Investigation into Friction.

Hazards

There will be relatively heavy masses involved in this experiment, so caution must be taken so that they do not fall off the desk onto a pupil’s foot, because they could incur moderate injury. The masses must also not be dropped, because they themselves could be damaged, or they could damage classroom furniture, such as desks. The force meters are quite delicate, so they will not be over loaded when pulling the masses. So that the masses involved do not get too high, a force meter that is only capable of pulling 30 N will be used.

Variables

Independent variables: this will be R, the force acting on the two surfaces, providing frictional force. Using different values of mass, placed on the wooden block, will vary this. The other independent variable that will be changed in this experiment will be the bottom surface. Smooth and rough hardboard will be used. The two independent variables will not be changed at the same time, so that the test remains fair. The first part of the experiment will be done using the smooth hardboard; the masses on the wooden block will be varied; then the experiment will be repeated exactly, but using the rough hardboard instead.

Dependent variables: this is the force it will take by pulling on the force meter to make the two surfaces slide over one another (F). This will be affected by the independent variable: the greater the force on the two surfaces, the greater the value of F will be. This variable will also be affected by the bottom surface being used – rough or smooth.

Fixed variables: these will be the force meter used and the block of wood where the masses will be placed. There is another fixed variable of sorts: when the smooth hardboard is being used as the bottom surface, this will be kept the same, until that part of the experiment has finished; when the rough hardboard is being used, this will be kept constant until that part of the experiment is finished.

Preliminary Work

The maximum weight that the force meter can pull is 30 N. This means that we will need to determine the maximum mass that can be added to the wooden block so that the force meter is capable of applying enough force to make the two surfaces slide. This will need to be done with both the rough and the smooth hardboard.

1. A wooden block of known mass was placed on the smooth then the rough hardboard.
2. Weights were added to the block, and the force meter was used to make the burden move.
3. The weights continued to be added until the force meter was using 30 N or thereabouts to make the burden move.
4. This amount of added weight was recorded. It is the maximum amount of weight that can be added to the wooden block during the experiment for the smooth and the rough hardboard surfaces.
5. The results were recorded in Tables 1 and 2.

Table 1.

Table 2.

Therefore, we can add the weights in the actual experiment to the wooden block in 10 N increments to a maximum of 90 N for the smooth hardboard and 70 N for the rough hardboard. This will give a total of nine readings for the smooth hardboard part of the experiment and seven readings for the rough hardboard part of the experiment.

Predictions

From the definition that Ordinary Level Physics gives us of the coefficient of friction, we can say that the rougher the surface, the greater the coefficient of friction will be. This can also lead to the prediction that the rougher surface, the gradient will be steeper than the gradient for the smooth surface experiment. When using the smooth hardboard surface, less force at F will be needed to make the surfaces slide over one another. The smooth surface provides less friction with the top surface, so less force at F will be needed to make the surfaces slide. But the rough surface causes more frictional force with the top surface, so the force needed at F will need to be greater to make the surfaces slide. We can also say that the greater R is – the more masses on the wooden block – the greater F will need to be to overcome the forces of friction and make the surfaces slide over one another. The greater the mass at R, the greater the resistive force of friction, and so the greater the force at F needed to overcome friction. The force needed at F is proportional to the resistive force at R. This is shown by the formula:

μ = F                     

      R         

We could also say from the formula that the graph that should be produced should have a straight line through the origin, with force (F) being plotted against the masses forcing the two surfaces together (R). This is shown in Fig 3. We could also say from the preliminary experiment that when the total weight is 93.28 N, the reading on the force meter will be 28 N for the smooth surface, and for the rough surface, when the total weight 73.28 N, the reading on the force meter will be 30 N.

Fig 3.

Selecting the appropriate equipment

There are several ways that we could approach this experiment. We could construct the apparatus shown below in Fig 4.

 

Fig 4.

This would have eliminated the need to use a force meter and having to actually pull on the burden. But we will not use this apparatus, because it is not as accurate, because it would be difficult to put masses on without pulling the block at the same time. Also, the experiment could only be done to the degree of accuracy of the smallest weight available. This means that the readings taken for the force needed would be more inaccurate. Another problem to using this type of apparatus would be that it would take more time to undertake the experiment and also to set up the experiment than it would with the apparatus in Fig 3, which we will be using.    

