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Lab 3-Conservation of Mechanical Energy

# Lab 3-Conservation of Mechanical Energy - Conservation of...

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Conservation of Mechanical Energy Experiment #3 May 1, 2007 Section 3 Lab Station 7 Introduction:

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0 1 ( ) 2 PE k x x = - The objective of this lab was to calculate the conservation of mechanical energy by utilizing our knowledge of springs and frictionless surfaces. By using a glider connected by two springs on either side, we are able to calculate the spring constant by measuring the total displacement that the system experiences while masses are hung off the end of it. This, in turn, allows us to see how much potential and kinetic energy is present while the system oscillates back and forth on the air track. After calculating the potential and kinetic energy, we are able to find the total energy of the system and conclude whether or not energy was conserved. Equations: F = ( F Mg k x x = - - 0 ( ) Mg k x x = - Potential Energy: Kinetic Energy: Total Energy = PE + KE Procedure: The first step of this experiment is to calculate the spring constant of the system. This is achieved by measuring the initial distance along the air track which will serve as the equilibrium point of the system. One must ensure that the air track is completely level during this process or else the spring constant will not be consistent for the rest of the experiment. After finding the equilibrium constant, a mass hung off of the table by a string which is connected to one of the notches on the comb which rests above the glider. This will move the glider over and allows us to measure the displacement for this particular weight by using the formula: M = mass of weight m = mass of glider g = acceleration of gravity k = spring constant x = displacement from equilibrium position x 0 = equilibrium position (x-x 0 ) = displacement v = velocity Glider Air track Glider Air track Position of photogate x = 0 0 5 10 15 20 M 1 2 glider KE mv =
0 ( ) Mg k x x = - After determining the spring constant, k , we then pull the glider past the photogate and release it. As the glider oscillates back and forth, the photogate registers the time between each notch of the comb. From this data we are able to calculate the velocity and energy of the system. We repeat this procedure with the mass on the string attached to the 5 th , 10 th , and 15 th notches. From these runs we were able to choose the one that most closely resembled the sample graph. Data: After doing three trial runs, we decided to use the data we received when the mass was attached to the 20 th tooth. Our other trials were not accurate enough so the remainder of our calculations will be done with this trial in hopes of receiving the most ideal results. Conservation of energy in a mass/spring system y = -0.0064x + 0.0213 R 2 = 0.6158 0 0.005 0.01 0.015 0.02 0.025 0 0.05 0.1 0.15 0.2 distance(meters) Energy(joules) PE(J) KE(J) Total E (J) Linear (Total E (J)) x-xeq (m) vel(m/sec) distance(m) PE(J) KE(J) Total E (J) 0.078 0.150943 0.002 0.018491702 0.002572 0.021064 0.074 0.19802 0.006 0.016643748 0.004427 0.021071 0.07 0.245399 0.01 0.014893054 0.006799

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Lab 3-Conservation of Mechanical Energy - Conservation of...

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