Session 8: Uniformly Accelerated Rectilinear Movement

Session 8 - UARM

Results

Table to show the results obtained while carrying out the experiment, (the time it takes for a marble to cover different distances, and how its acceleration, final velocity varies).

Graph 1 to show the relation between the distance the marble covers and the time it takes to do it.

Graph 2 to show the relation between the the time the marble takes to cover certain a distance and its final velocity

Graph 3 to show the relation between the distance the marble covers and the time it takes to do it squared.

Equations

- s=½ at2 → a=2s/t2

- v=at

- v= 2s/t

Conclusion

UARM (uniformly accelerating rectilinear motion) can be defined as “a movement in which velocity changes with time” ("Unit 7 - Forces", 2016). Our results have been collected in a graph and then used to show 3 different graphs:

The first graph shows the relation between time and space. Theoretically, the graph should show a curved line. This is because more space is covered in less time as the velocity increases while the acceleration remains constant. On the other hand, we can see that the line in our graph is slightly curved, but not as much as we would like it to be. This could be due to different reasons that will be analysed in the evaluation.

The second graph shows the relation between the time and the final velocity. Theoretically, they should be directly proportional and therefore the line shown in the graph should be a straight line. This can be explained with the formula; v=vo+at → (considering that the initial velocity will always be 0), v=at. As we said before, in UARM, acceleration will always be constant (uniform). So we could say that v∝t. The result is a straight line with a gradient of “a”. We can see in our graph, the direct proportionality of both variables. As the time increases, final velocity increases uniformly.

Finally, our third graph shows the relation between the space covered and the distance squared. In theory, this graph should show a straight line and a direct proportional relationship. This can be explained with the following formula; s=so+vot+½ at2→ (Considering that the initial velocity and the initial space covered will always be 0), s=½ at2. We know that acceleration is constant, so we could say that s∝t2. The result is a straight line with a gradient of “a/2”. Comparing this with the graph obtained, we could affirm that our results were correct.

By substituting a = 2s/t2 in v = a·t → v = (2s/t2)·t = 2s / t

Consequently, we can say that final velocities are proportional to times, while distances are proportional to the time squared.

Evaluation

There were several factors that could have varied our results from how they were meant to be.

To start with, there were different people with the stopwatch each time and each one of us has a different reaction time, therefore it is a human, random error. To stop this from happening one person should have always been in charge of the stopwatch.

Also, we could have used programmes such as "Tracker" in order to calculate more precisely our results and elaborate the graphs. However, because the marble was so small and it had to cover a long distance, we weren't able to record it properly and distinquish the marble.

Furthermore,  in this experiment we were talking about UARM, but sometimes the aluminium rail wasn’t straight and therefore the movement wasn’t rectilinear.  For the next time we should make sure that the rail is straight so that the marble travels in a straight line.

Moreover, air resistance is also a problem, as it slows the marble down. As a solution we could carry out this same experiment in a vacume so that there is no air and air resistance can’t exert any force on the marble slowing it down.

Another thing that  could have varied our results is the possibility of the angle formed by the wood pieces not being the same. A solution to this could be to make sure the angle is the same each time by using and angle meter.

Finally, we could have done more repetitions in order to collect more data and hence obtain more accurate results.

Although the method we used wasn’t perfectly accurate, it allowed us to see what happens during the experiment and make some conclusions as we can see above.

Bibliography

Straight line graphs. (2016). Practicalphysics.org. Retrieved 20 May 2016, from http://practicalphysics.org/straight-line-graphs.html

Unit 7 - Forces. (2016). Department of Natural Sciences. Retrieved 20 May 2016, from http://www.sciencesfp.com/unit-7---forces.html

Session 9 - Bending Investigation

Session 9 - Bending Investigation

Results

Table to show how much the ruler bends when we change the distance at which the force is applied

Graph to show how much the ruler bends when we change the distance at which the force is applied

Conclusion

As we can see in the table and the graph; the further away we put the plasticine ball (weight), the greater the bending will be.  To understand this we must understand the next equation:

Moment = force · distance

Force will always be the same in the equation (it will be constant) and if we multiply it to a number each time bigger, so will be its result. Therefore, as we increase the distance, then the moment will increase too. That’s why the bending is greater as we increase the distance from which we apply the force.

