Conservation of Mechanical Energy

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Conservation of Mechanical Energy Department of Physics, Case Western Reserve University Cleveland, OH 44016-7079 Abstract: In this lab, I have tested the laws of conservation of Mechanical Energy in two ways. Starting with the gravitational potential energy, I am able to calculate using a cart on a track being pulled across by a hanging weight. Using Logger Pro to collect data we were able to figure out the slope of the energy change per meter (∆E/∆y) is -46.91878 ± .42565 mJ/m. This was calculated by using the potential energy, and kinetic energy. We concluded that although our results were not zero as we had hoped, our experiment was still accurate with some random error that let to our calculated slope. The second part tested the spring potential energy using a spring with a hanging mass. With this we calculated the value of ε (the relative energy change) to be -.026 J ± .042. These measurements were calculated using the net change of the total energy divided by the change of gravitational energy. In this part we concluded that if all of the gravitational potential energy transferred to the stretched spring potential energy is conserved. By having a value close to zero, it proves that the energy is conserved. Over all this experimental calculations of the energy change per meter and the relative energy change proves that mechanical energy is conserved. Gravitational Potential Introduction and Theory: The gravitational energy theory states that the energy stored in an object as a result of its position and the gravitational pull of the earth. In our experiment we are going to assume that gravity equals 9.81 m/s2 although it is only an estimate. We will use the formula: Wnc= ∆K+∆U (1) where ∆K is the change in kinetic energy, ∆U is the change in gravitational potential energy and Wnc is the work. By combining the equations for kinetic energy and

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