Apparatus

• 10 N masses
• Smooth hardboard
• Rough hardboard
• Wooden block of known mass
• Force meter calibrated in Newtons
• String

Method

1. The apparatus was set up as shown in Fig 2.
2. The smooth hardboard was used first as the bottom surface.
3. Weights were added to the wooden block 10 N at a time.
4. The force meter was used to make the block move along the smooth hardboard.
5. The reading on the force meter was taken at the moment when the block moved.
6. This was repeated immediately for each weight.
7. The experiment was repeated using the rough hardboard as the bottom surface.
8. The results were recorded in Tables 2 and 3.

Results

Table 3.

Table 4.

Observations

When we did the experiment, we discovered that the force taken to make the masses move on the second reading on the smooth hardboard was greater than the preliminary experiment predicted. When the weight added was 70 N, the force needed to make the burden move was 30 N for the second reading. This meant that the following masses would be too heavy for it to only take 30 N to move them. The experiment for the smooth hardboard was then only continued to an added weight of 70 N.

Analysis of Results

The masses added in the smooth surface experiment did not reach 93.28 N, as predicted. This could have been because the surfaces were not exactly the same throughout the experiment, and so when it came to adding 90 N to the block, the surface had been changed significantly enough for the frictional force to have increased. Also, the place where the preliminary experiment was done could have been different to the place where the actual experiment took place. This means that we cannot support our prediction that “when the total weight is 93.28 N, the reading on the force meter will be 28 N for the smooth surface”. However, for the 73.28 N reading, the force needed was 27.5 N, showing that were it possible for 93.28 N to have been pulled, the reading on the force meter would have been greater than 30 N. This is probably because the conditions under which the preliminary experiment that determined the predicted results were different to those under which the actual experiment was done. For the rough hardboard, it was predicted that when 73.28 N was being moved, the reading on the force meter would be 30 N. This is different to the actual reading: 25 N. This probably happened for the same reason that the results from the smooth surface did not exactly match those that were predicted.

As the masses added increased, the force needed to make the surfaces slide increased. This proves our prediction that: “the greater R is – the more masses on the wooden block – the greater F will need to be to overcome the forces of friction and make the surfaces slide over one another”. For the experiment using the smooth hardboard as the bottom surface, the results of this can be seen in Table 3. The largest difference between the two readings is 5 N, for the 53.28 N of total weight. This is quite a large amount, and could be accounted for by the possible wearing down of the smooth hardboard, after the many times that the same place has had the block dragged over it. The surface is quite unpredictable, and so this explains this result. The averages of these two results will also be plotted, so this reading may cause a few inaccuracies when plotting the graph, but they should not be too great. The maximum force needed for the rough hardboard surfaces to slide was 25 N. The maximum force needed to make the smooth surfaces slide was 30 N. This does not prove our predictions that: “when using the smooth hardboard surface, less force at F will be needed to make the surfaces slide over one another. The rough hardboard surface will need more force applied at F than the smooth hardboard surface needs”. This could have been because the surfaces are very irregular and unpredictable in their frictional force. The results that were obtained from the smooth hardboard experiment are regular, and there are no anomalies. This shows that the experiment was done accurately enough for this application.

The results for the experiment using the rough hardboard are shown in Table 4. The largest difference between the two readings was for the 63.28 N of total weight, the difference being 1.5 N. This is not a very large amount, and so it will not cause too much of an inaccuracy in the graph, because the average of the two is being plotted. The results for the rough hardboard, on the whole, are quite regular, and there are no anomalies. From the results in the table, we can say that there are no readings that are very far away any other reading, and this indicates that this part of the experiment was also done accurately, and reliably.  