However, observing the graph we can see that the relation between the distance and the bending isn’t directly proportional as it is a curved line instead of a straight line. In our hypothesis we predicted that if we double the distance, the bending would double too. However, we can see that as the distance increases, the bending increases even more than we expected. This might be because we could have made some errors in the procedure and that's the reason why the line isn’t straight and both variables are directly proportional, as we predicted in our hypothesis.

Evaluation

There are several things that could have gone wrong whilst we carried out the experiment that could have affected our results. Although, the results are approximately the ones we expected in our hypothesis, they were used by us to observe the general tendency. The graph above should have shown a directly proportional relationship between our two variables, however we can observe an exponential curve, this suggests something must have gone wrong during our experiments. These are the main factors that could have affected our results and made them imprecise:

Firstly, the balance with which we weighed the mass (plasticine) could have not been calibrated and therefore the results are being manipulated as they are not the ones they should be. This is a systematic error as it always gives a result that is incorrect by the same amount. For the next time we should make sure the balance is calibrated and works correctly by trying to weigh the same thing with another balance and check that both results are the same.

Furthermore, as we held the ruler with which we saw how much the first one bended with the hand, it moved, and we couldn’t see exactly how much it bended, so, for the next time we should put it on top of a chair so it stays straight and on top of a stable material, and therefore measure it accurately and correctly.

Also, we might have not put the weight exactly at the right length, as it was quite big and so we couldn’t  measure it to. This could be considered as a random error. Next time we do the experiment, we should tie the wight with a rope to the exact position we want it to be.

The last thing that could have gone wrong whilst we carried out our experiment was the fact that the ruler could have moved from its original place as we were holding it there with our hands. The ruler that bends should have on top o the table 5cm and with the rest sticking out, but as we were holding it in place with our hands, this distance might have changed slightly and therefore changed our results. As a solution to this, next time we could use a weight or cellatape on top of the origin of the ruler to keep it in place and avoid these kind of problem

Bibliography

• BBC - KS3 Bitesize Science - Forces : Revision, Page 8. (2016). Bbc.co.uk. Retrieved 8 March 2016, from http://www.bbc.co.uk/bitesize/ks3/science/energy_electricity_forces/forces/revision/8/
• schoolphysics ::Welcome::. (2016). Schoolphysics.co.uk. Retrieved 9 March 2016, from http://www.schoolphysics.co.uk/age11-14/Mechanics/Statics/text/Balancing_/index.html

Session 7 - Evaporation Investigation

Session 7- Evaporation Investigation

Results:
Table 1: Showing the results obtained during the experiment

Graph 1 : Showing the amount of acetone evaporated in mililitres at different increasing temperatures

• Conclusion

From our results we can conclude that our hypothesis was correct. This is because, as we can see in the table and graph, most of the time, excluding the second column, the one of 25ºC, as the temperature of acetone increases, so will it the evaporation rate.This happens because as the liquid warms and it’s temperature increases, the molecules gain more kinetic energy and will therefore move faster, so they will escape at a faster rate as they gain energy to overcome the IMFs.

