(i) Method using pulley
The apparatus will be set up as shown on the diagram above. A block of wood will be attached to some weights with some string, via a pulley. Weights shall be added or removed until the block of wood just begins to move, for static friction, at which point the sum of the added weights shall be recorded (force needed to overcome the static friction). This will be repeated 2 times. Then, the surface the block of wood is being pulled over will be changed, and the mass of the block of wood will be altered by using weights. Only one variable, mass or surface used, will be changed at any one time, the remaining variables, surface area of the block of wood, and direction, will remain constant, to respect fair testing.
Apparatus:
-10g, 25g, 50g, and 100g weights
-A pulley
-Sand paper (P60E), and a plank of wood
-A rectangular block of wood (325g)
-An electronic scale
Table of results for method (i)
ii) Method using Force Newton meter
The apparatus will be set up as shown in the diagram above. A block of wood will be attached to a piece of string, which will in turn be attached to a force meter. The block will then be pulled along a clean horizontal surface. The force needed to overcome static and then dynamic friction will then be noted down, this will be repeated 2 times for the sake of fair testing. The same experiment will be repeated using different surfaces, and the mass of the block of wood will be altered using various weights.
Apparatus:
- A rectangular block of wood (325g)
- A spring balance, also called a force meter
- A piece of string
- Surfaces: Plastic surface of the table, wooden surface, sand paper (3M210-p120), sand paper (P60E green).
- 10g, 25g, 100g and 200g weights
- An electronic scale
Table of results for method (ii):
DYNAMIC FRICTION:
STATIC FRICTION:
iii) Method using force meter to investigate the effects of surface area on friction.
In this method I am investigating about the affect of surface area on friction. The apparatus will be set up as in the diagram above. In this method I will be repeating the method used in method (ii) concerning the force meter. The only difference is that the block will be turned onto its side and therefore the surface area of the block of wood in contact with the surface area is changed to a smaller surface area.
Apparatus:
- A rectangular block of wood (325g)
- A spring balance, also called a force meter
- A piece of string
- Surfaces: Plastic surface of the table, wooden surface, sand paper (3M210-p120), sand paper (P60E green).
- 10g, 25g, 100g and 200g weights
- An electronic scale
Method: A block of wood will be attached to a piece of string, which will in turn be attached to a force meter. The block will then be pulled along a clean horizontal surface, with the smaller surface area of the block of wood in contact with the chosen surface. The force needed to overcome static and then dynamic friction will then be noted down, this will be repeated 2 times for the sake of averages, accuracy, and to reduce error. The same experiment will be repeated using different surfaces, and the mass of the block of wood will be altered using various weights.
Table of results for method (iii):
DYNAMIC FRICTION
STATIC FRICTION
iv) Conclusion of preliminary results
The first method gave me, I believe, relatively accurate results, as the coefficients of friction for each surface stay quite the same as the mass of the block rises. The second method however gave me results for which the coefficients of friction fluctuated less than in method (i) when the mass changed of the block rises. In addition, the lines on the graph have a strong correlation (ie the points are close to each other and near to the line of best fit). Therefore I believe it is safe to use this method in the main experiment of the investigation, as it is a more secure method. I have also deduced from my preliminary results, that with the equipment available, the measure of static friction is more reliable and precise. This is because static friction is measured at a precise point in time, whereas dynamic friction must be measured on a longer scale of time. In addition, dynamic friction is harder to record with the apparatus available because the force meter must be pulled along with a steady hand at constant speed for enough time to make recordings. This can prove to be very difficult, and this is why the results for dynamic friction are very unstable and imprecise.
By comparing method (iii), that investigated the affect of surface area on friction, with method (ii), I have deduced that surface area does not have a great effect on friction, and the forces are similar whichever surface area is used.
However, through my preliminary results, I have decided that during the main experiment I will use a greater range of weights, to end up with a clearer curve. I have also decided that the weights should start higher (150g) and extend up to a larger weight (950g). This is because the smaller weights used in the preliminary experiments were harder to record, and therefore were not always accurate, and I was more liable to error by using them.
Another factor that I decided from my preliminary results was which surfaces to use. Both the plastic surface of the table and the wood surface, had minimal friction, and therefore they are not very interesting or accurate for measuring static friction. However, I believe it is more interesting to investigate the difference in the three sandpapers available, as I could discover if the size and shape of the granules affects the friction. I am less likely to acquire errors if I measure larger values of F (N).
Hypothesis and prediction
From my background and scientific knowledge, but also from the results of my preliminary results, I can predict that as the weight of the block of wood increases, so will the force required to push it along or move it.
6. METHOD
Set up diagram of apparatus
The apparatus shall be set up as shown in the diagram above. A rectangular block of wood will be massed carefully. A piece of string will be attached to it. A force meter will then in turn be attached to the string. The block will then be pulled along a clean, horizontal surface. The force needed to overcome static friction will be noted down. The same thing will be repeated with 7 different masses. These will be 150g, 300, 500, 650g, 800g, and 950g. The mass of the block will be altered using masses of 50g, 100g, 1kg and so on.
The same experiment will be repeated using three different surfaces. This will include 3 different types of sand paper. All the readings will be written down carefully, averages will be calculated and graphs will be plotted for clear analysis of the results.
Each reading will be repeated three times for the sake of accuracy and precision.
Safety precautions: There are no major safety precautions to be taken, as this experiment does not involve electricity or chemicals. However, caution has to be taken when operating the equipment as not to damage it or anything else in the lab.
