22-Mar-2017: Modeling Friction Forces

Lab 7: Modeling Friction Forces
22-Mar-2017
Idea: Be able to model friction forces using a mass-pulley or external forces, and use it to predict/derive its various components.

Summary/Analysis
Part 1: Static Frictions

1) First, we hung various masses off a table with a string connected to a block via a pulley.

2)We increased its mass in increments of 10 grams until the block, also increasing in increments of 200 grams per every test case, began to slide. Thus we obtained 4 test cases wherein the block just begins to slide.

3) Using logger pro, I then plotted this data and using a line of best fit, obtained a slope that was my coefficient of static friction over the masses of my four test cases.

 Part 2: Kinetic Friction
1) I attached a calibrated force sensor to the block, and again increased the mass of the block in increments of 200 grams, and recorded the force readings from the sensor.

 2) In Logger Pro, the sensor gave me the following graph, and the line of best fit for each case would give me my forces.
 3) This time, I plotted my previously recorded Force data as well versus the weight of my block (which is the normal force) of the 4 test cases, and the slope of this graph gives the coefficient of kinetic friction.

Part 3: Static Friction From a Sloped Surface
1) I then placed the block on the surface and inclined the board until it slipped, which turned out to be at an angle of 21 degrees. I then used this to calculate the coefficient of static friction between the block and the surface.

 2) When calculated, I got a value of 0.386.

Part 4: Kinetic Friction From Sliding a Block Down An Incline
1) I repeated the same experiment as part 3, except with a motion detector to record the acceleration of the block as it slid down the incline.

2) By finding the slope of the data where it seemed best reliable, I got an acceleration of 1.466 for the block. Using this, and the known angle of the incline, I was able to calculate this coefficient of kinetic friction.

3) Compared to the value of static friction that I got in Part 3, this value of 0.223 is expectedly lower than the coefficient of static friction, which was 0.386. Therefore I believe that this value is very reasonable.

Part 5: Predicting the Acceleration of a Two-Mass System
1) Finally, I set up experiment 1's mass-pulley system but with a motion sensor to record the acceleration, with the block and a single mass of 60 grams hanging off the pulley, so that the system would start moving once I let go of the block. This slope would be my experimental result for acceleration. Logger Pro gave me a value of 0.7627 m/s/s.

2) In order to calculate the acceleration, I set up free body diagrams for the masses and solved for acceleration, and plugging my values for the block and the hanging mass gave me a calculated value of acceleration of 0.828 m/s/s.

Conclusion/Percent Error
In calculating the percent error of my yielded accelerations in Part 5, I used my calculated acceleration vs my experimental value. 0.7627 was my model value, and 0.828 was my calculated value. Using these values, I got a percent error of 8.7%.

1) Initially,  major source of uncertainty would be in the mass-pulley system itself, as the point at which the block would begin to slide were extremely inconsistent. For example, the block would slide at 180 grams, or 145 grams.
2) For Part 5, seeing as I'd gotten a percent error of 8.7%, it was not as accurate as I would have hoped, but it is reasonable considering all of the possible sources of uncertainties in this experiment.From the mass of the block, friction, etc, all of which played into calculating each component of the system.