• Evaluation:

We used a fairly accurate method to complete our experiment, although it wasn’t perfect and contained some errors as we can see in the table and the graph( when we heated acetone up to 25ºC the amount evaporated should have been smaller than when acetone was heated up to 35ºC), but the results were precise enough for us to see if our hypothesis was correct.The first thing we should mention is that we started trying the experiment with water, although we realised that water had high boiling point(100ºC) so we wouldn’t have time to do it in two lab sessions as it took very long for water to evaporate. We then decided to do it with ethanol, however it still didn’t evaporate fast enough. Finally, we decided doing the experiment with acetone instead than water as its boiling point is lower(56ºC). We also had to make several modifications in the temperature, we had to increase it to make acetone evaporate faster and making sure that the higher temperature didn’t overcome the boiling point. Furthermore, at first, we were doing the experiment using measuring cylinder as containers. However, the liquid didn’t evaporate at all (*1). Finally, we realised that the liquid needed a larger surface area so we used beakers instead. Our results could have slight errors due to the fact that we decided to put three beakers at a time to have more accurate results and an average, but as the beakers were put in the water bath one after the other, they haven’t been exactly the same amount of time in the water bath.Also, despite we tried to maintain the temperature as accurate as possible, that was impossible as it increased and decreased a few degrees constantly. It wasn’t 25 degrees exactly, but 26 or 27. Besides, when we cleaned the beakers, we cooled them down and this could have affected the results too. Finally, when warming up/cooling down the liquid to 15ºC, as we couldn’t do it with the hot water bath we had to put the beaker in a sink with cold water and ice. This could have varied our results slightly and make them less accurate. Moreover, in order to cool down the water bath quicker, we had to remove some hot water with beakers and then add cold water again. We could have avoided all these temperature problems using a more accurate material and having more time to do the experiment.In addition, when the amount of acetone evaporated was smaller than 1 mL we had to use smaller measuring cylinders in order to measure the results more accurately. 

(*1)

Session 6 - Job´s method

Session 6 - Job´s method
Stochiometry- Balanced equation
   K2CrO4+BaCl2 --> 2KCl+BaCrO4

Table 1: Showing the results obtained during the experiment

Graph1: Showing the relation between the average height and the volume of BaCl2

Conlcusion:

The graph is consistent with the expected results. The height increases when the volume of BaCl2 is lower than the volume of K2CrO4, then it stays the same when there is equal amount of both substances and finally, the height decreases again as the is more BaCl2 than K2CrO4. The height was the highest when there was the same amount of BaCl2 and K2CrO4. Whe can also see that we must balance the equation K2CrO4+BaCl2 → BaCrO4+KCl by adding a 2 in front of KCl =  K2CrO4+BaCl2 → BaCrO4+2KCl. We need to balance the equation because of the law of conservation of mass: matter can be changed from one form into another, mixtures can be separated or made, and pure substances can be decomposed, but the total amount of mass remains constant. (Chem.wisc.edu, 2016)

Evaluation:

The first thing that could have varied a bit the results and made them less accurate was the fact that when the test tubes came out of the centrifuge, we had to measure the centimetres of solid that were concentrated at the bottom, but the amount wasn’t at the same level, so we had to smoothly hit it against the table, so that it came down and all of it was more or less balanced, but though we did this, it didn’t fully balance, therefore we had to search for a point between the lowest and the highest so that it is as accurate as possible, it wasn’t though, because we can’t know the exact point. We believe this is a random error, because each one of it has a different change in level, which is unpredictable.

A solution we propose for this is to let the test tubes in the same place for a day, so that all of the solid comes down the test tubes and rests on the bottom, just the same that the centrifuge does in less time, but this way we know that everything will be at the same level and that we will be able to measure it accurately.

Another thing that could have varied our results, was the difficulty that caused measuring with such a big pipette, sometimes it wasn’t really accurate  because a few drops were spilled in the process of transporting the solution from the beaker to the test tube. A solution to this is to use a small beaker next time.

It’s very probable we haven’t filled the tube exactly with the amount needed each time, so we have to take into account a parallax error.  Also, the tube was filled by a different member of the group each time, so can be the cause of the mistake.This could have maybe originated a mistake because not all humans have the same view. Maybe, one of  my partners filled more or less the tube than I did and saw the meniscus differently every time, this could be considered as a random error. We could solve this by making sure the tube is filled by the same person every time and to get rid of the parallax error we could be careful and consider the meniscus to make the measuring precise.

