lab report 3

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Jan 9, 2024

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Physics 001-06 Lab Report Name: Kristian Morgan ID: @02937236 Lab: Rectilinear Motion
Objective: The goal is to determine the relationship between the angle of an incline, the normal force, and the parallel forces acting on an object. Then we calculate the coefficient of friction and the value for gravity, using the acceleration of the object at different incline levels. Theory: The results of the experiment should imitate the quadratic curve of a position vs time graph. Since the materials used for the experiment are consistent, with the only difference being the height of the incline and therefore the acceleration, our calculated values for the coefficients of friction, and therefore the calculated values for gravity, should all be very close. Apparatus: 1.2m Pascar Dynamic track with PasCar, Computer interface (Science Workshop), Motion sensor, (2) 500 mg weights, caliper, and level. Procedure: First we check the height of the track compared to the desk it is sitting on, which will be our h0. Then we adjust the level of the track and measure the height of the incline 3 times to get our h1, h2, and h3. Then the car is set 10cm from the motion sensor, and let go to move down the incline while we press the start button in Data Studio. When the car reaches the bottom, we press stop. Using ‘fit-quadratic” in the program, we can record the coefficients. The first coefficient is equal to half of the acceleration. This process is repeated for each of the incline levels. Multiplying each of the first coefficients by two, we get the acceleration for each trial. Using the data collected, we are then left to complete our calculations using the equations given. Calculations and Results: We start by calculating our frictional coefficients for each trial. With a given L value of 1 meter and a g value of 9.8 m/s^2, we use the equation μ1|2|3 = (h1|2|3)/L – (a1|2|3)/g. For the first frictional coefficient, we know that h1 is 14.8mm, or .0148m, and our a1 value is .11 m/s^2. Therefore, (.0148/1) – (.11m/s^2)/(9.8 m/s^2) is equal to .0035755. Note that there is no units because they cancel out during our calculation. This same process is done to find μ2 and 3. Using these coefficients or using the accelerations, we then calculate r21. We can use that r21 value to find μ21. Lastly, g is calculated by replacing the μ1 in the final equation with μ21. This process is repeated with each combination, so we must find r31 and r32, and continue calculating to end up with μ31, μ32, and the g value for each combination. We calculate the percent error in g using μ31, μ32, and μ21, and then find the averages of the coefficients, from both u21, 31, and 32 as well as μ1, 2, and 3. The final values for g21, 31, and 32 were 9.5, 9.7, and 10.5 respectively. Compared to our given g value of 9.8, the percent errors are -3.06%, -1.02%, and 7.14% Sources of Error: Possible sources of error could be an incorrectly calibrated caliper or an error in the DataStudio program. Conclusions: Our final values for the frictional coefficients were fairly close, and when substituting them in for μ1 in the final equation, we get values that are close to the gravitational constant. The graphical data from the computer represented the shape of the graph that we were looking for.
Data Sheet: h 1 h 2 h 3 a 1 a 2 a 3 72.8 mm 89.3 mm 104.9 .11 m/s^2 .266 m/s^2 .42 m/s^2 h0 = 58mm
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