LAB 06 Momentum and Energy

10/25/2023 PHY 121 L69 TA: Chamathka Wijewardhana Momentum and Energy Conservation

Introduction: An object possesses momentum when it combines mass and velocity, meaning any moving object carries momentum. To maintain the conservation of momentum, it's crucial to ensure that no external forces interfere with the system. In this experiment, we will explore the behavior of the iOLab device concerning its position along the x-axis and velocity along the y-axis. As we observe the device's motion influenced by the spring force, both position and velocity oscillate. When we plot these variables against each other, we generate a phase space in the form of a circle. This lab encompasses two types of energy: kinetic and spring potential energy. Therefore, the overall energy is represented as E=1/2mv^2+1/2kx^2. During the second part of the experiment, when the iOLab device collides with a solid object and bounces off, the Force vs. Time plot will show distinct force impulses during the collision. It is expected that the area under this plot will represent the impulse applied to the device during the collision. Furthermore, we expect that the change in velocity during the same time period, when multiplied by mass, will provide a value comparable to the area under the Force vs. Time plot. This comparison will help us understand the relationship between impulse and change in momentum during a collision. Method/Procedure: Part I: 1. Plug in the iOLab device dongle into your computer and turn on the device. 2. Calibrate the iOLab device. 3. Attach the force screw to the force sensor of the iOLab device. 4. Attach the long spring to the force screw. 5. Turn on the wheel sensor on the iOLab device. 6. Find a table and tilt it so that it is in a vertical position. 7. Place the iOLab on the top edge of the table with the wheels facing the table. 8. Pull the device down and allow the device to oscillate. 9. Parametrically plot the Velocity vs. Position data. Find the Mass of the iOLab Device: 1. Plug in the iOLab dongle into the computer and turn of the iOLab device. 2. Recalibrate the iOLab device. 3. Attach the screw to the bottom side of the iOLab device. 4. Place the device down so that the y-axis is pointing downwards.

Impulse (Ns) Initial Velocity V i (m/s) Final Velocity V f (m/s) Initial Momentum (kgm/s) Final Momentum (kgm/s) Change in Momentum (∆p) 0.097 -0.215 ± 0.120 0.177 ± 0.039 - 0.044 ±0.030 0.036 ±0.012 0.08 ±0.042 Calculations: Figure 5. The region before the peak is highlighted in Part II of the experiment. Figure 4. The peak is highlighted from part II of the experiment. Figure 7. Data table of Figures 4,5, and 6 graphs. Figure 6. The region after the peak is highlighted in Part II of the experiment.

F g = mg m = − 2.002 ± 0.042 − 9.803 ± 0.029  0.042 − 2.002 × 100 =− 2.098% 0.029 − 9.803 × 100 =− 0.296% m = − 2.002 ± 2.098% − 9.803 ± 0.296%  2.098 + 0.296 100 = 0.024 m = 0.204 ± 0.024 kg p i = mV i  ( 0.204 ± 0.024 ) × ( − 0.215 ± 0.120 )  0.024 0.204 × 100 = 11.76 0.120 0.215 × 100 = 55.81  55.81 + 11.76 = 67.57%  0.6757 × 0.044 = ¿ 0.030 p i = − 0.044 ± 0.030 p f = mV f  ( 0.204 ± 0.024 ) × ( 0.177 ± 0.039 )  0.024 0.204 × 100 = 11.76 0.039 0.177 × 100 = 22.03  22.03 + 11.76 = 33.79%  0.3379 × 0.036 = 0.012 p f = 0.036 ± 0.012 f − ¿ p i ∆ p = p ¿  (0.036 ± 0.012) – ( − 0.044 ± 0.030 ¿ = 0.080 ± 0.042 Percent Error = Expected − Actual Actual × 100  | 0.080 − 0.097 0.097 | × 100 = 17.53% Discussion/Conclusion In our lab experiment, the inward spiral observed in the conservation of energy plot indicates that energy is not conserved. This inward spiral suggests that the total energy of the system does not remain constant. A conserved energy system would display a constant radius in the phase space plot, forming a closed curve. However, in our case, the inward spiral signifies that energy is being lost from the system over time.

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