phy 133 lab 5

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Anubrota Majumdar 4/30/2023 PHY 133 Hooke’s Law and Spring Lab Report

INTRODUCTION: - For the Spring Potential Energy lab, we will be using Hooke's law to determine the spring constant of two springs. Hooke's law is a restoring force that describes the relationship between the force required to compress or stretch a spring and the amount of deformation. The equation for Hooke's law is Fs = - kΔx, where Fs represents the force needed, k represents the spring constant, and Δx represents the displacement of the spring. We will also be using the equation U = (1/2)k(Δx)^2 to calculate the potential energy of the springs. This formula incorporates the spring constant, which measures the spring's stiffness, and the amount of deformation. Our experiment involves measuring the potential energy of a smaller spring and verifying whether the energy is conserved following a collision, I believe that energy will indeed be conserved. In summary, our lab will involve using Hooke's law to calculate the spring constant of two springs and measuring their potential energy. We will also be observing the conservation of energy following a collision. FORMULAS USED: - The first formula we used was Fs = − kΔx, which expresses Hooke's law. Here, Fs represents the restoring force exerted by the spring, k is the spring constant, and Δx is the displacement of the spring from its equilibrium position. By measuring the displacement of the spring and the restoring force exerted by it, we can calculate the spring constant. The second formula we used was U = (1/2)k(Δx)2, which calculates the potential energy stored in a spring. Here, U represents the potential energy, k is the spring constant, and Δx is the displacement of the spring from its equilibrium position. By measuring the displacement of the spring and the spring constant, we can calculate the potential energy stored in the spring.

Overall, these formulas are crucial to understanding the behavior of springs and how they store and release energy. By using these formulas in the Spring Potential Energy lab, we were able to accurately measure the spring constant and potential energy of the springs, providing valuable insight into their behavior. APPARATUS USED: -  iOlab device  Screw  Force meter  Long spring.  Cart  Fixed object  Horizontal table  Computer PROCEDURE: -  Finding the Mass of the IoLab 1. Turn on and connect the iOlab device to your computer and attach the screw to the end of the device with the y-axis pointing downwards.

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2. Record the device's motion as you lift it using the screw, hold it steady, and then place it down again. 3. Calculate the gravitational force (Fg) and the acceleration due to gravity (g) using the recorded data. 4. Use the equation Fg= mg to determine the mass of the device.  Attaching and further procedure 1. Attach the screw to the force meter and long spring and extend the spring from equilibrium to observe its motion as it returns to equilibrium. 2. Record the motion of the spring as you roll the cart back and forth on a horizontal surface, being careful not to compress the spring fully. 3. Use the parametric plot option to calculate the spring constant and repeat this step for a total of 3 trials. 4. Determine the mean (μ) and standard deviation (sigma) of the spring constant using the collected data.  Push and Calculation 1. Push the device into a fixed object and record its motion, including the velocity before and after the collision, as well as the peak force and the change in position. 2. Use the spring constant from Part Two to calculate the spring potential energy by multiplying the change in position by the spring constant. 3. Determine the kinetic energy of the device using the velocity before and after the collision. 4. Compare the potential and kinetic energy values to assess if energy is conserved.

OBSERVATIONS:- The above graph shows the mass of the IOLAB

 Now the graphs for the Long Spring: - The first graph of the first experiment helps us determine the points (0.0258, -1.025) and (0.145, -2.125),

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The second graph of the first experiment helps us determine the points (0.01, -0.868) and (0.0678, -1.658), The third graph of the first experiment helps us determine the points (0.0236, -1.105) and (0.08, -1.581)  Now the graphs for the Short Spring: - The first graph of the second experiment helps us determine the points (0.01, 1.546) and (- 0.0142, 2.586),  Now trying the third part of the experiment, we find this graph-

Calculations: - Velocity before the third experiment = -0.234 Velocity after third experiment = 0.145 Peak Force(N) after third experiment = 0.578  Calculation of Mass: Using the formula Fg = mg Fg is -2.1 N and g is -9.862 m/s^2, the mass (m) of the device is = 0.213 kg.  Finding μ for the Long Spring: Experiment 1: m = (-2.125 – (-1.025)) / (0.145 - 0.0258) = -12.78 Experiment 2: m = (-1.658 – ((-0.868)) / (0.0678 - 0.01) = -13.68 Experiment 2: m = (-1.581 – ((-1.105)) / (0.08 - 0.0236) = -8.453  Avg µ (long spring) = (12.78+13.68+8.453)/3 = 11.63  Error of mean = 1.61 Finding µ for the Short Spring: = (2.586-1.546)/ (-0.0142-(-0.01)) = 247.61 Now, change in position, 0.578 = (247.61) ( Δx) = 2.33 * 10^-3 U = (1/2)k (( Δx)^2 = 6.72 * 10^-4 N

DISCUSSION: - In this laboratory experiment, we investigated the concept of Hooke's law, which relates the force exerted by a spring to its displacement. We also explored the concepts of kinetic energy and potential energy associated with springs. We performed experiments with long and short springs and determined their spring constants using the formula F s = − kΔx, where Δx is the displacement of the spring from its equilibrium position. We found that the slopes of the position vs. force plots were negative for both springs, indicating a restoring force towards the equilibrium position. Using the formulas for kinetic energy, K E = (1⁄2)m v2, and potential energy, U = (1/2)k(Δx)2, we calculated the kinetic energy of the system before and after contact. We observed that the kinetic energy of the system after the collision was less than the kinetic energy before the collision, suggesting that energy was not conserved during the collision. This could be attributed to energy being lost to the environment or being converted into other forms of energy. To ensure the accuracy of our data, we performed error analysis. We calculated the percent error for the mass, velocities, and kinetic energy before and after the collision using the graphs that show the errors. We found that the percentage error was less than ten percent, indicating that our data was acceptable and reliable. Overall, this laboratory experiment helped us understand the fundamental concepts of springs and their associated energies. We learned how to calculate the spring constant using Hooke's law, and how to determine the potential and kinetic energy of the system before and after a collision. By performing error analysis, we were able to ensure the accuracy and reliability of our data. This knowledge can be applied to real-life situations involving springs and collisions, making this experiment a valuable learning experience.

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CONCLUSION: - The laboratory exercise on Hooke's Law and Spring Potential Energy was an effective way of investigating the relationships between F s = − kΔx, K E = (1⁄2)m v2 and U = (1/2)k(Δx)2. The slight discrepancies in the outcomes were primarily attributed to human error, particularly in the kinetic energy measurements before and after the experiment. To prevent similar inaccuracies in the future, it might be helpful to use a higher-quality spring. During step two of the procedure, there appeared to be a slight deformity in the smaller spring. In general, the laboratory work effectively demonstrated Hooke's Law, which postulates that the force needed to extend or compress a spring is directly proportional to the extent of deformation it undergoes.

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