Online Lab #9 - Springs

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Dec 6, 2023

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PHY111, 161 ON-LINE LAB, Springs Lab #9 and 10 (counts as two) NAME: Lana Manzanares Working with Springs NAU User ID: lbm85 Download and save this document to your computer. Answer the questions directly on this document. When you are done, SAVE the file and return it to your TA via BB Learn. Please contact your TA with any questions or other issues. Introduction: Hooke's law states that the force (F) which is required to stretch or compress a spring by a given distance (x) , increases or decreases linearly with respect to that distance. F Spring = -kx where k is a constant which is characteristic of the spring, and x is the distance stretched and which is relatively small compared to any possible deformation of the spring might suffer. Hooke’s Law is named after 17th-century British physicist Robert Hooke. Task #1 Go to the PhET simulation at: https://phet.colorado.edu/en/simulation/hookes-law Click on the Intro Icon Take some time to familiarize yourself with how the controls work and the variables that you can change. 1

PHY111, 161 ON-LINE LAB, Springs Procedure: Check all the boxes in the gray box to the upper right. 1. Try a variety of applied forces to pull the spring. What do you notice about the resulting spring force ? In your own words explain why this result makes sense. The spring force is always equal to the applied force in the opposite direction. This makes sense as according to Hooke’s law, the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position. 2. Set the applied force to +50 N. Now change the spring constant , trying out several different values. What happens to the applied force ? What happens to the spring force ? Explain why this result makes sense. The applied force and spring force are still equal to each other due to the fact that the force is in equilibrium. 3. Now, watch what happens to the displacement vector as you change the spring constant . Using Hooke’s Law explain the results. When we change the spring constant, the displacement vector of the spring changes. Changing the spring constant affects the force required to stretch or compress the spring and the displacement of the spring for a given applied force. A larger spring constant means a larger force is required to stretch or compress the spring, and a smaller displacement of the spring for a given applied force. 4. Now click on the icon with two springs. This will allow you to compare and contrast two springs with different spring constants and/or applied forces . Set both systems so that they are identical. With the same applied force and the same spring constants, like the image below. (you may choose different values) 2

PHY111, 161 ON-LINE LAB, Springs The first, or top spring system, will act as your standard and you’ll make changes to the bottom system. Make only one change at a time. Make comparisons (like: “it doubles”, “it triples”, “it stays constant”, etc.) and record your data in the table below. CHANGES YOU MAKE Effect on the displacement vector Double the original spring constant displacement vector is half of the original spring displacement vector Triple the original spring constant displacement vector is about a third of the original spring displacement vector Half the original spring constant displacement vector is slightly more than double the original spring displacement vector Double the original applied force displacement vector is almost double the original spring displacement vector Triple the original applied force displacement vector is almost triple the original spring displacement vector Half the original applied force displacement vector is half the original spring displacement vector 5. How would you scientifically define, in words, the relationship between the spring force , the displacement , and the spring constant ? The force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position and the spring constant. As the displacement of the spring increases, the force exerted by the spring also increases, and this increase is proportional to the spring constant. 3

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PHY111, 161 ON-LINE LAB, Springs This is the exact process that Robert Hooke followed in establishing the law that bears his name. He tested many different springs of varying strengths (spring constants), and applied multiple forces to each. He then carefully recorded the displacement in each case, and the simple relationship of F Spring = -kx , emerged from the data. Task #2 Now we are going to put some of what we have learned about Hooke’s law to use. Go to the PhET simulation at: https://phet.colorado.edu/en/simulation/masses-and-springs Click on the Intro Icon Take some time to familiarize yourself with how the controls work and the variables that you can change. One important thing to notice is that when you place a weight on a spring, you can stop the system from oscillating by clicking on the stop sign icon. Place the 250g mass on spring #1. Press the stop button to stop the oscillation. Check the Natural Length and Equilibrium Position boxes. Place the smallest unknown mass on spring #2. Press the stop button to stop the oscillation. (Do not change the spring constants, be sure they remain the same for both springs). Bring out the ruler and use it to measure the displacement distance of the 250g mass and the unknown mass, then do the same for the medium and the large mass. Record your measurements in the table below. HANGING MASS DISPLACEMENT 250 g 41cm Small ? 12cm Medium ? 25cm Large ? 33cm Now using Hooke’s law and a tiny bit of algebra, you can easily calculate the masses of the three unknown weights. Put your calculated masses in the table below. HANGING MASS Calculated Mass (in grams) Small ? 73g Medium ? 152.2g Large ? 200.9g 4