Conclusions from the graph

Graph 1 shows the readings on the force meter (F) in the smooth hardboard experiment plotted against the weight being pulled (R). The points are correlated moderately well, with only a few plotted points being far from the line of best fit. This graph resembles the predicted graph. This also shows that there are few inaccurate results i.e. there are no points that are very far from the line of best fit so that they are anomalies. However, the line of best fit does not go through the origin, as it should, if F was directly proportional to R. Graph 2 shows the readings on the force meter (F) in the rough hardboard experiment plotted against the weight being pulled (R). As we can see from Graph 2, there is good correlation of the points. The graph that we have produced is quite similar to the predicted one in Fig 3, showing that the results that we obtained are quite accurate, but that there are few results that we should consider unreliable. These would be the 53.28 N reading and the 73.28 N reading. This is because they are both 2 N away from the line of best fit. These inaccuracies could have been caused by the burden not being placed in exactly the same place for every reading, and therefore, the surface that was being used would not have been exactly the same for each reading. Another explanation for these inaccuracies could be that the position on the rough surface where the burden was placed for readings could have been worn down by the dragging of the burden over it. This would mean that the surface would become less rough, and so there would be less friction between the two surfaces, meaning that the force at F needed to overcome the frictional forces would have been less, leading to the results obtained. This line of best fit does not go through the origin either, as predicted. This could be because of the changing friction between the surfaces, as they are worn down and smoothed off. It could also have been caused by the position where the burden was dragged being changed, and so causing the friction between the surfaces to go up, because that part of the hardboard had not been used in the experiment before.

The gradient of the graph of the plotted results shows the coefficient of friction for that surface. Both the units of F and R are Newtons. This means that the gradients will not have any units, because N ÷ N = 0 units. This means that the coefficient of friction is a dimensionless quantity. Graph 3 shows the gradient of the graph of the results for the smooth hardboard experiment. The coefficient for the smooth surface is 0.34. Graph 4 shows the gradient of the graph of the results of the rough hardboard experiment. The coefficient for the rough surface is 0.35. The gradient of the graph of the results for the rough hardboard experiment is steeper than that of the smooth hardboard experiment. This is because for a given value of weight, one would expect the limiting force of friction to be greater for the rougher surface. This means that the value of μ will be greater. This supports the prediction that was made: “the rougher the surface, the greater the coefficient of friction will be”, and the prediction that the gradient of graph of the results the rougher surface will be steeper have been supported. Although the smooth hardboard experiment took more force to overcome friction overall than the rough hardboard experiment, the fact that the coefficient of static friction for the rough hardboard is greater than that for the smooth hardboard adds reliability to the experiment and our results.

Accuracy

We need to work out the maximum percentage uncertainty for the graphs of the results that we have produced. To do this, we can use the distance any point is from the line of best fit, and divide it by the point where it should be, on the line of best fit. To find the maximum percentage error in the whole experiment, we have to follow the steps below:

if point is below line of best fit:  

point on line of best fit – plotted point = distance out

distance out ÷ point on line of best fit x 100 = percentage error

if point is above line of best fit:  

plotted point – point on line of best fit = distance out

distance out ÷ point on line of best fit x 100 = percentage error

The point on Graph 1 that has the greatest percentage error is the 13.28 N reading. The percentage error was worked out as follows:

6 – 5.75 = 0.25

0.25 ÷ 6 = 0.042

0.042 x 100 = 4.2

Therefore, 4.2 % is the maximum percentage error for the results for the rough hardboard experiment. This percentage error is not that large, and so this shows that the results that were obtained from the smooth hardboard experiment were quite accurate.

The point on Graph 2 that has the greatest percentage error is also the 13.28 N reading. The percentage error was worked out as follows:

6 – 4.75 = 1.25

1.25 ÷ 6 = 0.21

0.21 x 100 = 21

Therefore, 21 % is the maximum percentage error for the results for the rough hardboard experiment. This percentage error is relatively large, and this shows that the results that were obtained from the rough hardboard experiment are not as accurate as the ones from the smooth hardboard experiment. This is probably because the rough surface was continually being worn away, and therefore, the first result that was taken would have had a larger percentage error in comparison to the other readings.

        Another way of working out the accuracy of the experiment is to find the standard deviation of the results from the line of best fit on the graphs. For Graph 1, the smooth hardboard, the distances of the plotted points from the line of best fit are as follows in Table 5.

Table 5. 

The standard deviation of the points plotted in Graph 1 from the results of the rough hardboard experiment is 0.19. For Graph 2, the rough hardboard, the distances of the plotted points from the line of best fit are as follows in Table 6.

Table 6.

The standard deviation of the points plotted in Graph 2 from the results of the smooth hardboard experiment is 0.67. The rough hardboard results have the greatest standard deviation, and so we can say that the largest deviation of any force meter reading from its line of best fit in the whole experiment is 0.67 N. This is not a very large value, and this shows that although there is a maximum percentage error of 21 %, the standard deviation of the points shows that there were few results that were totally inaccurate.

