The coefficient of limiting friction μ and the coefficient of sliding friction μ1 are:
μ = F / R and μ1 = F1 / R
Where F = limiting frictional forces
F1 = Sliding frictional forces
R = Normal reaction
μ = F / R
Therefore mg sin 0 = F and mg cos 0 = R
μ = mg sin 0
mg cos 0
And μ = tan 0
The first thing I have to show is that there are two types of friction. I must also show that they have two different values. To do this I am going to do a simple experiment with a tray, 3 books and a Newton metre. This is shown below.
Pull
Tray Friction Newton mass
My results show that the sliding friction is slightly less than the static friction. This backs up what I said in my outline.
I then decided it was necessary for me to do a trail run of my experiment. The equipment for my experiment is set up below
The experiment will require the following equipment.
- A plank of wood to make the ramp
- A 1 metre ruler
- 3 block of different mass but same material (Wood)
- Top pan balance
- Clamp stand
The method of the experiment is as follows:
- Collect all equipment which is listed above
- Weigh the blocks of wood and take them mass down
- Place the plank on the desk
- Next you need to set up the ruler in the clamp stand making sure it is facing the right way so u will be able to take readings
- Place block 1 on the plank and slowly move the plank up noting the height at which it starts to slide
- Note the height and replete readings
The only safety issue I must take note of is the fact that the block could hit someone when I comes off the ramp to over come this I will do my experiment away from people and also have a tray to catch the block.
I hope to find that different weight and different size block have different frictions and will slide down the ramp at different angles.
My first set of results is:
Note the length of the plank is 89.5cm
There are a few anomalies in my results like B’s second result, which is totally out on all my other results.
This could be down to the board sliding. In my experiment I never kept an eye on if the board was sliding. I am going to repeat the experiment but on the desk I am going to place a piece of tape to mark out the point at which the board should be. Also I must make sure that the blocks must go straight down the plank so that the surface is the same.
My repeated experiment using the same equipment above but using a piece of tape on the desk to mark out the starting point of the board
0 Tan = X / B
These results for block A are better although my second and third result look like anomalies. The range of the angles for these results is quite big 4.68 and this could be down to the fact that I was out by a few mm when reading the height of the ramp.
0 Tan = X / B
The angles I have found are all very close as you can see from the range of 1.39. I am happy with these results the range of results for block B are better than results for block A.
0 Tan = X / B
The angles I have found are all very close as you can see from the range of 1.31. I am happy with these results the range of results for block C are better than results for block A.
I am happy with these results only having two main anomalies from the test done on block A. The second and third go. The only reasons I can think off why I got these results could have been to the speed I raised the ramp although I tried to keep it the same each time my speed would have altered and this could have affected my results. Also the path which the block travelled down the slop if this altered then the friction would have changed and not stayed constant.
Angle of ramp was calculated by using tan.
On all three of my graphs I have done error bars to take into account that I might be a few mm out with my readings so this is to overcome that feature. I also got the computer to produce a line of best fit so I could see how many of my results hit the line. None of my results were exactly on the line.
In conclusion I am very happy with the results that I got for my experiment. I f I was to do this experiment again thought I would try different materials and see how the coefficient limiting friction differs from different materials. From my results you can see that every two surfaces have a different friction level between them although the wood I used
The few anomalies, which occurred during my experiment, could be down to a few factors:
- The board or ramp could have move slightly making the block to slide
- The block might have took a different path down the slope although I used a smooth surface the surface in places could have altered causing the friction to change
To stop these from occurring I could have made a better ramp system rather than me lifting the ramp I could have had a mechanism doing if for me. The factor that the block might have took a different route down the slope I can really over come other than to repeat the results and take an average to take out any anomalies that may have occurred. As I took 6 readings with each block I think that any anomalies that may have occurred will have been cancelled out.
Books Used
A level Physics Forth Edition Roger Muncaster
This book was useful to me as it had a few pages on the different types of friction and also showed a experiment to show the coefficient of friction and how to calculate this.
Websites
This website provided me with some simple notes on the different aspects of friction noting to complex.
This website was off a lesson which a school had taught there was only a small section on friction.
This website listed the different types of coefficient. It also show experiment to show these different types of coefficient.
