Trial run
We conducted a trial run to see if our preliminary method would provide us with satisfactory results. We took 11 readings, with the cart at 11 different masses, from 1000g, the mass of the cart with no extra mass added, up to 2000g, after we had added 1000g in mass.
The trial run enabled us to find errors in our primary method, which would prevent us from gaining inaccurate results when recording the final data.
Results from trial run:
The graph has several anomalous readings that do not show the exponential curve that is present on the graph that is generated when the results from the formula are input. This is for many reasons, and we will change how we carry out the experiment when we come to take our final readings. The method we employed during the trial run did work to an extent, as the basic shape is present, and readings 1, 3, 4, 8, 9, 10 and 11 are near to what we expected.
Diagram (After modifications)
Method (After modifications)
As the results from the trial run were not accurate enough to help us answer the question, we modified the method to gain this accuracy. During the trial run, we approximated the mass of the cart to 1000g. The exact mass of the cart during the final experiment is 850g; this is including the timing card and the plastecine used to hold it in place. The exact mass will help us gain a greater accuracy.
- To start with, we measured the mass of the cart: This was 850g.
- We attached a timing card to the cart. Modification: originally, we used two light gates, and a solid piece of card; this method was less accurate, and required two light gates. Then we used a piece of card with a slot cut from it, and using one light gate, we were able to measure the acceleration. As we had made the timing card ourselves it was less accurate. In the final experiment, we used a purpose built timing card, made from plastic, which enabled us to achieve a much greater degree of accuracy.
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We attached 500g (5N) to a piece of string, and then attached the string to the cart, running the string over a pulley, to reduce friction, and ensure that the masses were falling directly downward. We made sure that the cart and the card had passed through the light gate, before the masses had reached the floor, so the cart was still accelerating when it passed through the light gate.
- We set up the light gates and the data logger.
- We took three sets of results for each mass. Modification: During the trial run we took one set of results for each mass; taking three, and finding an average, will increase accuracy, again helping us to answer our question.
Equipment
- Cart, to measure acceleration. We added 100g masses in-between each reading.
- One light gate, instead of using two light gates, one increases the accuracy of the results.
- Timing card, this was used to measure the acceleration of the cart.
- Data logger, this electronic device was connected to the light gate, and logged the results from the light gate. The data logger then can be connected to a PC, to retrieve the data.
- Microsoft Excel, this software enabled us to graph out information, and to put the results from the data logger into a table.
- Plastecine, to hold the timing card in place, on the cart.
- 100g masses, we added masses to the cart systematically, 100g masses were added after each set of readings at a certain mass.
- Pulley, this was used to direct the string from the cart to the masses that were pulling the cart.
- String, connected the cart to the pulling force.
- A block of wood to prevent cart running off the end of the table, and a mat to protect floor from the masses.
- 500g, we used a pulling force of 5 Newtons (5N) to pull the cart; this was in the form of five, 100g masses pulling the cart.
Controls and Variables
To make the experiment a fair test we had to have controls, or constants and variables, theses were:
Controls:
- Length of Run
- Position of light gate
- Size of pulley
- The pulling force (5N)
- Starting point for the car
- Length of string
- Position of timing card
Variable:
- Mass of car – to answer question, and to find relationship between mass and acceleration
Working out acceleration
By connecting the light gate to a data logger we were able to calculate the acceleration of an object at one point. The data logger and light gate were used to do this. When the light beam is broken, the length of time that it is broken and re-broken is recorded by the computer. The timing card has two 3 cm sides that break the beam (see diagram). The gap between them is 9.5cm but does not affect the results. The computer works out the time the light gate was broken when the first 3cm side passed, and then the time the light was broken for the second side of the card. It then works out the difference in time and the amount the cart has increased in speed between the two readings and therefore, the computer is able to calculate acceleration.
Results
Graphs
Hand drawn graph
Conclusion
From my results I have concluded that the relationship between the mass of an object is inversely proportional to its acceleration:
y=k/x – This formula represents inverse proportionality. Its outcome is exactly the same as Force=Mass x Acceleration rearranged; Mass = Force / Acceleration
y = Mass
x = Acceleration at A
k = constant (force)
Mass=k/Acceleration
Mass = 0.85kg
Acceleration = 3.22 m/s² (Average from 3 results using mass of 850g)
0.85=k/3.22
0.85*3.22=k
k=2.737N
Force =2.737N
This result does not match my prediction as the force should be a lot nearer 5N, as this was shown using the formula, Force = Mass x Acceleration. Using this formula I can show that my results were not very accurate due to problems in the method:
F= M x A
5N = 0.85kg x A
5N / 0.85kg = 5.88 (m/s²) (Rounded to two decimal places.)
This shows that the results where the mass was least were inaccurate. This is shown as the graph that is created using the formula F = M x A (see page 2) shows more clearly a curve showing exponential decay. This is not created on the three graphs created from the results and averages from the real experiment. The curve does not start so high and sweep down as it does on the graph for the formula. This is proved by the result I found above, as the result I should have gained if our method was correct should have been 5.88 m/s², but it was only 3.22 m/s², this being the average for 850g. To see if this problem was true for all readings I can test out a result from the experiment where the mass was much greater, as the second half of all the graphs looked similar to that of the formula.
1.85=k/1.93
1.85*1.93=k
k=3.57N
Force = 3.57N
As the force is 3.57N it shows that the results recorded from where the mass is more, are more accurate. Although the acceleration I should have gained when the car had a mass of 1850g can be shown using the formula.
F= M x A
5N = 1.85kg x A
5N / 1.85kg = 2.70 (m/s²) (Rounded to two decimal places.)
This shows that the result was too little, as I should have got a result of 2.70 m/s². This is for many reasons that are explained in the evaluation.
I conclude that as the Mass of an object increases the Acceleration of that object decreases at an inversely proportional rate. The relationship is not directly proportional as this would create a straight line graph, and as this is not achieved the relationship must be inversely proportional, again this is proved by the formula; y=k/x.
Evaluation
We received many anomalies during the experiment, due to many reasons. The graph in my prediction shows exponential decay, whereas the graphs created from the results do not. There were some problems that could have caused this. Firstly, if the timing card had tilted slightly forward, the acceleration would have decreased, this could account for anomalies where the mass of the car was greater, as I showed in my conclusion, and the acceleration was too low, when shown using the formula. This would also agree with the card slipping as the card may have slipped when the cart had been through 20 or more runs. This would have been caused by the sharp acceleration and deceleration of the cart itself, causing the card to slip. Another problem with the method that could have accounted for the anomalies was that when the cart accelerated the masses slipped from their positions, as they were moving in the opposite direction to the cart, they would have become weightless, and therefore irrelevant to the results. This would have decreased the mass momentarily and therefore increased the acceleration as the mass was less. This could have been an explanation for results that were above the trend line, for example the anomaly on the hand drawn graph, where the mass equalled 1650g; this would have meant there were seven 100g masses added. To overcome this problem I could have used a light weight jig, or blue tack to hold the masses in position when it accelerated, so that they were effective during the whole run.
Overall the results we gained were very similar to what we had expected, as the shape of the graph we had predicted was achieved, although the results were not as accurate as we had expected, due to the reasons explained above. To get more accurate results I could have added more mass on at a time so that the results represented a greater reading of mass. This should help me to achieve better results. The results that we got were enough to answer the question, and looked like those from the prediction so we did not have to conduct the experiment more than three times. I think my prediction was correct in that the relationship between the mass of an object is inversely proportional to its acceleration.