PHY111, 161 ON-LINE LAB, Springs 6. If you were to use one of the other masses, the 100 g or the 50 g mass, would you get the same results? Explain. Yes, if we used 100g or 50g mass, results would have been the same as k depends on the property of the spring and not the mass used. The displacements would be different in this scenario. Task #3 Our final task with springs is going to involve energy. Specifically, you will be analyzing how energy is conserved in an oscillating spring system but also how different types of energy are changing over time. In the same PhET simulation click on the ENERGY Icon at the bottom of the page. As before, take some time to familiarize yourself with how the controls work and the variables that you can change. Once you are ready, take a close look at the left-hand side of the screen. There are five types of energy represented. 7. Kinetic Energy ( KE ); Gravitational Potential Energy ( PE grav ); Elastic Potential Energy ( PE elas ); Thermal Energy ( E therm ); Total Energy ( E total ). You probably understand intuitively what each of these types of energy represent, but take a moment and look up a scientific definition for each and record those definitions here: Kinetic energy: a form of energy that an object or a particle has by reason if its motion Gravitational Potential Energy: energy an object possesses due to its position in a gravitational field Elastic Potential Energy: energy stored as a result of applying a force to deform an elastic object Thermal Energy: the energy contained within a system that is responsible for its temperature Total Energy: the sum of kinetic and gravitational potential energy 5

PHY111, 161 ON-LINE LAB, Springs Before running the simulation, in the gray box to the upper right, change the gravity to “Jupiter”. This will make the changes in the types of energy more apparent. Now hang the 100g mass on the spring and pull it all the way down to the zero-height line. Observe what happens to each of the types of energy over time. 8. Take a moment and write down a few initial impressions. Does the spring keep oscillating, or does it eventually stop? What happens to the Total Energy of the system over time? The spring eventually stops. The total energy stays the same, but the factors within the total energy such as gravitational potential energy, elastic potential energy, kinetic energy, and thermal energy will change while the spring is oscillating until it stops. You may want to run it several times. You can slow the time down by clicking on the “slow” button. 9. Now run the simulation again. But this time focus only on Kinetic Energy ( KE ). How does it change over time? How does it change in relation to the position of the mass in its oscillation cycle? Any other observations? The kinetic energy decreases over time. The kinetic energy reaches its maximum when the weight is initially put on the spring causing it to oscillate. The kinetic energy reaches zero as the spring is stretched to its maximum distance, but will gain kinetic energy as the spring bounces back up again. As the spring continues to oscillate before reaching a complete stop, the kinetic energy decreases until it reaches a complete stop in which the kinetic energy is zero. 10. Answer the same questions for Gravitational Potential Energy ( PE grav ) The gravitational potential energy never reaches zero as the spring continues to oscillate over time. The maximum gravitational potential energy is when the mass is first added to the spring. The gravitational potential energy will decrease slowly, but will never reach zero. 11. Answer the same questions for Elastic Potential Energy ( PE elas ) The elastic potential energy reaches its maximum when the spring is stretched to its maximum. Again, the elastic potential will decrease over time but never reach zero. 12. Answer the same questions for Thermal Energy ( E therm ) The thermal energy slowly increases over time as the spring comes to a stop. This is the only time that the thermal energy will change as it does not change when the spring is changing directions. 13. Answer the same questions for Total Energy ( E total ) The total energy stays the same throughout the entire oscillation cycle. What contributes to the total energy will change throughout the experiment. 6

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PHY111, 161 ON-LINE LAB, Springs 14. Now let’s put it all together. Explain briefly and in your own words, how an oscillating mass and spring system displays the principle of conservation of energy, even though it eventually slows down and comes to a stop. The oscillating mass and spring system displays the principle of conservation of energy by converting energy back and forth between potential and kinetic energy throughout its motion. The total mechanical energy of the system remains constants, even though the system eventually slows down and comes to a stop due to damping. Save this document and return it to your TA via BB Learn. 7

Online Lab #9 - Springs

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