A similar leather strap would be placed on the opposite side of the motor, as shown in the diagram on the right, which shares the tension across the straps and avoids too much damage of the bearings in the motor (which would be more of a risk if there was only one strap involved in the experiment).
The torque would be measured by taking the tension of the straps and multiplying that by the radius of the motor.
The angular velocity can be measured by using a stroboscope, which determines how many turns the motor makes per second.
Method of Choice
I have chosen to use Method 2, because it is much more practical to carry out, in that I don’t need to go and find a tall building and mark the wall all the way up.
The results produced from Method 2 would also be more accurate than those that I would get with Method 1, because measuring how long the weight takes to travel between two marks on the building would be open to human error and quite difficult to time accurately. It would also be extremely difficult to judge at what time the weight had reached a steady speed.
Preliminary Experiment
For my preliminary experiment, I had to test how much strain the leather straps could cope with. I tested the apparatus at increasing tensions, and discovered that over 11N the straps became very hot and began to smoke. I therefore decided not to take measurements of tensions over 11N in my main experiment.
This would not only be safer in the conduction of the experiment, but it will also avoid damage to the leather straps through melting, which would affect further readings from then on, as the leather straps have to be placed at exactly the same point each time.
Precautions for Safety
To take precautions for safety, I will have to take down the readings from the Newton meters fairly quickly, as the friction on the leather straps could cause a high increase in heat with higher tension.
I will also have to avoid taking measurements for tensions over 11N, or the apparatus can become very hot due to friction, and produce a lot of smoke.
Thirdly, I will have to keep my motor running at 12V at all times, not only to keep it a fair experiment, but also to make sure that the voltage doesn’t get too high for the motor.
Apparatus
The following apparatus would be needed to carry out my main experiment:
- Shunt wound motor
- Two leather straps
- Retort stands
- Newton meters (that can measure up to 15 N)
- Clamps
- Wooden bars
- Power supply
- Stroboscope
- Ammeter
- Voltmeter
- Wires
The following diagram shows how this apparatus will be set up:
Effects Which Might Affect the Results
The most obvious factor that could affect the results is human error. When using the stroboscope to calculate the number of turns per second, there is quite a wide margin for error in judging at what point the stroboscope is at the correct frequency.
Also when using the stroboscope, it is important to make sure that as little light as possible is on the apparatus, to make it easier for me to determine at what point the stroboscope is at the correct frequency.
As it is difficult to reproduce exactly the same conditions each time a reading is repeated, this may cause discrepancies in the data collected for my repeat readings. A change in the positioning of the leather strap on the motor could have an effect, and it is also very difficult to get the tension in the straps exactly right.
Results
I ran the experiment at 12V. The readings I took were the four Newton meter readings while the motor was turning, and the frequency of the turns with a stroboscope.
I calculated the applied torque with the equation: [(F1 – F2) + (F4 – F3)] *0.014 where 0.014 is the radius of the motor. The angular velocity is calculated by 2f. The power is calculated from IV. And the efficiency is [(angular velocity * applied torque)/power]*100
Here are the results for my first set of readings:
Here are the results for my repeat readings:
Anomalous data above is shown in red. I calculated whether or not data was anomalous by putting 5% error bars on the graphs and identifying the points which were still far from the line and the edge of the error bars.
Graphs
The graphs on the following pages show the results.
When producing my graphs, rather than averaging my original readings with my repeat readings, I produced separate graphs for both sets of readings. This was because they both turned out quite different from each other, because I took the two sets on different days.
Evaluation
As you can see on the graphs above, there is a very wide margin for error – on some of them up to 11% error. This is because the experiment can be very unreliable and inaccurate (see Effects Which Could Affect the Results above).
There are three main reasons why my results are not very accurate, and the repeat results are quite different to the original results (see Graphs). Firstly, the actual method itself is not very reliable – which means there is a wide margin of error. Secondly, I carried out my first results and my repeat results on separate days, which could have had an effect on the results – especially as the apparatus was set up in a fairly busy laboratory for a period of several days. Thirdly, at the end of my first set of results, the apparatus was becoming very hot and the leather strap melted slightly onto the motor. This changed the shape of the inner strap and could have had a marked effect on the repeat results. This may also explain the large numbers of anomalies in my data.
However, although the results are not as accurate as I would have hoped them to be, the graphs still follow a similar shape as I expected them to, and there is still sufficient evidence to support my conclusion.
Conclusion
I conclude that there is a linear relationship between torque and angular velocity. There is also a linear relationship with positive correlation between the power input and the torque. Thirdly, there is a clear relationship between torque and efficiency up to about 0.25 Nm where it reaches a peak and begins to decrease.