Partners: Matthew Ibarra, Billy Justin
Date of Lab: 21 September 2016
Lab 7 Modeling Friction Forces
Mission Statement: To conduct five different experiments involving friction, with derivations and measurements included to explain each part of the lab.
Theory: Friction is the reciprocal force experienced by objects which either prevents or hampers their movement by countering any applied force. The kind of friction which prevents movement is known as static friction (SF), and the kind which hampers movement is known as kinetic friction (KF). Both kinds of frictional forces should be equal to the normal force experienced by the object multiplied by some coefficient of friction between 0 and 1, with the coefficient of SF typically being higher than the coefficient of KF. This experiment was divided into 5 different parts, detailed below
Experimental Procedure and Explanation Part 1:
. For Part 1, essentially, we were operating a hanging mass-pulley-sliding mass system, with the sliding mass being a block with an acrylic bottom which would resist sliding until the weight of the hanging mass proved to much. The weight of the hanging mass would be increased ever so slightly by adding more and more metal plates to it, thereby allowing us to pinpoint the precise weight required to overwhelm the SF being experienced by the object, shown below.
We would then plot the two important quantities (SF and the object's normal force, itself equal to the weight of the object) and produce the graph shown below.
The slope of the SF verses normal graph should be our particular coefficient of SF, which was 0.2693 in this case, very much a reasonable figure.
Experimental Procedure and Explanation Part 2:
For the second part of the experiment, we calibrated a force sensor which, when tied to the object with a string, could detect the average force being exerted on the object if we pulled the object at constant speed (so as to have zero acceleration). Additionally, we collected the masses of the object and then the object with one, two, and three other objects mounted atop it. We proceeded to plot the force being detected by the sensor over the duration of the pull four different times, corresponding with the four different masses, shown below.
With the information provided by the above graph, we were now equipped to plot our KF verses normal force graph, shown below.
From this experiment, we determined that the coefficient of kinetic friction is equivalent to the slope of our KF verses normal force graph, which in turn resulted in a value of 0.3049, reasonable to be sure, but oddly higher than the SF value from Part 1, which we did not anticipate.
Experimental Procedure and Explanation Part 3:
For Part 3, we inclined the slab on which we conducted Parts 1 and 2, setting the angle to be 19 degrees, shown below.
Using this known angle, we proceeded to calculate the coefficient of KF, shown below.
We obtained a value of the coefficient of KF to be 0.344, which is 0.0391 off of our experimental value for the coefficient of KF we determined in Part 2, and even higher than our experimental value for the coefficient of static friction we found in Part 1.
Experimental Procedure and Explanation Part 4:
Next, for Part 4, we mounted a motion sensor at the top of the incline to measure the acceleration of the block as the block slide downward to determine the coefficient of KF between the block and the slab. Plotting the data being collected by the motion sensor as the block descended, we constructed the following graphs of position v time and velocity v time.
We highlighted the region of the velocity verses time graph corresponding with the block's uninterrupted descent, the slope of which was the acceleration, possessing a value of 2.829 m/s/s.
With this value for the acceleration, we could now carry out our calculation to determine the particular value of the coefficient of KF for this particular trial, shown below.
The value of the coefficient of KF this time turned out to be 0.244, which is much more reasonable than the values collected during Parts 2 & 3 since it is below the SF value of 0.2693 we determined for Part 1.
Experimental Procedure and Explanation Part 5:
For Part 5, we were finished with the hands-on component of the lab and proceeded to a purely computational component. Using the coefficient of KF we determined from Part 4, we proceeded to derive an expression for what the acceleration of the block would be if you used a hanging mass sufficiently heavy to accelerate the system, shown below.
Our calculation is shown below.
Following our calculation, we obtained a value for the acceleration of 2.96 m/s/s, which is slightly higher than the acceleration value of 2.829 we collected during Part 4.
Experimental Procedure and Explanation Part 1:
. For Part 1, essentially, we were operating a hanging mass-pulley-sliding mass system, with the sliding mass being a block with an acrylic bottom which would resist sliding until the weight of the hanging mass proved to much. The weight of the hanging mass would be increased ever so slightly by adding more and more metal plates to it, thereby allowing us to pinpoint the precise weight required to overwhelm the SF being experienced by the object, shown below.
Experimental Procedure and Explanation Part 2:
For the second part of the experiment, we calibrated a force sensor which, when tied to the object with a string, could detect the average force being exerted on the object if we pulled the object at constant speed (so as to have zero acceleration). Additionally, we collected the masses of the object and then the object with one, two, and three other objects mounted atop it. We proceeded to plot the force being detected by the sensor over the duration of the pull four different times, corresponding with the four different masses, shown below.
For Part 3, we inclined the slab on which we conducted Parts 1 and 2, setting the angle to be 19 degrees, shown below.
Experimental Procedure and Explanation Part 4:
Next, for Part 4, we mounted a motion sensor at the top of the incline to measure the acceleration of the block as the block slide downward to determine the coefficient of KF between the block and the slab. Plotting the data being collected by the motion sensor as the block descended, we constructed the following graphs of position v time and velocity v time.
With this value for the acceleration, we could now carry out our calculation to determine the particular value of the coefficient of KF for this particular trial, shown below.
Experimental Procedure and Explanation Part 5:
For Part 5, we were finished with the hands-on component of the lab and proceeded to a purely computational component. Using the coefficient of KF we determined from Part 4, we proceeded to derive an expression for what the acceleration of the block would be if you used a hanging mass sufficiently heavy to accelerate the system, shown below.
Conclusion- This laboratory was admittedly rife with uncertainty, predominately random uncertainty. In terms of systemic error, we followed the instructions and set up everything accordingly, so I am led to assume that the professor's initial remarks about how friction is very difficult to precisely model could best explain why our coefficients of KF for Parts 2 and 3 were actually higher than the coefficient of SF for Part 1. The best explanation I could provide would appeal to the fact that despite seeming smooth, both the white slab and the acrylic bottom of the block possess countless microscopic imperfections which compounded to contribute significantly to the dependencies noted above as the block continued with its motion.
No comments:
Post a Comment