Coefficients of Friction


AP Physics B


Introduction


The coefficient of friction is a representation of the roughness of two surfaces in contact with each other. There are two types of coefficients of frictions: the static coefficient is used when the two surfaces are relatively stationary; the kinetic coefficient is used when the two surfaces are sliding along each other. The purpose of this lab was to study the relationship between static and kinetic friction; to determine different coefficients of friction for different pairs of surfaces; and to discover how coefficients of friction relate to what is perceived as the relative “smoothness” of surfaces. As a class, many different pairs of surfaces were tested in order to determine both the static and kinetic coefficients of friction. This report is the compilation of the efforts of the AP Physics B class in determining a number of coefficients of static and kinetic friction for various surface pairs.



Friction Theory

Causes of Friction

Friction is a force caused when two objects are in contact and one of them moves or attempts to move horizontally. Friction acts in the opposite direction of the movement of the object and parallel to the surface. It is caused by the microscopic jagged edges of each object exerting forces on each other. When one object moves, these create a frictional force and slow down the object's movement. There are two types of friction: static friction and kinetic friction.

Static Friction

Static Friction is the friction present when two surfaces are touching and neither are moving, even though a force parallel to the two surfaces is being applied to one of the objects. The coefficient of static friction is higher than that of kinetic friction because it requires more force to get an object moving than it does to keep it moving. An example of static friction is when a car is stopped, there is a forcing being applied to the wheels by the engine to make them turn, but the coefficient of static friction of the brakes is too high for the force of the wheels to overcome, so they cannot turn. The equation for static friction is coefficient of static friction multiplied by normal force.

Kinetic Friction

Kinetic friction is the friction present when two surfaces began sliding over one another. Kinetic friction occurs at the spot where the two surfaces come into contact with each other and it opposes the object that is moving relative to the other surface. For example, kinetic friction opposes the wheels of a car skidding out of control on the road because the wheels are moving relative to the road and creating friction where they come into contact with the road. The magnitude of the force of kinetic friction is related to the normal force, but it is independent of the speed and the area of contact between the two sliding objects. The equation for kinetic friction is the coefficient of kinetic friction multiplied by the normal force.


Procedure


To begin this experiment, we first set up the LabPro computer program to collect data for 10 seconds at 60 samples per second. Our graphs on the LabPro were already set up with our y-axis representing friction and our x-axis corresponding with time. Then, we placed one of the sides of the block on our chosen surface and placed an appropriate mass on it to increase normal force. (We ended up using a felt side of the block, but any material used on the side of the block is appropriate.) It was necessary to place weights on the block so that the computer program could accurately graph the increasing static friction. Next, we pulled the block horizontally and initially began with a small amount of force and gradually increased our force applied until the block began to slide. We wanted to place the block horizontally in order for the normal force of the block to equal its weight. If the block were to be inclined at an angle, the block's weight wouldn't have been an appropriate measurement for its normal force. We tried to pull the block at a constant velocity afterwards. Afterwards, we examined our graph and determined the maximum force of static friction and the force of kinetic friction and recorded our results. We repeated these exact steps using the opposite side of the block (the opposite side of the block used different material than the initial side) on the same surface. Finally, we repeated the entire process on an additional two different surfaces, leaving us with a total of six graphs displaying the different static and kinetic coefficients of friction.


Results


Results for Nikhil/Tarun/Andrew/Annelise's group:

1. In all cases, the coeff of static friction was greater than coeff of kinetic friction, as hypothesized.
2. Both friction coeffs of sandpaper on surface were greater than felt, as one would imagine.
3. Sandpaper on carpet had particularly high coeffs of friction, and nearly double those of felt on paper. One issue that we ran into was that sandpaper on carpet dragged in such a way that the force required to pull it was prone to spikes and sharp dips, because the sandpaper randomly hooked itself into carpet with varying friction.
4. The total weight of our block was 371g (121g of the block + 250g weight) This exerts a normal force of .371kg x 9.8m/s^2 = 3.6358 N. To get the coeffs of friction listed below, we divided the force value obtained by experiment for static and kinetic, and divided by the normal force.


Coefficient of Static Friction
Coefficient of Kinetic Friction

Surface



Nikhil's Group Results:

.811
.71

Sandpaper on Cardboard




.531
.509

Felt on Cardboard




1.939
1.659

Sandpaper on Carpet




1.136
.866

Felt on Carpet




.4895
.3664

Sandpaper on Table




.242
.226

Felt on Table




Domnic, Ellis, and Davis's Group Results:


.263
.223

Felt on Force Plate




.345
.327

Duck Tape on Force Plate




.726
.574

Felt on Carpet




.379
.334

Duck Tape on Carpet




.215
.188

Felt on Table




.233
.161

Duck Tape on Table



These results follow the aforementioned trends. Note that we had significantly different felt on carpet coefficients. Duck Tape on table had the biggest difference in between static and kinetic.

Shannon, Peter and Chris
1.03
.64
Shoe on Hallway Tile
.42
.28
Felt on Hallway Tile
1.16
.84
Shoe on Red Tile
.50
.21
Felt on Red Tile
.73
.33
Shoe on Wet Tile
.62
.33
Felt on Wet Tile

These results follow the trends of static coefficients being greater than kinetic coefficients and they are reasonable in that the felt produced lower coefficients than the shoe. The Hallway tile seems to be the most rough, followed by red and then wet tile.


Thomas, Claire, Charlotte, Janay:

0.292
0.214
Felt on Commons Tile
0.496
0.473
Foam on Commons Tile
0.868
0.697
Felt on Carpet
0.855
0.707
Foam on Carpet
0.232
0.199
Felt on Table
0.120
0.111
Foam on Table


Follows the trends of static being greater than kinetic, and follows what one would hypothesize. Carpet has highest frictions, then commons tile, then table.


Conclusions



As the results show, static friction is generally significantly larger than kinetic friction. Also, in general, the surfaces that included Duck Tape had higher coefficients of friction than those that had felt. Sandpaper overall was the biggest contributor, yielding the highest coefficients of all the surfaces done by different groups in the experiment.
The major source of error in the experiment was probably the sensitivity of the force detector. In order to obtain any kind of useful measurement, the experimenter has to pull in an excruciatingly slow motion. It is very possible that inaccuracies could have resulted from the person failing to pull the block at a constant rate or horizontal angle.
A possible way that researchers can build on the experiment in the future would be to run trials on much more significantly jagged surfaces, and see the rate at which the coefficient of friction changes as the surface becomes more uneven.