Another thing that could have made our result less precise is that we believed the substances that were given to us were really BaCl2 and K2CrO4 but maybe there weren’t as the containers weren’t labelled. If the substances weren’t the ones they were supposed to be, our results will be completely imprecise.  A solution to this is to make sure the containers  containing the substances are labelled.

We should have repeated each individual experiment a few times to reduce random errors.

As we can see, there are lots of things that could be improved for the next time we repeat the experiment by carrying out the solutions we have proposed and receive more accurate results.

References:

 Chem.wisc.edu,. (2016). Retrieved 26 January 2016, from http://www.chem.wisc.edu/deptfiles/genchem/sstutorial/Text1/Tx14/tx14.html

Using the pipette, put 0.5 mL of potassium chromate in the first tube,
1.0 mL in the second, and so on up to the ninth.

Repeat the process filling the tubes with barium chloride making sure that finally each tube has 5 ml in total

Use the centrifuge to settle the solid to the bottom of the test tube.

 Finally, measure the height of the remaining substance and collect all the data in a table

Session 4 - Calculating the gas constant, R

Session 4 - Calculating the gas constant, R

Mg+2HCl -> MgCl2+H2

Ideal Gas law: PV=nRT

Table 1: Showing the results obtained during the experiment

Table 2: Showing the lab conditions

Table 3: Showing useful information needed for the calculations

• Calculations Explanation

We had to convert all our data so that it came out with the corresponding SI unit. We did this because in order to calculate R (gas constant), we needed to use the Ideal Gas law, in which pressure is measured in atm, volume in L, temperature in K, the gas constant in atm*L/K mol and the number particles in moles.

First of all, we measured the pressure in atm as it is the SI unit for pressure. We knew that the pressure of the room was 767.0 mmHg. We also knew that 1 atm= 760 mmHg. So we transformed it by dividing 767.0/ 760 multiplied by 1. The result was 1.009210526. When we divide, we must maintain the smallest number of significant figures, in this case 4. So, the final result was 1.009 atm.

Secondly, we measured the volume in L as it is the SI unit for pressure. We had it in mL, therefore we’ve got to convert it into L by dividing it by 1000, as 1 L is equal to 1000 mL.

So, as we had 11.1 mL, if we divide it by 1000, it comes out as 0.0111 L. This is because when we are dividing, we must maintain the smallest number of significant figures which in this case is 3.

Then, we measured the water temperature, which SI unit is K (kelvins). The thermometer gave us the temperature in celsius (ºC) so we had to convert it by adding 273: 273+22.2=295.2K. (When adding we must maintain the smallest number of decimal places, in this case 1)

Furthermore, we measured the number of moles of magnesium with the equation: moles= mass(g)/molecular mass(g/mol). We know that we have 0.0100 g of the substance and its molecular mass is of 24.31 g/mol. With this information, we can replace the values we know to find out the number of moles of magnesium like this: 0.0100/24.31= 0.0004113533525 moles. As we know that when we are dividing data from the lab, the result comes out with the less number of significant figures, which in this case is 3, therefore our result will be: 0.000411 moles of magnesium.

Moreover, as we know from studying stoichiometry last year, Mr Canning has given us the reaction equation, and both H2 and Mg have the same coefficient, so we know that they both have the same amount of moles, so therefore there will be 0.000411 moles.

Finally, we replace all of the results we’ve got from the calculations in the Ideal Gas Equation, now that we’ve got all of them with the right measurements (SI units), so that we can calculate our gas constant and compare it to the one it would actually be and calculate the percentage error to deduce some conclusions.

