We did five experiments involving friction in order to figure out different equations to calculate static friction and kinetic friction based on the prompts we are assigned.
Part 1: Static friction
Set-Up:
In this first part of experiment, we needed four blocks, a mass balance, two Stoferoam cups, a string, and a pulley. We let the block lie on the table, connect the block with a string. Then we hang the string over the pulley and connect to the empty Storeforam cups. Since we knew that static friction is a friction force acting between two bodies when they are not moving relative to one another. We were going to add water into the Storefoam cup until the block started to slip. Figure 1 shows the apparatus of the experiment.
Figure 1: The apparatus of part 1 experiment.
Blocks are kept adding until we got 4 blocks in total. On the other side, water is added to make the block slip. We recorded the mass of block and cup with water. Here is our data (Figure 2).
Figure 2: The mass of block and cup with water.
The coefficient of static friction in this experiment equals the maximum value of static friction between the surfaces divided by the normal force N that squeezes them together. Below is an equation to calculate the coefficient static equation.
𝜇friction = (𝑓friction, maximum / N)
Calculating the coefficient of static friction force (Figure 3)
Figure 3: Setting up the equation to calculate the coefficient of static friction based on the data obtained. As a result, the slope of weight of block vs. (cup+water) graph would give us the value of coefficient of static friction.
Since we figured out the slope of weight of block vs. (cup+water) graph was the value of coefficient of static friction, we entered our data into Logger Pro, and let it graph for us. Figure 4 is our result for 𝜇friction .
Figure 4: The slope m=0.2567 gaves us the value of 𝜇friction = 0.2567.
Part 2: Kinetic Friction
Set-Up:
In this part, we still used the same four blocks like before; however, we needed a force sensor as an apparatus of this experiment. First we calibrated the force sensor by using a 500-gram hanging mass. Because we used the same four blocks in part 1, we didn't need to measure the mass again. We then hold the force horizontally and zero the force sensor. The force sensor was connected to the block through a string. We next pulled the force sensor horizontally at a constant speed along the surface of the table. We did the same process until we reached four blocks. As we knew the mass of four blocks, the Logger Pro helped us the task of recording the mean value of the pulling force.
Figure 5: The set-up of part 2. We held a force sensor and ready to pull it at a constant speed. Blocks are tied by a string which connected to the force sensor.
Data Analysis:
Our goal in part 2 is to find the coefficient of kinetic friction force based on the mass of block and the pulling force recorded by the Logger Pro. Our results of the mean value of the pulling force is shown below.
Figure 6: The mean value of the pulling force corresponding to 1, 2, 3, and 4 blocks.
We then set up equation to calculate the coefficient of kinetic friction force.
Figure 7: Setting up equation for coefficient of kinetic friction force.
The coefficient of kinetic friction force equals the slope of Force and (M*g) graph. Thus, we entered our data into Logger Pro and graph it to obtain the slope which is the value of kinetic friction coefficient.
Figure 8: The normal force vs. force acting graph.
The slope of graph m=0.2541 is the result we wanted. Thus, the coefficient of kinetic friction is μk = 0.2541
Part 3: Static friction from a sloped surface
Set-up:
The device we needed for this part was just an angle measurement and a block. We placed a block on a horizontal surface. Then we slowly tilt one end of the surface until the block started to slip. We measured that angle in order to determine the coefficient of static friction between the block and the surface.
Data Analysis:
The angle we got is ⦶ = 16° ± 2°
Calculating the coefficient of static friction between the block and surface.(Figure 9)
Figure 9: The result of coefficient of static friction.
μs = 0.2867
Part 4: Kinetic friction sliding a block down and incline.
Set-up:
The apparatus of this experiment includes a motion detector, a block, an angle measurement, a sledge, and a clamp to hold a sledge. We set up the sledge is steep enough that a block will accelerate down the inclined, measure the angle of the inclined and the acceleration of the block. We then determine the coefficient of kinetic friction between the block and the surface from our measurements.
Figure 10: The apparatus of the experiment.
Data Analysis:
As the motion detector is connected to the Logger Pro, when the block accelerated down the incline, we would get a velocity vs. time graph on Logger Pro. The slope of the graph would give us the value of acceleration which needed to calculate the coefficient of kinetic friction.
%2Bacceleration.PNG)
Figure 11: Plotting velocity vs. time graph in order to obtain the value of acceleration (a= 1.194 m/(s^2)).
Since we got the value of acceleration, the mass of a block, and the angle, we then calculated the coefficient of kinetic friction between the block and the surface.
Figure 12: Calculating the coefficient of kinetic friction.
μk = 0.3934
Part 5: Predicting the acceleration of a two-mass system.
Set-up:
We let a block lie on a horizontal surface, attach a block with a string. Hanging the string over the pulley which is connected with another mass. A motion censor was put behind the block to capture the movement of the block when it started to accelerate. Below is our apparatus.
Figure 13: The set-up of this experiment.
Data Analysis:
When the block accelerate, the motion detector and Logger Pro helped us capture the movement. We obtained the velocity vs. time graph in Logger Pro, and its slope gave us the value of acceleration which is an experimental value of acceleration.
%2Btwo%2Bmass%2Bsystem.PNG)
Figure 14: Velocity vs. time graph. The slope m=0.2396 gave us the value of acceleration.
With the value of coefficient of kinetic friction from part 4, we were able to calculate the "true" value of acceleration in order to compare with the experimental value. The calculation for "true" value of acceleration is shown below.
Figure 15: Calculating the "true" value of acceleration.
Since we have both experimental value and "true" value, we calculated the percent error to see how far we were off from the actual result.
Figure 16: Our result for percent error. % error = -27.79%
Conclusion:
In this lab, we learned how to model friction forces. Each part we came up with different equation to calculate the coefficient of either static friction or kinetic friction. The results for each part was pretty reasonable. For part 1, we got 𝜇static = 0.2567. For part 2, our result was 𝜇kinetic = 0.2541. Part 3 and part 4 we got in order 𝜇static = 0.2867 and 𝜇kinetic = 0.3934. For the last part, we compared the experimental value and "true" value by calculating the percent error. Our results was %error = -27.79%. Although the percent error was "quite" high, our experimental value of acceleration was a=0.2390 m/s^2 which isn't far from the true value a=0.3310 m/s^2.
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