between the stopping distance and the velocity squared up to a certain point (according to my results). So I have ½ proved and ½ disproved my prediction!
In my plan I talked about this equation:
½ M x V2 = F x d
I was then able to shorten it to this by removing the constants in the equation and replacing the equals sign with the proportional sign:
D . V 2
I based my second prediction on this new equation. I stated that distance is proportional to velocity squared. I said I would be able to prove or disprove this further on in my coursework. I am now able to do so. As you can see from my graph above the distance is proportional to the velocity squared up to a certain point, when the distance hits about 70cm. So I have proved my equation up to this point but after this point my results level out showing that the distance is no proportional the velocity squared. I cannot be sure why this is but earlier in my coursework I have given some suggestions.
I have gathered a set of good results that show good trends and similarities’ proving that as the speed of the model car increases the stopping distance of the car does.
Evaluation
Ways of improving my experiment
I was thoroughly pleased with the set of results I processed but if I was to do the experiment again there would be certain things I would change / do differently:
- I tried to make this test as fair as I could but as always there are certain things that can go wrong, I think one of these things in this experiment is the work surface I used; it was not at all smooth or in anyway ideal for this experiment, if I was to do this experiment again I would ensure I used a smoother and more suitable surface (such as a plastic topped desk).
- The ramp I used was also not ideal for the experiment; it was wooden with dents and divots in its surface.
- I could also have taken my measurements to a higher degree of accuracy this would have given me a more accurate set of results to work from.
- There is much room in this experiment for human error and I think there are ways we could eliminate this error, either by us being more careful or relying more heavily on our equipment to take readings for us for example.
These are a few ways we could improve the experiment and its accuracy. Personally I was pleased with my results but I do not think they have a suitable degree of accuracy or cover enough results to be used for any other more important reason, such as commercial usage. The set-up I used was perfectly suitable, in my eyes, for the information I had to gather and that accuracy if I had to do it to a detailed extent I would have to change the procedure.
Commenting on my evidence
If you look back at my results table you can see that I have a few anomalous results, all on the same run and I can only presume that this during this particular run the car hit the ruler or met some other obstruction which I failed to noticed during the run.
I think my evidence is fairly reliable, it all seems very correct and related. The results look like what the should do and they seem to steadily increase then level off; even though this was slightly un-expected I can understand several reasons why they may do so and this makes a lot of sense to me. I believe the results I have recorded are great to make conclusions from and to base my summaries on; it is clear and concise with only one run of anomalous results, which I have omitted from my calculations.
My evidence supports my conclusion, that as the speed increases so does the stopping distance of the model car and that the stopping distance is proportional to the velocity squared.
Further Work
Apart from the obvious thing we could do, that is to take more readings to a higher degree of accuracy there are other things that we could investigate in the experiment, such as adding more predictions to prove / disprove. We could also do the experiment on a much larger scale with real cars to take an example or we could increase the weight of the car for each different set of runs; this would work by running a car of say 50g down the run at 2 blocks high then running a car of say 100g down the same ramp again at 2 blocks high. This would give us more data to work from and would allow us to create more detailed predictions such as:
As the mass of the car increases so do the stopping distances.
Again we could look at the relationship between the two results and I would be able to gather and form more complicated results from them.
Summary
I have found out all the data I have said I will found out in my plan and I have noticed, investigated and described certain patterns and predictions that I have made. I have processed my own results and I have been able to draw conclusions from them and to notice any trends / patterns that have formed, I have also noticed anomalies and any stray data in my results and I have pointed these out and talked about them and the reasons that I have them.
Over-all I think this has been successful project for me and I have learnt much about the relationships between stopping distances of the car and it’s speed.