3/18 Modeling Friction Forces

Purpose: To determine static and kinetic frictional force using different experiments. 

Procedure:

PART ONE: Static Friction

FIGURE (1)

For the first part of the lab, we were determining static friction between a block and the tabletop. We did this by attaching a pulley to the table attaching a string to the block and a cup. We hung the cup off the edge of the table while the block sat on top of the table. We then proceeded to add water to the cup until the block started to move just a little. That meant that the weight of the cup and therefore tension in the string was great enough to overcome the static friction. ( f_static≤µ_sN) By obtaining the mass of the cup we were able to calculate the maximum force one can apply before overcoming static friction (FIGURE (1)). We did this process four times with four different masses and we recorded the mass of the cup with water each time. We then calculated the normal force and frictional force created a Friction v. Normal graph (FIGURE (2)). 

CORRECTION IN FIGURE (2): The mass of the blocks was entered incorrectly. The data should read from top to bottom: 131, 252, 359, 485. 

FIGURE (2)

The slope of this graph gives us the coefficient of static friction: µ_s=.3475 ±.01287

PART TWO: Kinetic Friction

For the second part of the lab, we were determining the kinetic frictional force between the blocks and the tabletop. This time, we had the block sitting on top of the table with a string attached to it. We set up a force probe and tied it to the other end of the string. We then pulled the force probe horizontally while collecting data in LoggerPro (FIGURE (3)). We did this three additional times with larger block masses each time. 

FIGURE (3)

After we finished collecting or data we plotted it on a graph again. (FIGURE (4)) The slope on this graph again gives us the coefficient of static friction: µ_s=.2712 ± .009813. We then know that the coefficient for kinetic friction is anything greater than that. (f_kinetic=µ_kN). 

FIGURE (4)

PART THREE

For the third part of the lab, we placed a block on a horizontal piece of plywood and lifted one end (the one closest to where the block sat) until the block started to slip. We then measure the angle where that occurred. The calculations to find the coefficient of friction are shown in FIGURE (5).

FIGURE (5)

PART FOUR

In the fourth part of the lab we did a similar procedure as part three but we measured speed with a motion detector. From measuring speed, we can calculate the kinetic friction between the surfaces by obtaining acceleration from our graph (FIGURE (6)). We know that the acceleration would be the slope of the velocity graph. Therefore, the acceleration is .7825 m/s^2.

FIGURE (6)

Once we have the acceleration we can use the angle and acceleration to calculate the coefficient of kinetic friction. The steps to find µ_k are in FIGURE (7).

FIGURE (7)

PART 5

In the first part of the fifth part of this lab, we were to derive and equation for acceleration using the coefficient of kinetic friction from part four. The work for that is shown in FIGURE (8):

FIGURE (8)

FIGURE (9)

The second part of the experiment was to calculate the mass that would be required to overcome static friction and move the block, if the unknown mass was attached to a string and to the block and then hooked up to a pulley (FIGURE (9)). After we found the unknown mass we could plug the into our equation for acceleration and get an estimate for acceleration as well. The work for this is shown in FIGURE (10).

FIGURE (10)

When we tried the experiment with our calculated mass (we had to use 40g), the block moved a little bit but it was not a steady movement. We got a steady movement at 50g, which probably means that the precise mass is somewhere between 40g and 50g. We also set up a motion sensor so we could obtain a velocity v. time graph as well as the acceleration. (FIGURE (11))

FIGURE (11)

The graph shows that the acceleration of the block was .573m/s^2. This value is not very to the one we calculated. Errors that may have attributed to this include errors in initial measurements such as the angle measured in part three. This would have led to an error in out calculation of the coefficient of friction and an even bigger error in part 5 calculations. When we were doing the experiment, our motion sensor was also acting very strange. It would take measurements differently each time, and our initial test looked completely different from our final test (shown).

Conclusion:
Overall, the purpose of this lab was fulfilled. We demonstrated everything that we had learned in class about friction and most of our calculations and experimental results were accurate. There were many possible errors in this lab since we did five different experiments. The possible errors may have included: (part (1)) we could have added to much water to the cup. This would obviously lead to a great mass of the cup and therefore a greater frictional force. When we were adding drops to the cup we were not adding drop by drop by drop, because that would take a long time and we did not have that much time in lab; (part (2)) When we were pulling the force sensor we could have pulled it at a slight angle instead of parallel to the table. The force sensor also could have been calculated inaccurately and we would lose accuracy. Also, it it highly doubtful that we were able to pull the blocks at a constant speed and the same speed every time we took new data.; (part (3)) As previously stated, an error in the part could have been the angle we calculated. We could have read the measurement incorrectly or we could have stopped at an angle greater than when the block first started to slip. This would give us a greater frictional value and coefficient of friction.; (part(5)) we could have recreated the 20 degree angle inaccurately which would give the block greater acceleration and therefore a different coefficient of friction.; (part(5)) As previously mentioned, our previous measurements could have given us inaccuracy in this part of the lab. Also, there was the problems with our motion sensor.