Rushikesh Palodkar PHY133L#05 (1) (1) (1)

Rushikesh Palodkar 10/10/22 PHY 133 L69 Saba Shalamberidze Hooke’s Law and Springs

Introduction: Using Hooke's law, we will determine the spring constant of two springs as part of the Spring Potential Energy lab. According to Hooke's law, which is a restoring force, the force required to extend or compress a spring is inversely correlated with how much the spring is stretched or compressed. Fs = − k Δx is the equation that expresses Hooke's law. U = (1/2) k (Δx) 2 . will be used to calculate the potential energy of the two springs as well. The spring constant, a spring attribute that effectively gauges the stiffness of the spring, is represented by the symbol k in the two equations for two variables. In this experiment, we'll figure out the smaller spring's potential energy and see if the energy is preserved following a collision. I believe that the energy will be preserved following the collision. Procedure: Part One: Finding the Mass of the iOlab Device: 1. Obtain the iOlab device and turn it on and plug it into your computer. 2. Attach the screw to the end of the device and turn the device so that the y-axis is pointing downwards. 3. Press the record, and then use the screw to lift the device, hold it steady for a few seconds, and then place it down again. 4. Use the data obtained to find the F g and g. 5. Use the equation F g = mg to find the mass of the device. Part Two: 1. Attach the screw to the iOlab device, and attach the screw to the force meter and the long spring to the screw 2. Allow the gadget to restore to equilibrium by extending the spring from the equilibrium. The spring should then be compressed while you observe its motion. 3. On a horizontal table, while holding onto the end of the spring, press record and roll the cart back and forth. Be careful not to compress the spring all the way. 4. Using the parametric plot option, find the spring constant. 5. Repeat this for a total of 3 trials. 6. Use the data obtained to calculate the mean μ and sigma of the spring Part Three: 1. Push the device into the fixed object. 2. Find the velocity before, the velocity after and the peak force. 3. Find the change in position. 4. Calculate the spring potential energy by multiplying the position change by the spring constant from section two. 5. Using the velocity before and the velocity after, find the kinetic energy of the device.

Figure 4: This is the first graph to be used to determine the long spring's spring constant. Using the analytic technique to determine the of the first experiment, the points (0.02, -1.0) and (0.12, -2.0) were acquired. Figure 5:This is graph number two for calculating the long spring's spring constant. Using the analytic method to determine the of the second experiment, the points (0.00, -0.90) and (0.08, -1.80) were acquired. Figure 6: This is graph number three for calculating the long spring's spring constant. Utilizing the analytic method to determine the of the third experiment, the points (0.02, -1.10) and (0.08, -1.50) were acquired.

For Short Spring: Figure 7: This is the first graph to be used to determine the short spring's spring constant. Using the analytic method to determine the of the first trial, the points (-0.01, 1.5) and (-0.015, 2.50) were acquired. Figure 8: This is the graph for part three of the procedure. This graph represents the velocity after. Figure 9: The third step of the procedure's graph is shown here. This graph shows the previous velocity.

(0.578 N) = -(-200) (Δ x ) Δ x = 0.00289 U = (1/2) k (Δ x ) 2 = (1⁄2) (-200) (0.00289 ) 2 = -0.000835 J Error Analysis: Mass: percent error of acceleration + percent error of force = percent error of mass 0.20 % error + 1.83 % error = 2.03 % error Velocity(before) = 9.80 % error = Kinetic Energy before Velocity(after) = 6.45 % error = Kinetic Energy after Discussion: In this lab, Hooke's law, which states that F s = − kΔx , K E = (1⁄2)m v 2 and U = (1/2)k(Δx) 2 , were evaluated. We computed the average for the long and short springs using these formulas, and we then calculated the kinetic energy prior to and following the contact. Since the spring force may be directed in many directions, we were able to compute the for both springs using the slope from the position vs. force plots. For both springs, the slope was negative. There was a resorting force, as evidenced by the object's location and the springs' equilibrium position. Using Hooke's law, we were also able to determine the spring's maximum potential energy. This lab's objectives were to ascertain the smaller spring's potential energy and demonstrate how energy is preserved following a collision. All of the figures made sense when compared to the kinetic energy prior to the impact, the spring potential energy, and the kinetic energy following the contact. After conducting the collision, the KE before did not equal the KE after instead, it was less than after the collision which indicates that energy wasn’t conserved. An explanation for these numbers not being the same could be that some of the energy must have been put into the surroundings or some of it may have converted to another form of energy. In addition to this, the error analysis of this lab was calculated using the graphs on which the error is given. The percent error for both the mass, the velocities, and Kinetic energy before and after was under ten percent indicating that the data collected in this lab is acceptable. The KE before did not equal the KE after after the collision was conducted; instead, it was less than after the collision, indicating that energy was not conserved. These numbers not being equal can be explained by the fact that part of the energy must have been dispersed into the environment or transformed to another kind of energy. Additionally, this lab's error analysis was calculated utilizing the graphs that show the mistake. The data gathered in this lab is acceptable since the percent error for the mass, velocities, and kinetic energy before and after was less than ten percent. Conclusion: This lab, Hooke’s Law and Spring Potential Energy, is a great way to study the relationships between F s = − k Δ x , K E = (1⁄2)m v 2 and U = (1/2) k (Δ x ) 2 . The fact that the lab's results didn't precisely match what was anticipated was primarily due to human error. The inaccuracy was due to the fact that the kinetic energy before and after was not equal. Employing a superior spring in the future may be avoided. When doing step two of the

technique, the smaller spring seemed to be somewhat twisted. Overall, this lab did a fantastic job of demonstrating Hooke's Law, which states that the force required to expand or compress a spring is proportionate to the amount of stretch or compression the spring experiences.