        The method that was used to undertake this experiment is a little inaccurate in itself. The reading on the force meter had to be taken the moment that the block moved. The force reading was only visible for taking the reading off for a very short period, because as soon as the block started to slide over the surface, the reading on the fore meter went down, because the coefficient of friction was not longer that of static friction, but of dynamic friction. The reading on the force meter after the block started to slide was much less, and so the reading needed to be taken at the exact moment of movement. This is difficult for the human nervous system to judge, and so, the readings them selves may have been a little inaccurate, compared to the results that might have been obtained if the experiment had been done with a piece of technical or electronic equipment. For this reason, the results as a whole are inaccurate compared to what they might have been if they had been taken more accurately. But the results that we have are sufficiently accurate for the application of a school investigation.

Suitability

In this experiment, we were able to take seven readings for each surface. This amount of readings in any experiment is enough to make a valid and thorough analysis of. In this investigation, we were really only wanting to look into the coefficients of friction on different surface types. This means that a larger range of results would not really be necessary, because we are only looking to find out whether the coefficients of static friction were different for various types of surfaces, and we have achieved this aim. The increments of weight that were added to the block were small enough for relatively accurate graphs to be produced, and so the adding of 10 N weights was suitable for the aims of this investigation.  

Reliability

The experiment in itself was not that accurate. This is because of the irregularity in the ‘roughness’ or ‘smoothness’ of the surfaces being used. Also, the method of taking the readings added unreliability to the results of the experiment. The reading could have been taken after the block moved, and this could explain the results where the force needed was lower than the line of best fit. Because the method was done in the same way as much as possible for every reading, if all other contributors to the reliability of the experiment’s results were in order, the experiment would have been far more accurate. However, that is totally impossible in the conditions under which did this experiment. For instance, the hardboard is not totally regular in its irregularities, and so the forces of friction in parts of the board will be different to those in others. Also, it was difficult to position the block in exactly the same place for each reading, and this would have affected the reliability of the results, because of the differences between the amounts of friction in various places on the hardboard

Improvements to the method

To improve the reliability of the results that were obtained, we could have used a physically bigger force meter with more space in between each increment. This would mean that it would be easier to read off the force, and so increase the reliability and accuracy of the results. We could also have taken he readings with an electronic force meter, or one that recorded the highest force reading. This would have made the results far more accurate, because they would not be reliant on human sensitivity, and reaction times, which add unreliability to the results and experiment. Another method of measuring the force needed to overcome friction would be to set up apparatus where the block with the weights on it was put behind a pressure sensor. The force meter would not be used, with the burden being pulled using string. The pressure sensor would be placed so that it was not touching the block, and was about 2 mm away from it. The sensor would be connected to some sort of recording and data logging device. The block would be pulled in the same way as the original experiment. The data logging device would record the data received from the pressure sensor. The sensor would have to be capable of measuring the value of the pressure being exerted on it. Where there was a sudden increase in the pressure exerted on the sensor, that would be taken as the force that was needed to move the block. The pressure sensor would have to be moveable, and this could be done by mounting it on rollers or castors. Regularly rough hardboard could be used, so that the frictional force on one part of the hardboard would be the same as on another part. This would also reduce the uncertainties in the results.    

Improvements to provide additional evidence

If the pressure sensor was used, the coefficient of dynamic as well as static friction could be investigated. Using the method described above, when the block touched the pressure sensor when it just started to move, the data logger would record the force needed. But because the pressure sensor is moveable, after the block has touched it, if the block kept being pulled, the pressure sensor would come with the block. This would mean that the force needed to keep the block and weights moving could be recorded. This could be used to give us the coefficient of dynamic friction, and we could then compare the two coefficients of static and dynamic friction, on different surfaces.

        We could also investigate how the speed at which the force at F is applied affects the coefficient of friction for different surfaces. This would be done by pulling the burden at different speeds. To make sure that the speed was regular, markings could be made on the board, indicating the position that the burden needed to be in after a certain time. For instance:

speed = distance ÷ time

If the speed was to be 0.001 m/s, then the block will have to have moved 1 cm in 1 second, 2 cm in 2 seconds etc. The centimetres could be marked on the hardboard, and the ‘puller’ would have to pace himself so that the block was passing the centimetre mark on the second. This method could be used for any speed. The affect that the speed that force is applied at could then be investigated, extending the original experiment.    

Graphs

Graph 1.

Graph 2.        

Graph 3.

Graph 4.

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