Lab 1

1 (1 point) Title of the Experiment: Constant Velocity Motion in One Dimension (along a straight line) Student’s name: Devin Pridgeon Section SLN: 188357 TA’s Name: Harish Hemming Week of the experiment: Week 1

2 OBJECTIVE (3 points) : The concepts to be investigated in this experiment are the principles of position, distance, displacement, and velocity in one-dimensional movement with constant velocity, by modeling this motion using graphs. PART 1: Object moving away from the motion sensor. EXPERIMENTAL DATA (1 point): Table 1 Run # Time ( seconds ) [Initial & End] Position ( meters ) [Initial & End] Distance ( meters ) Displacement ( meters ) Speed ( meters per second ) Velocity ( meters per second ) 1a 𝑡𝑡 1 = 4.000 s 𝑡𝑡 2 = 15.000 s 𝑥𝑥 1 = 0.4645 m 𝑥𝑥 2 = 1.6267 m 1.1622 m 1.1622 m 0.1057 m/s 0.1057 m/s 1b 𝑡𝑡 1 = 3.25 s 𝑡𝑡 2 = 3.2813 s 𝑥𝑥 1 = 0.3841 m 𝑥𝑥 2 = 0.3874 m 0.0033 m 0.0033 m 0.1054 m/s 0.1054 m/s 1c 𝑡𝑡 1 = 14.7188 s 𝑡𝑡 2 = 14.75 s 𝑥𝑥 1 = 1.5965 m 𝑥𝑥 2 = 1.5999 m 0.0034 m 0.0034 m 0.1090 m/s 0.1090 m/s Table 2 Run # Slope ( meters per seconds ) Y-intercept ( meters ) 1 0.1059 m /s 0.04164 m 2 0.4185 m /s -0.3639 m /s Name of Physics quantity (i.e. position, distance, etc.) Average Velocity Initial position Table 3. Run # Average Velocity, ( meters per second ) Standard deviation ( meters per second ) 1 0.1060 m/s 0.002489 m/s 2 0.4189 m /s 0.002322 m /s

4 For run 1 and 2 calculate the percent difference between the average velocity from the slope of the x(t) graph and mean velocity from v(t) graph. Percent difference of Run #1 = |0.1059 − 0.1060| (0.1059 + 0.1060) 2 × 100 = 0.09% Percent difference of Run #2 = |0.4185 − 0.4189| (0.4185 + 0.4189) 2 × 100 = 0.10% Using equation 5, substitute in your slope and y-intercept to create an equation that describes the motion of the cart: Run 1: 𝑥𝑥 ( 𝑡𝑡 ) = 0.04164 + 0.1059t Run 2: 𝑥𝑥 ( 𝑡𝑡 ) = − 0.3639 + 0.4185 𝑡𝑡 PART 2: Object moving toward the motion sensor. EXPERIMENTAL DATA (1 point): Table 4 Run # Slope ( meters per second ) Y-intercept ( meters ) Name of Physics quantity (i.e. position, distance, speed, etc.) 3 -0.2082 m/s 2.521 m Position, Starting position from origin. 4 -0.6329 m/s 2.614. m Position, Starting position from origin. Table 5. (Use Logger Pro for statistical data to calculate avg. velocity and uncertainty) Run # Average Velocity, ( meters per second ) Standard deviation ( meters per second ) 3 -0.2081 m/s 0.002710 m/s 4 -0.6326 m/s 0.002775 m/s

