Example of calculation using data in column 1:
ConclusionThe graphs show that there is a positive correlation between force applied and speed of rotation, as well as a positive correlation between radius and speed. Both of this satisfies the centripetal acceleration formula a=v^2/R
For test 1, force is being increased and mass is constant, thus the acceleration will increase base on Newton’s second law F=ma. Since the radius is kept constant, as acceleration increases, v^2 should increase, and so will v. Therefore it is true that a positive correlation occurs between the force applied and the speed. But us we can see from the graph, the line thus not go through the origin, suggesting that they are not directly proportional.
For test 2, force and mass is kept constant, therefore acceleration would stay the same base on Newton’s second law F=ma. Hence as the radius is increasing, v^2 should increase and so will v. This supports the experimental results which show that there is a positive correlation between radius and speed. Yet they are not directly proportional as the line do not cut through the origin.
Yet for both graphs the line should cut through the origin. For test one instead of cutting through the origin, the line has a y-intercept of around 1.3.This is obviously ridiculous as it is suggesting that when there is the force is 0N, the object will is rotation at 1.3ms^-1, and thus accelerating constantly. This is obviously impossible as an object cannot accelerate without force applied. It is obviously that there are errors in this experiment that cause this problem. Indeed there are several systematic and random error. The main systematic error is neglecting the effect of frictional force on the moving object. The random error being simply human reflexes, which can have significant variations. These errors will be further explained in the Evaluating procedures section.
Evaluating Procedures
There are a number of errors in this experiment which needs to be addressed.
The first error is to neglect the frictional force on the moving object. This is a systematic error as it affects every measurement the same way and thus creating a constant deviation from the “real” values. The frictional force would slow down the object, making the speed slower than it should be (in a frictionless world), causing the speed to be lower than the accept value.
Another main error that affects the result of this experiment is human reflex. A human reflex is a type of random error, as it could vary a lot from one measurement to another. Yet one can still say the human reflex is also a systematic error, and it does affect every measurement, it is just the magnitude of the effect that is different. Now let examine how the affect of human reflex can enlarge the difference in values as the speed increases (time decreases). Let use test 1 as example. Test 1 states that the radius remains constant for all measurements (which means the length in which the object circulars remain the same. Thus as the force increases (leads to an increase in acceleration), the time decreases. Lets take the 2 extreme cases, 4.87 sec and 2.52 sec. lets assume that the experiment as an 0.1 sec of reflex time, that is, the experiment will push the stop button 0.1 sec after the object stops moving. Now lets calculate the percentage of human reflex in these 2 measurements. The results are 0.1/1.14=2.05% and 0.1/0.64=3.97%. This shows that the human reflex accounts for a larger portion of the recorded time as the length of the time is shortened (ie, faster speed). This is how the human reflex error can have a larger effect when the acceleration is faster, thus deviating the value from the true value.
The human reflex error can cause another problem for in this experiment. Lets take a look at the last test in test 1. The average time over 10 rotations is 2.52 seconds, an average of 0.252 seconds per a rotation. 0.252 seconds is an extremely short time span, and humans might not be able to react in such a fast time, making the object rotate more than it should be.
Due to the influence of the systematic and random errors above, the accuracy and precision of this experiment are still relatively low. Even though the data are not very accurate and prise, there are ways to improve it, which would be discussed in the next section.
A few of variables are controlled during the course of the experiment to make this a fair test. In test 1, the radius in which the object rotates, the mass of the object are kept constant. Whilst in test 2, the force applied and the mass of the object are kept constant.
Improving the Investigation
A number of weaknesses have been identified in the previous section. Lets examine and see what could have been done to minimus the effect of these errors and thus improve the both accuracy precision of the data.
The first weakness is ignoring the effect of friction on the rotating object. The most obvious way to solve this problem is to take into account of the friction in the calculation, and thus calculate all the frictional force acting on the body. Yet this method is indeed not very practical, as it is extremely difficult (at least for us student) to measure all the fictional. Even if we managed to measure all these fictions it would still be too trivial to calculate and thus have the risk of making arithmetic errors. So maybe the most practical way to solve this problem is just assign an overall estimate of the frictional force, this could minimus the error (better than when friction is not taken into account), and hence hopefully improve the accuracy of the data.
The second major weakness in this experiment is the human reflex problem, which causes the result to deviate away from the true value. A practical solution would be to increase the radius of rotation and the mass object. Why? As we see from above sections, the reaction time has a larger effect well the time frame is smaller. By increase the radius and mass, the time in which the object travels is lengthened, and thus minimus the effect of human reflex in the data.
There is another minor problem with the stop watch, we have pre-knowledge of the result of the experiment (ie, in test 1 I know according the Newton’s second law, the time should decrease). This would tend to make the experimenter to manipulate the results, and unconsciously press the stop button faster, thus making the measurements fairly inaccurate. This problem is hard to solve and the only solution is to have an electric sensor.
The small range of data is also a minor problem in this experiment, especially at the timing aspect. 3.24s and 3.64 is so small that humans don’t actually feel the difference, thus making the measurements very inaccurate, and thus it is advisable to increase the range of the data.
