Measuring Motion



Conservation of Mechanical EnergyObjectiveThe purpose of this lab is to first determine the spring constant for a spring by hanging weights and measuring the distance (x) between the stretched length and relaxed length of a spring.In the second part of the lab, we will calculate the total mechanical energy in the system at different points by calculating the elastic potential energy and gravitational potential energy. Those results will be compared to determine if mechanical energy is conserved in an oscillating spring.BackgroundRobert Hooke determined the relationship between the displacement of a spring and the force of restoration. We use that relationship in this lab to calculate the value of k, used in our energy equations to calculate elastic potential energy. His equation F=-kx , known as Hooke’s Law, will be used in the first part of this lab to calculate the spring constant.In the second part of the lab, we take advantage of the fact that the mass will momentarily come to a rest at both the top and the bottom of the oscillation. This lets us remove kinetic energy from our equations and focus only on the gravitational potential energy and the spring potential energy.MaterialsRing Stand, clamp, ruler, meter stick, spring indicatorSet of hooked weightsSpring, rubber bandProcedurePart 1 – Determining the value of k for your springSet up your test stand as shown by your instructor. Make sure to include a sketch of the setup in your lab report.Use a rubber band or clamp to attach the ruler to the ring stand.Record the initial position on the scale. Make sure you convert your position to meters before using it for calculations.Find a mass that will stretch your spring between one and two times the length of the spring.Set up a data table with four columns and eleven rows. Label the first row Trial, Mass (kg), Stretched Length (m), Force (N). Label down the first column for trials 1 through 5.Record the value of the mass and the final position of the indicator in your table.Repeat the test choosing a different mass for each trial. (The weights can hook under each other to get additional combinations of values.)Repeat the experiment with a rubber band using the bottom five rows for the rubber band data.Part 2 – Determining whether mechanical energy is conservedCreate a second data table with three columns and eleven rows. Label the first row Trial, Highest Point (m), Lowest Point (m). Label down the first column for trials 1 through 5.Measure the distance from the table to the initial position of the spring indicator. Record this under as Initial Distance (m) near to the second data table.Find a mass that will stretch the spring to about twice its original length. Record the mass.Raise the weight until the pointer is at the zero position, the position where you measured the Initial Spring measurement.Gently release the weight to let it drop. Watch closely to identify the high and low points of the oscillation. Record the high and low points in your data table.Repeat this several more times using a different mass for each trial. Record all the data in your data table.Repeat the experiment with a rubber band using the bottom five rows for the rubber band data.AnalysisUse the data from your first table to calculate the elongation of the spring. Use the equation elongation = initial spring – stretched spring.For each trial, convert the mass use into their force equivalents.For each trial, calculate the spring constant using the equation Take the average of all trials and use this value as the spring constant. Calculate the spring constant for the rubber band as well.Use your data from the second data table to calculate the elongation of the spring at the highest and lowest point for each trial.For each trial, calculate the elastic potential energy at the highest and lowest points.Calculate the height of the mass at the highest and lowest point for each trial. Then use that height to calculate the gravitational potential energy at the high and low points of the oscillation.Find the total potential energy at the top and the bottom of each oscillation.Use the data to create a table of the total mechanical energy at the top and the bottom for each trial.QuestionsBased on your data, is mechanical energy conserved in the oscillating mass on the spring? Explain how your data supports your conclusion.Assuming that mechanical energy is conserved, calculate the speed of the weight at the midpoint of the oscillation. Make sure you show all your work.What would you do to improve this lab for next year’s students? ................
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