5 DATA ANALYSIS ( 2 points ): For run 3 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. Percent difference of Run #3 = | − 0.2082 − ( − 0.2081)| ( − 0.2082 + ( − 0.2081)) 2 × 100 = 0.05% Percent difference of Run #4 = | − 0.6329 − ( − 0.6326)| ( − 0.6329 + ( − 0.6326)) 2 × 100 = 0.05% Using equation 5, substitute in your slope and y-intercept to create an equation that describes the motion of the cart: Run 3: 𝑥𝑥 ( 𝑡𝑡 ) = 2.521 + ( − 0.2082) 𝑡𝑡 Run 4: 𝑥𝑥 ( 𝑡𝑡 ) = 2.614 + ( − 0.6329) 𝑡𝑡 DISCUSSION AND CONCLUSION PART 1 and PART 2: (4 points) Motion is the change of an object’s position with time, thus motion has a couple quantities to describe it, such as position, time, displacement, distance, speed, velocity. We can use these variables of an object’s motion to conduct a motion graph of an object, to determine it’s position we simply locate it on the graph and measure (or mathematically deduce) how far from the origin it is. Time is an axis of this graph and tells us when that object was at a certain position. Displacement is the change in position, indicated by a vector that tells us the magnitude of change in position over what direction. While distance is just a measure of change of position with no telling of direction. Similarly, speed is the measure of an object’s change in position over time, but with no indication of direction, while velocity indicates the direction as a vector value. An object can have a constant velocity, meaning it’s changing its position in the same direction at the same rate, we expect an object with constant velocity to have a linear motion graph and have equal movement per recorded step (each interval must be equal). The major results for the 4 runs in part 1 and 2 suggest the theory of motion, position, time, displacement, velocity, speed, etc .... are all related. As we saw, many of the calculations are functions of time, such as determining the position of an object knowing its velocity and position equation or finding the velocity over time of this function (by taking the slope of this line). The position equation shows us where an object will be, while the velocity line shows how fast the object is moving in a certain direction to get to a certain position, and this velocity line is obtained from the slope of the position line! Simply having a negative velocity is movement means moving back towards our referenced origin, while a positive means it moves away (in a one-dimension).

7 PART 4: (3 points) Run 6: Show calculation (use eqn. 5) used predict the final position of the cart after 2 s or 3 s from the moment it crosses the 90 cm mark on the track. It is the choice of the student the time interval. Prediction: − 20 cm/s = Displacement 2 seconds Displacement = − 20(3) = − 40 cm Position of cart after 2 seconds = 100 cm − 40 cm = 60 cm Experimental result from the table/graph. Position of the cart: Time ( seconds ) [Initial & End] Position ( meters ) [Initial & End] 𝑡𝑡 1 = 1.2188 s 𝑡𝑡 2 = 3.2188 s 𝑥𝑥 1 = 0.9993 m 𝑥𝑥 2 = 0.5993 m Time Elapsed = 3.2188 s − 1.2188 s = 2 s Distance traveled after 2 s = 0.9993 m − 0.5993 m = 0.4 m Final Position = 0.5993 m Discussion Run 6: (3 points) The relationship between the position as a function used was the connection between average velocity and displacement (a measure of change in position) over a change in time. If this relationship didn’t exist, then we could not accurately calculate where the cart will be with constant velocity, such as we did.

8 RESULTS ( 3 points ): Table 6. PARTS 1 & 2 (Report results below with 4 significant figures) Average velocity ( meters/second ) Run # Position vs. Time graph Velocity vs. Time graph % Difference 1 0.1059 m /s 0.1060 m/s 0.09% 2 0.4185 m /s 0.4189 m /s 0.10% 3 -0.2082 m/s -0.2081 m/s 0.05% 4 -0.6329 m/s -0.6326 m/s 0.05% Table 7. PARTS 1 & 2 Equations of motion Run # Substituted Equations of Motion ( equation 5 ) 1 𝑥𝑥 ( 𝑡𝑡 ) = 0.04164 + 0.1059t 2 𝑥𝑥 ( 𝑡𝑡 ) = − 0.3639 + 0.4185 𝑡𝑡 3 x ( 𝑡𝑡 ) = 2.521 + ( − 0.2082) 𝑡𝑡 4 𝑥𝑥 ( 𝑡𝑡 ) = 2.614 + ( − 0.6329) 𝑡𝑡 Table 8. PART 4 final position of cart after t,s Predicted position: ( centimeters ) Experimental position: ( meters ) 60 cm 59.93 c m Discussion_Summary: (2 points) The objective of this lab was to analyze the motion of a cart by recording its position and velocity over time, and to validate the consistency between experimental and predicted values by using equations we have learnt over the first week. This lab provided insight into how much theoretical predications can match experimental, as my percentage differences in actual versus theoretical were low. The lab objective was achieved, as the equations acted as a great model for motion and determining, what, where, and when an object will be.