The purpose of this experiment was to explore the properties of static and kinetic friction and their effects on two systems in contact. Their application to different situations as well as their diverse dependence on different situations was investigated. Lastly, friction was used to predict the behavior and change in motion of an object due to external forces.
Apparatus:
This experiment consisted of five parts. The first part of the experiment involved finding the coefficient of static friction by hanging a mass on the system that barely starts it to move. To do so, the apparatus consisted of five blocks, with one block containing red felt on the bottom side. The apparatus also consisted of a styrofoam cup that was used as the hanging mass; its weight was changed by adding and removing water. A balance was also needed to measure the mass of the blocks and the styrofoam cup. Lastly, string and a pulley were needed to allow hanging of the styrofoam cup.
The second part of the experiment involved finding the coefficient of kinetic friction by measuring the pull force required to keep the object in constant motion. A computer with LoggerPro was required in order to measure the value of the pull force over an interval of time. A force sensor was also needed to allow the computer to measure the force of the pull on the system. A 500 gram mass was also used to calibrate the sensor by hanging it and getting a reading close to 4.9 N by the force sensor. Four different blocks were also needed, with one block containing the red felt on the bottom side. Lastly, a balance was needed to measure the mass of the blocks.
The third part of the experiment involved finding the coefficient of static friction on a sloped surface by finding the maximum static friction on the system, which was done by creating a slope that causes the object to just begin sliding. The equipment needed for part 3 included a metal slide or plank, a magnetic protractor to measure the angle of the metal surface and a vertical stand with a bar perpendicular to it to hold the metal surface raised up. A block with red felt on its bottom side was also needed. Lastly, a balance was needed to measure the mass of the block.
Figure 4: Apparatus for part 4 of the experiment
The fourth part of the experiment involved finding the coefficient of kinetic friction of a sliding block on an angled surface by measuring the acceleration of the block.The equipment needed for this part of the experiment included a motion detector to find the acceleration of the block, a metal slide, a block with red felt on its bottom and a magnetic protractor to measure the angle of the metal surface. A computer with LoggerPro software was also needed to record the motion of the block from data measured by the motion detector. Lastly, some sticky noted were needed to paste onto the block so that the motion detector is able to notice the block's presence.
Figure 5: Apparatus for part 5 of the experiment
Part 5 of the experiment involved predicting the acceleration of a block using the coefficient of kinetic friction calculated from the fourth part of the experiment, then comparing the expected acceleration with the acceleration recorded from performing the experiment with equal measurements and situations (i.e same masses, same situation with a hanging mass, etc). The equipment needed for this experiment included a pulley, a metal slide, a styrofoam cup containing 50 g and 10 g weights whose function was to act as the hanging mass, string, and a motion detector to record the motion of the system. Lastly, a block with red felt on its bottom side was used as the system, and sticky notes were pasted onto the block to allow the motion detector to detect the presence of the block and its change in motion.
Procedure (Part 1):
Once the apparatus was set up, the mass of the block with red felt on its bottom side was measured. Then, water was slowly added to the hanging cup until the block just barely started to slide.Once the block began to just slide, the mass of the cup and water were measured and recorded.
Next, an additional block was obtained and its mass was recorded. Then, it was added on top of the first block with everything in the same position as before. Again, more water was added until the blocks began to just move. The mass of the cup and water was then recorded again. The same procedure was performed again for three and four blocks.
With the masses of the blocks and the masses of the cup with differing amount of water, a graph of maximum static friction force vs. normal force was created.
Discussion (Part 1):
Comparing the formulas of static friction and the equation of a line, :
1.
it can be seen that the force of static friction is the value for y, the normal force is the value for x, and the coefficient of static friction is the value for m, or the slope of the graph.
The normal force was calculated by finding the weight of the block(s), since the normal force is equal to the weight of the blocks. The force of static friction was found by finding the tension in the string, which is equal to the weight of the hanging mass. The free body diagrams that display the method for finding the normal force and static friction force is seen below:
Figure 6: Free body diagrams and equations for part 1 of the experiment
Using this method, the data table of normal force and force of static friction was constructed, seen below:
Figure 7: Data table of normal force and static friction
Using the data from the table above, the graph of static friction force vs normal force was constructed:
Figure 8: Graph of static friction force vs normal force
As explained earlier, the slope of the above graph is the coefficient of static friction between the red felt and the table top. The coefficient of static friction is:
2.
There is a very small (0.9%) uncertainty in the coefficient of static friction, which shows that the modeling of the static friction force was accurately portrayed.
Procedure (Part 2):
Once all of the equipment needed was obtained, the force sensor was connected to the computer containing LoggerPro. The force sensor was then calibrated using a 500 gram hanging mass. The force recorded during the calibration should have been around 4.9 N. Once the force sensor was calibrated, it was placed horizontally onto the table and with no forces other than its weight and normal force, it was zeroed. Next the mass of the block with red felt was obtained, and the block was tied to the force sensor using a string. Then, the force sensor and block were pulled such that they were in constant motion. The force of tension in the string measured by the probe was collected by LoggerPro over an interval in time. The average tension force was then obtained.
