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# Download Math 193-0667

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Calculus II The Spring Project Conservation of Energy Law: The sum of all the energies in a system is constant, which in the case of a mechanical system amounts to the work-energy relationship: The work done on an object is equal to the change in its kinetic energy. System: A glider is moving on its track, attached to a spring. Objective: To empirically check the conservation of energy law, by computing the kinetic energy + potential energy of the system at different positions as the spring is moving the glider along its track. The kinetic energy + potential energy must be constant (we will assume there is no friction). You must work in groups of two for this project. Each group must turn in two separate results for parts 1, 2, 3 and the evaluation. Part 4 must be done jointly. pole photogate Spring low friction car paper start track table clamp Timer 1. Determine the spring’s constant k in N/m By Hooke’s law F ( x) kx ; stretch the spring by attaching weights of mass 10gr, 20gr, 30 gr, 40 gr,…150gr and get 15 measurements of the displacement. Remember that g = 9.80 m/sec2 in your calculations. 2. Attach the glider to the spring and setup a photogate to measure the velocity of the glider at different positions along its track motion. Measure the velocity at 5 different locations, 5 times for each location. 3. For each of the five locations you have chosen, 1 2 mv 2 b) calculate the change in the potential energy of the spring : W = work done in stretching the spring to that location from the equilibrium point in two ways: a) analytically, by computing the definite integral Fdx using your estimate for k. b) a) calculate the kinetic energy of the glider: K empirically, by measuring the force an the distance directly. 4. Work with a partner and make a table for the sum of the total energy of the system at 10 different locations. Is the total energy of the system constant? Note: a) When you take your measurements, please remember to measure the equilibrium length of the spring when it is horizontal. b) Please keep your units consistent in the SI system (pg. 496 of the text) so that mass is measured in kg, work is measured in joules (J) etc. In about 30-50 words, please evaluate yourself, your partner and this project. (Each student must complete his/her own evaluation) Did you work well together? Did you learn a lot from the project? How long did it take you? Were you able to complete the work on your own? Where did you go for help? Etc.