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Lab 08 Prelab Assignment1. A Hooke’s Law spring of constant k=5 N/m hangs vertically from a rod, and a mass of 200 g is hung from it. How fardoes the spring have to stretch to reach equilibrium?5N/m200g original equilibriumdnew equilibrium200g2. Consider a Hooke’s Law spring with constant k hanging vertically from a rod. A mass of m is hung from the spring,stretching the spring to a new equilibrium position, like in question 1. Next the spring is stretched or compressed by anamount x relative to the new equilibrium position and released:d dm x mthe mass will accelerate upwardright after being released Draw force diagrams for the hanging mass in both cases. Use N2 to write down a relationship between the weight and thespring force in case 1, then show that the net force is given by F kx net = when we release the mass in case 2. This factmeans that our hanging spring/mass system behaves exactly like a sideways spring/mass system if we measurestretch/compression relative to the equilibrium obtained by hanging the mass.Lab 08: Hooke’s Law SpringsIn this course, we assume that all spring are “ideal”, meaning that they follow Hooke’s Law: the force required to stretchthe spring is proportional to the stretch distance (in other words, it takes twice as much force to stretch the spring twice asfar). Stating Hooke’s law in terms of magnitude:Hooke’s Law: F kx =In this formula, k (the spring constant) is a measure of the stiffness of the spring, while x is the displacement from the naturallength of the spring.Spring potential energy is the energy stored in a spring that is compressed or stretched (for example, the spring guns for theprojectile motion lab were storing spring potential energy before you pulled the trigger). Spring potential energy iscomputed by the formula:Spring potential energy: 1 2s 2PE kx =1. Measuring the spring constant:We showed in the prelab that a vertical spring/mass system has the exact same physics as a horizontal system, providedwe take the equilibrium length to be the length with the mass already attached. It can be difficult to accept, but once weproved that F kx net = , there is no need to think about gravity for the rest of the lab!First, we need to find the spring constant, k, for this spring. We will use a force sensor mounted on a rod to measure theforce exerted by the spring as it stretches through a large range of values. Directions will be given in class to help youcalibrate the force sensor and set the motion sensor to record “toward” as the positive direction. The initial position andforce should also be set to zero by “zeroing” the sensors before taking any data.IMPORTANT NOTE: keep in mind that the position sensors can’t see anything closer than about 15 cm.Hooke’s Law spring force sensor aluminum massposition sensortable topRemember, we can ignore gravity because this system is completely equivalent to a horizontal spring/mass system withthe shown equilibrium position. When you exert a force downward on the mass, we ignore gravity and say that the forceexerted by the force sensor is equal to your applied force, provided the mass is moved slowly.Take data on the applied force and position as you slowly move the mass above and below equilibrium by about 20-25cm. Use Logger Pro to display the data on a Force vs. Position graph. Display the best-fit line on this graph and use it tofind the spring constant. Print and attach the graph.k = ________________2. Potential energy and the work done on the spring:a. Using the spring constant measured in part 1, compute the potential energy stored in the spring at x=20cm.Make your work clear.PEspring = __________ Jb. Take force and position data as you slowly push the mass down by 20cm, being careful to never reversedirections (reversing directions confuses LoggerPro’s integration tool). Make a plot of Force vs. Position. Nowhighlight the interval from x=0 to x=20 cm, and use Logger Pro’s integral tool to compute the area under thecurve. The area gives you the total work you did while stretching the spring. Make sure to print and attach yourgraphs.Won the spring = __________ JSince the work done on the spring should equal the change in potential energy for the spring, these two quantitiesshould be equal. Compute a percent error to compare them.% error = _____________ %

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