Figure 9: Average tension forces (mean) of the four runs
Then, the mass of a second block was recorded and it was place on top of the first block. Next, the blocks and force sensor were pulled at constant speed and the force of tension was collected. The average tension force was then obtained. This procedure was repeated with three blocks and four blocks, as in part 1.
Using the masses of the blocks each trial and the average tension force, a graph of maximum kinetic friction force vs. normal force was created.
Discussion (Part 2):
Similar to part 1, comparing the equations of a line and kinetic friction,:
3.
it can be seen that the force of kinetic friction is the value for y, the normal force is the value for x, and the coefficient of kinetic friction is the value for m, or the slope of the graph.
Using free body diagrams (shown below), it can be seen that the normal force is equal to the weight of the blocks. The force of kinetic friction can also be found because it is equal to the tension force, or the average force recorded by the sensor.
Figure 10: Free body diagrams and equations for part 2 of the experiment
Using this method, the graph of kinetic friction force vs normal force was made, and the slope was obtained. Using the same options in LoggerPro as in part 1, the data table and graphs were made:
Figure 11: Data table of normal force and kinetic friction
Figure 12: Graph of kinetic friction force vs normal force
The coefficient of kinetic friction was calculated to be:
4.
The uncertainty in the coefficient of kinetic friction (3.8%) is fairly small, which shows that the model of the kinetic friction force was accurate.
Procedure (Part 3):
Once all of the equipment was obtained, the metal slide's angle was adjusted until the block with the red felt just began to slide. The angle was then measured and recorded and the mass of the block was obtained.
Discussion (Part 3):
Using the mass of the block and the angle of the surface, the coefficient of static friction between the felt and metal slide can be found through a free body diagram, summing the horizontal and vertical components, with acceleration in all directions equal to zero. The free body diagram is shown below:
Figure 13: Free body diagrams and equations for part 3 of the experiment
The coefficient of static friction was calculated to be 0.344. It makes great sense that the coefficient of static friction on the slope is larger than on the level ground since more friction is required to keep the system at equilibrium due to some of its weight wanting to push it down the slope. In addition, the metal slides are rougher than the table tops.
Procedure (Part 4):
Once all the equipment was set up, an angle higher than 19 degrees was needed in order for the block to accelerate downward. The angle was chosen at 30 degrees. Using the motion sensor, the acceleration of the block with red felt down the slope was measured by creating a velocity vs time graph , then taking a linear fit to find the slope of the graph. The mass of the block was then measured.
Discussion (Part 4):
The graph of velocity vs time of the block down the slope is shown below:
Figure 14: Velocity vs time graph of the block down the slope
The linear fit provides a constant slope for the graph, which also provides the average constant acceleration of the block down the slope. The acceleration of the block was found to be 1.08 m/s/s.
Using the angle of the slope, the mass of the block, and the acceleration, the coefficient of kinetic friction can be determined using a free body diagram and summing the horizontal and vertical components, as shown below:
Figure 15: Free body diagrams and equations for part 4 of the experiment
The coefficient of kinetic friction was calculated to be 0.450. It may seem unusual at first that the coefficient of kinetic friction is larger than the coefficient of static friction in part 3. However, the reason for so is because the angle of the slope was increased by more than 1.5 times as much. As the angle is increased, more of the weight of the system is trying to cause the system to slide down, so a larger friction is needed to counteract the slippage.
Procedure (Part 5):
Once all of the equipment was set up, the acceleration of the block was measured by the motion sensor, like in part 4. Similar to part 4, a velocity vs time graph was constructed, and a linear fit was performed to find the acceleration of block. The acceleration of the block was recorded to be 0.193 m/s/s.
Then, using the coefficient of kinetic friction from part 4, the expected acceleration of the block was derived and calculated using free body diagrams shown below:
Figure 16: Free body diagrams and equations for part 5 of the experiment
The calculated value of acceleration is 0.158 m/s/s. There is a 19.9% percentage difference between the calculated and experimental value.
Conclusion:
Most of the uncertainty and large difference in experimental and actual values in this experiment are caused by the equipment being not accurate enough. This can be seen in the uncertainty of the static friction in part 1 versus the uncertainty in the accelerations in part 5. No measuring devices were used in part 1, resulting in a very small uncertainty (0.9%). However, most of the experiment in part 5 required the use of measuring devices, resulting in much larger uncertainties or differences (19.9%). If better equipment was used, such as more accurate motion detectors and newer versions of LoggerPro and measurement kits, a lot of the uncertainty that is present now would diminish.
Also, in order to lower error in this experiment, more trials should have been performed for the last two parts. In order to do so, more time for this experiment should have been allotted.
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