7. Hypothesis and predictions
-The force required to move the block of wood will increase as the mass of the block of wood increases.
Part 2) Obtaining evidence
Table of results
Tables of Averages
In these tables of averages, a column for weight has been added, so as to measure the downward force.
Weight = mass x gravitational force
Weight = R, mass (kg), g =9.8
Part 3) Analysis
The graphs that I have made show that the results are regular and form a strong correlation around the lines of best fit. A line of best fit was used to reduce error. In all three surfaces, the graph shows a straight line through the origin, this means that mass and the average force needed to overcome static friction are directly proportional.
I will now find the gradients of all three graphs, using the general equation for a straight-line graph:
Y = mx + c
Because the y intercept is 0 the lines go through the origin, therefore, c = 0 , m = gradient, so: m = y/x
From the line of the surface of sand paper P60E, m = 9.2/ 12000
m =0.000767
From the line of the surface of sand paper 3M210 P120,
m = 8.6/ 1100
m = 0.00782
From the line of the surface of sand paper 18 036C, m = 6/1000
m = 0.006
In my prediction, I predicted that as the weight of the block of wood increases, so would the force needed to overcome its static friction and move it. I therefore did some more background research, and discovered the term coefficients of friction.
I shall now talk in more detail about coefficients of friction, by using my information on limiting equilibrium. If a horizontal force P is applied to an object lying on a horizontal surface, the magnitude of the frictional force is just sufficient to prevent motion.
The frictional force F for a particular surface is not constant. It increases as the applied force P increases until the force F reaches a value Fmax beyond which it cannot increase. The object is then just about to move and is said to be in a state of limiting equilibrium. At this point, friction is said to be limiting. It can be shown experimentally that Fmax is proportional to R (downward force, or weight), fmax=μR
The constant of proportionality, which is always given as the symbol “µ”, is called the coefficient of friction.
In general, therefore, F≤µR. Clearly F≥0 and is only zero when the surface is completely smooth.
If you compare the two equations to do with the graph, you can see that they are the same.
y = m x + c and F = µ R
The gradients of each line of best fit should be equal to the coefficient of friction. Gradient = μ (coefficient of friction)
y = m x + c
F = µ R + 0
So, F = μ
Therefore, the coefficient of friction is a measure of the frictional characteristics of the surface.
The coefficients of friction will now be measured, to compare them with gradients, which they should be equal to.
To do this is used the equation F =μR
μ = F/ R
TOTAL AVERAGE COEFFICIENTS OF STATIC FRICTION
In my calculations of the total average coefficient of friction, I disregarded certain anomalies:
-In sand paper P60E: I disregarded the 0.99 value, as it was in a margin with the other results.
- Although in the sand paper 3M 210 P120, there were certain marginal results, like 0.69 and 0.90, they were in quite close range, so I included them in the calculation.
- in the sand paper 18 O36, the results were all mainly in close proximity to one and other, although the 0.47, was a bit lower than the others, but I still included it to find the total average.
Comparing the gradients and the coefficients of friction, I have found very different results. This could be due to many factors, the use of different units, and the margins of error in the graph, and of course all experimental error.
Conclusion: Because the correlation on my graph is positive, this proves that my hypothesis was correct, that as the weight of the block of wood increased, so did the fore needed to overcome it.
As the weight of an object increases, the friction occurring between the object and the surface it is resting or moving on increases proportionally to the weight of the object, no matter which surface is used.
Part 4) Evaluation
It is normal that there is experimental error, because of many factors. First there is the possibility of anomalies being present I the experiment, so there must be a margin of error. I could also have made a mathematical error, or a measurement error. However the apparatus is the most responsible factor in the experimental error, as the apparatus available was not precise. For example the weights were not precise, and the smallest weight was 5g, and the surfaces were damaged. Friction in the force meter, and although it is negligible, it still affects the results. The string also had resistance, although it was also negligible. I have calculated a percentage of error, by using the following equation:
Δx X 100 = percentage error.
x
TOTAL AVERAGE PERCENTAGE OF ERROR FOR EACH SURFACE
Sand paper P60E: 6.8%
Sand paper 3m 210 P120: 5.9%
Sand paper 18 O36C: 4.8%
Both from the gradients I have calculated, and the coefficients of friction, I can deduce that although the sand papers P60E and 3M 210 P120 where very close in their results, the sand paper 3m 210 P120 has the smallest gradient and largest coefficient of friction, and therefore is the surface that grips the most. From the results, it is apparent that sand paper P60E was very close and has a high grip surface. The third sand paper, however showed a strong difference to the other two. It had a much lower coefficient of friction, and a much bigger gradient. This meant that this surface gripped a lot less to the block of wood. I have made these deductions, because higher coefficient of friction means the surface grips more.
From further research, I have found an explanation for this. When a surface has smaller grains, the grains get pushed into the crevices in the wood’s surface, and in effect, cause it to grip a lot more. However, when a surface has larger grains, they do not get pushed into the crevices, and the block will slide along the surface more easily.
FURTHER WORK
There were a few other ways of performing the experiment, and other factors that I did not have time to investigate. For example, an incline plane, instead of the horizontal one used in my experiment. The deduction would have been, that as the angle of incline (θ) increased the force (F) would have also increased, until at a particular angle θ, the block starts to move, at this point F is at it’s limiting friction.
I could have repeated my results a further time, to decrease error, and used a more precise range of weights. I could also have investigated other types of friction, not including dynamic and static.