Use of motion data

Week of the experiment: 4 OBJECTIVE (3 points): The objective of this lab is to gain a more complete conceptual understanding of 2-D kinematics. We will explore the concepts of position distance velocity and displacement through the use of the motion data gathered with a cart simulation. This will be used to extrapolate and calculate graphs and equations for the positions and velocity. EXPERIMENTAL DATA (3 points): PART 1: Object moving away from the motion sensor. Table 1 Run # Time interval (s) Position (m) [Initial & End] Distance (m) Displacement (m) Speed (m/s) Velocity (m/s) 1a 8.187 to 9.843 0.85 to 1.70 0.850 0.850 0.513 0.513 1b 7.09 to 8.06 0.28 to 0.78 0.500 0.500 0.515 0.515 1c 9.281 to 10.06 1.41 to 1.81 0.400 0.400 0.513 0.513 Table 2 Run # Slope (m/s) Y-intercept (m) Name of Physics quantity (i.e. position distance etc.) 1 0.5160 +/- 0.0001203 -3.376 +/- 0.001031 Position 2 1.645 +/- 0.0001288 -1.982 +/-0.0002569 Position Using equation 5 substitute in your slope and y-intercept to create an equation that describes the motion of the cart: Run 1:y=0.5160x -3.376 Run 2: y=-0.00260x+0.5383 Table 3. (Use Logger Pro for statistical data to calculate avg. velocity and uncertainty) Run # Average Velocity (m/s) Standard deviation (m) 1 0.5162 0.002718 2 1.661 0.002959 PART 2: Object moving toward the motion sensor. Table 4 Run # Slope (m/s) Y-intercept (m/s) Name of Physics quantity (i.e. position distance speed etc.) 3 -.8242 +/- .0001528 3.108 +/- .0004052 Position 4 -1.235 +/- .0002127 7.175 +/- .001075 Position Using equation 5 substitute in your slope and y-intercept to create an equation that describes the motion of the cart: Run 3: Position = -.8242t + 3.108 Run 4: Position = -1.235t + 7.175 Table 5. (Use Logger Pro for statistical data to calculate avg. velocity and uncertainty) Run # Average Velocity (m/s) Standard deviation (m/s) 3 -.8370 +/- .002111 .002778 4 -1.275 +/- .01070 .003428 PART 3. Matching position vs. time graphs Run 5: Include in the Discussion the methods used to reproduce the graph. Insert the best match for the position vs time graph. DATA ANALYSIS (10 points): the section includes equations calculations and error analysis if required. Be sure all equations are present! PART 1 & 2: Show the equation with the plugged in numbers you used in run 1 to calculate the cart’s: ·Distance: xFinal – xInitial = Distance traveled 1.70 m – .85 m = .85 m ( ·Displacement: xFinal – xInitial = Displacement 1.70 m – .85 m = .85 m ·Average speed: Displacement / Time = Average speed .85 m / (9.843 – 8.187) s = .513 m/s ·Average velocity: Displacement / Time = Average velocity .85 m / (9.843 – 8.187) s = .513 m/s For run 2 and 4 calculate the percent difference between the average velocity from the slope of the x(t) graph and mean velocity from v(t) graph. Let x=slope of x(t) & v=mean velocity of v(t) % Difference = 100 * |x+v|/((x+v)/2) Run #2: 100 * |.516+.5162|/((.516+.5162)/2) = 0.0387% Run #4: 100 * |-1.235+-1.275|/((-1.235+-1.275)/2) = 3.187% PART 4: Run 6: Show calculation (use eqn.

5) used to make a prediction for the final position of the cart after 2 s from the moment it crosses the 80 cm mark on the track. x(t) = x0 + v(t-t0) x(t)= (80cm) + (-20m/s)(2s-0s) x(t)=80cm +(-40cm) x(t)=40cm RESULTS (3 points):

Table 6. PARTS 1 & 2 (Report results below with 4 significant figures) Average velocity (m/s) Run # Position vs. Time graph Velocity vs. Time graph % Difference 1 .516 .5162 0.0387% 2 1.645 1.661 0.9679% 3 -.8242 -.8370 1.541% 4 -1.235 -1.275 3.187% Table 7. PARTS 1 & 2 Equations of motion Run # Substituted Equations of Motion (equation 5) 1 x(t) = x0 + .5162(t-t0) 2 x(t) = x0 + 1.661(t-t0) 3 x(t) = x0 + -.8370(t-t0) 4 x(t) = x0 + -1.275(t-t0)

Table 8. PART 4 final position of cart after 2 s Predicted position: Experimental position: 40.0cm 40.7cm DISCUSSION AND CONCLUSION (10 points):

Requirements: 300 words