PV=nRT // 1.009·0.0111=0.000411·R·295.2 // 0.0112=0.121·R // R=0.0112/0.121 // R= 0.0923 atm l /K mol. Throughout all the operations we considered the number of significant figures, so finally, as we know that we dividing or multiplying we must maintain the least number of significant figures, which in this case is 3, so it will finally come out as:

R=0.0923 atml/Kmol

• Conclusion

Considering the Literature value of R is 0.082 the one we obtained ,  0.0923 , is really close to it, although it is slightly bigger than the Literature one and this could have  been originated  by some mistakes we will mention in the Evaluation.

Now, we will calculate the percentage error to see the accuracy of our results:

% error = Experimental Value of R- Literature Value of R

             _______________________________________ *100

                       Literature Value of R                                       

% error = 0.0929- 0.082                % error=  0.0109                

                 ____________  *100//                 _______ *100//  % error=  0.1329268292682927*100//

  

                        0.082                                           0.082                             

       

% error= 13.29268292682927 This will eventually come out as 13%. The percentage error we obtained is low, so this means we didn’t  make lots of mistakes when doing the experiment. Although, Mr. Canning told us the percentage error must be under 10 to consider the experiment totally precise.Even though the results we obtained weren’t perfect, they were clear and precise enough for us to see what  happens during the experiment.

Image showing the reaction between Magnesium and Hydrochloric acid.

 Image showing pieces of Magnesium used during the experiment.

• Evaluation:

We used an accurate method to collect the data for this experiment. Although, there could have been several errors that could have spoiled the experiment. Magnesium was exposed to air  so it could have started to react a little bit and could have vary the results. Also, when we weighed it probably it wasn’t pure Magnesium but maybe Magnesium Oxide due to the air. This could have affected the final value of R and made it more inaccurate.This is a random error. We took turns to fill the beaker: The first time it was Ainhoa who filled the beaker and the second time I filled it. This could have maybe originated a mistake because not all humans have the same view, so this is a random error. Maybe, Ainhoa filled it a bit more than I did or vice versa. This could be improved next time by establishing an exact quantity of water to fill the beaker with and making sure the beaker is filled by the same person always. While doing the experiment we assumed that the pressure of the room was equal to the pressure of the tube and this was probably incorrect. This can have caused the value of R we obtained to be incorrect and can be considered a random error. This can be improved by using a small pressure sensor and putting it inside the tube to control the pressure.Probably the temperature of the gas wasn’t the same as the temperature of the water.This is also considered a random error and could be improved by putting a thermometer inside the test tube to control the temperature. An error that could have caused variations in our results was the incorrect calibration of the balance, which is a systematic error. We had to weigh the magnesium several times because we obtained  different weights each time. This could be improved by making sure the balance is well calibrated and by weighing several times the substance used to make sure the weight the balance shows is correct.  Other very common mistake in experiments like this is the incorrect reading of the thermometer or the meniscus. This is called a Systematic Parralax Error. This could be improved by placing  your eye at the level of the appropriate measurement marking when measuring the level of a liquid in a graduated cylinder. Read the lower part of the curved surface of the liquid (the meniscus) to obtain an accurate measurement and avoid parallax errors. It’s also really important to deep the piece of Magnesium in a bit amount of acid for a short period of time to clean and purify it. We didn’t take into consideration that maybe the pieces of Magnesium weren’t the same size and so this could have made our results imprecise, so next time we have to make sure all the pieces of magnesium have the same size. Maybe, we didn’t close well the top of the test tube so a bit of gas escaped while the reaction occurred, next time we should make sure it’s well closed. Another mistake that could have altered our results is that maybe we didn’t pour the distilled water as slowly as we should have done and this could have caused the mix and spread of Hydrochloric Acid. A A thing that is crucial for the results of  an experiment to be reliable is to use new equipment or clean it and dry to avoid substances to mix and vary results. Also, we could have done more tests to get more precise and reliable results as this reduces random errors, but we didn’t have time to do it.

As we can see above, there are lots of things that can be improved for the next time we repeat this experiment and make it more precise.