PHYS 261 Lab Report 2

Lab Report 2 C. LeBlanc 12/19/23 Lab Report 2 Physics 261-001 Author: Corinne LeBlanc Lab Partners: Makenzie Davis, Anna Flowers Date: 12/12/23

Lab Report 2 C. LeBlanc 12/19/23 Objective: The objective of this experiment is to explore how components like position, velocity, and acceleration are related. These relationships are studied by observing a moving cart on track that is level as well as a track that is inclined. To analyze these, Logger Pro will be used to make graphs of each component. Theory: Kinematics involves multiple variables, including position, velocity, and acceleration. Each of these can be measured using sensors and then analyzed using the Logger Pro software. Each of these variables also has equations to relate its components. The equation for velocity is below. Delta X in this equation represents change in position and time changes. vt =  t/  x Eq. 2-2 In order to explain when the velocity is not constant, acceleration is used and us solved using the equation below, where a is acceleration and t represents the time. a(t) =  v/  t Eq. 2-2 From these equations and definitions of acceleration and velocity, we can now understand that velocity is a slope based on position and acceleration is in turn the slope of velocity. However, when acceleration is zero it means that the velocity is constant and different equations must be used, which are shown below where the position has a linear relationship with time. v(t)= v 0 Eq. 2-3a x(t) = v 0 t + x 0 Eq. 2-3b Furthermore, when the acceleration is a non-zero constant, different equations must be used yet again to explain the change in relationship between velocity and acceleration. These equations are shown below where the position is quadratic with time. v(t) = at +v 0 Eq. 2-4a x(t) = 1/2at 2 +v 0 t + x 0 Eq. 2-4b The last special case with acceleration and velocity occurs when the motion is taking place on an inclined plane. This case also uses its own equation, shown below. a=gsin  Eq. 2-5 Procedure: To begin, the Go-Direct Sensor Cart was turned on to initiate data collection. The Vernier Graphical Analysis program was opened on the laptop and the cart was connected wirelessly. Once this was done, 3 Graphs was selected to show a position vs. time graph, velocity vs. time graph, and an acceleration vs. time graph. For the first run, we began collected data and then moved the cart back and forth while studying the curves caused by the movement

Lab Report 2 C. LeBlanc 12/19/23 For procedure C, the cart was released from rest from the top of an incline. The results are shown in figure 3. Figure 3. Motion of the cart when released from rest from the top of an incline. For the final procedure of the lab, the cart was pushed up the same incline used in procedure C before it reached the top and moved backward down the track. The results of this trial are shown in figure 4. Figure 4. Motion of the cart as it was pushed up and incline and rolled back down. Analysis: A table comparing the slopes to the average values was created and is shown below.

Lab Report 2 C. LeBlanc 12/19/23 Quantity Measured Value Uncertainty % Difference of Slope vs. Average Velocity Slope of x-curve 1.111 NA NA Average of v- curve 1.111 0.013 0 Acceleration Slope of v-curve - 0.09326 NA NA Average of a- curve -0.088 0.0101 5.80 Table 1. Comparison between the acceleration and velocity of the cart in procedure B. To further compare the acceleration and velocity values and averages, Logger Pro was used to find the slope of the position graph as well as the average and standard deviation of the velocity graph. Similarly, for procedure C and D, two duplicate tables were created to compare the acceleration that was measured in both. Tables 2 and three are shown below. Quantity Measured Value Uncertainty Acceleration from measurements Coefficient of x-curve fit 0.3912 NA 0.7824 Slope of v-curve 0.7831 NA 0.7831 Average of a-curve 0.762 0.026 0.762 Average acceleration 0.7758 Table 2. Data showing the acceleration of the cart and the uncertainty from procedure C. Quantity Measured Value Uncertainty Acceleration from Measurements Coefficient of x-curve -0.4081 NA -0.8162 Slope of v-curve -0.816 NA -0.816 Average of a-curve -0.797 0.043 -0.797 Average acceleration from measurements -0.8097 Table 3. Data showing the acceleration of the cart and the uncertainty from procedure D. Conclusions: From this lab and the data that was collected, it clearly shows how position, velocity, and acceleration are all related and have an effect on each other. All of the graphs that were produced from the data supported the equations that we used and adhered to throughout the lab. In procedures C and D, it was possible to determine the slope of the track since acceleration due to mass and gravity are inherently related to all of the components of motion that were involved. Also, the velocity in procedures C and D reached zero when the cart slowed to a stop at the bottom of the track and at the top before rolling backward. The uncertainties that were calculated from the data were very low and consistent with the data being reliable. Possible sources of error in this experiment include the track not being level and calculations being incorrect or inaccurate.