Download PHY 113Uniformly Accelerated Linear MotionPHY 113OBJECTIVE(S and more Lecture notes Accounting in PDF only on Docsity!
PHY 113
Uniformly Accelerated Linear Motion PHY 113 OBJECTIVE(S) ( 3 points ): The objectives of this lab are to understand graphical presentation of uniformly acceleration motion and to gain understanding of relationships between position vs. time and velocity vs. time for uniformly accelerated motion; to determine the experimental value of the gravitational acceleration g on Earth using kinematic equations and video analysis; justify the equations of position as a function of time for uniformly acceleration velocity motion. EXPERIMENTAL DATA ( 3 points ): Obtain experimental data that will be used for further calculations from the graphs.
PART 1: Uniformly Accelerated Motion on a Dynamic
Track
Table 1. Run 1a Time interval (s) Coordinates (m) Distance (m) 1-2 0.114 / 0.4476 0. 2-3 0.4476 / 1.1223 0. After plotting a curve of best fit for x(t) in Logger Pro, fill in these tables with the corresponding curve fit coefficients. Pay close attention to the direction of the velocity and acceleration. Table 2. Position vs. Time Curve Fit Coefficients Run # A B C Acceleration ( m/s2 ) 1a 0.1699 +/- 6.792E- -0.1753 +/-
0.1188 +/- 0.3434 0.3401 +/- 0. 1b 0.2551 +/- 8.042E- 0.3455 +/- 0.3477 0.1911 +/- 0.3497 0.5106 +/- 0. 2 -0.1701 +/- 5.905E- 0.2614 +/- 0.2892 1.828 +/- 0.3263 -0.3403 +/- 0. 3 -0.1712 +/-
1.441 +/- 0.1777 -1.203 +/- 0.2022 -0.3440 +/- 0. 4 0.2419 +/-
-1.928 +/- 0.1730 3.130 +/- 0.1181 0.4350 +/- 0. Table 3. Position vs. Time Curve Fit Parameter Definitions
Coefficients Name of Physics quantity (i.e. position, distance, velocity, etc.) A ½ Acceleration B Initial Velocity C Initial Position After plotting a line of best fit for v(t) in Logger Pro, fill in the following tables with the corresponding linear fit parameters. Table 4. Velocity vs. Time Linear Fit Parameters Run # Slope Y-intercept Acceleration ( m/s2 ) 1a 1b 0.3401 +/- 0. 0.5106 +/- 0. -0.1764 +/- 0. -0.3469 +/- 0. 0.3401 +/- 0. 0.5106 +/- 0. 2 -0.3403 +/- 0.2144^ 0.2619 +/- 0.5375^ -0.3403 +/- 0. 3 -0.3440 +/- 0.2290^ 1.446 +/- 0.6194^ -0.3440 +/- 0. 4 0.4350 +/- 0.8067^ -1.849 +/- 0.1209^ 0.4350 +/- 0. Table 5. Velocity vs. Time Linear Fit Parameter Definitions Coefficients Name of Physics quantity (i.e. position, distance, velocity, etc.) m (slope) Acceleration b (y-intercept) Initial Velocity Insert x(t) and v(t) graphs for Runs 1-4 here. Run1: Cart speeds up while moving away from sensor Run2: Cart speeds up while moving towards sensor Run3: Cart slows down while moving away from sensor. Run4: Cart slows down while moving towards sensor Run1A
Run 1B
Run 3
Run 4
Run 2
Run: Freefall
PART 2: Free Fall
After recording data from the video and fitting a curve of best fit to the x(t) graph and line of best fit to the v(t) graph, fill in the tables below. Table 6. Position vs. Time graph Curve Fit Parameters A B C Acceleration ( m/s2 ) -5.250 +/-
20.70 +/- 0.3430 -13.12 +/- 0.4543 -7. Table 7. Velocity vs. Time graph Linear Fit Parameters Slope Y-intercept Acceleration ( m/s2 ) -10.27 +/- 0.2482 20.00 +/- 0.6660 -10.27 +/- 0. Table 8. (Use Logger Pro to calculate mean time and uncertainty from the time given) Mean Time ( s ) Uncertainty ( s )
PART 1:
Acceleration (m/s2) Run # Position vs. Time graph Velocity vs. Time graph Direction of acceleration and velocity compared to each other 1a 0.6609 0.2554 Positive, positive 1b 0.6437 0.3324 Positive, positive 2 1.457 -0.3060 Negative, negative 3 0.9122 0.0251 Negative, positive 4 1.106 -0.1944 Positive, negative PART 2: Free Fall Part: (gravitational acceleration ± error) (m/s2) 2A -10. 2B -9.347 +/- 0. DISCUSSION AND CONCLUSION (10 points): This experiment was very cool to conduct, and I was able to learn a lot about the one-dimension relationship between velocity and acceleration. During run number one, the cart was placed to the far left and was released on a negative two-degree angle, which makes the cart move quicker down the track versus if the track was set at zero degrees or at a positive angle. Run number two, the track angle was set to positive two degrees making it slightly more difficult for the cart to climb a positive angle. Finally, for run number four, it was determined that the cart had a more difficult time going uphill (going from right to left) when the track was set to a negative angle of 2.5 degrees. Overall, it was concluded that the cart has an easier time when going downhill versus going uphill. The chart below expresses the key results. The independent variable in this experiment is the degree of the track angle and the dependent variable is the cart and its movement. In the second part of this experiment (freefall), a statistical error would be each of the three different times that were recorded. These errors are considered statistical due to the calculations of the mean values of the times to help mitigate the errors. In a systemic error, it could be due to the 0.2s human response time when collecting data.
