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