Lab Report Conservation of Energy

1Conservation of Energy – Background and Theory Objective In this laboratory activity, students will observe the transfer and conservation of energy in a simple pendulum system. Students will observe conservation of energy in a system in cases with and without friction to see how total system energy can be conserved, even when mechanical energy is not. Theory Kinetic and Potential Energy In this experiment, we will be considering two forms of mechanical energy. The first is Kinetic Energy (represented here as KE). Any object that is in motion has kinetic energy that can be calculated by Equation 1 below: KE= 1 2 mv 2 (Eq. 1) Where m is the mass of the object and v is the velocity. Notice that since velocity is squared (v2), there is no distinction between opposite directions of velocity. In addition, another form of energy that we will observe is gravitational potential energy (represented here as PE). This is a representation of the amount of work that gravity can perform (and thus transfer energy) on an object, it is given by: PE=mgh (Eq. 2) Where m is the mass of the object, g is the acceleration due to gravity (~9.8 m/s2) and h is the height of the object above some point. For simplicity, it is best to use h as the height above the lowest point that an object can reach, as we will in this experiment. In a pendulum system, the potential energy can be calculated using the angle and length of the pendulum: h = L (1 – cos θ) (Eq. 3) where L is the length of the pendulum and θ is the angle, as shown in Figure 1. Figure - Pendulum with height measured as the vertical distance from its lowest point Conservation of Energy The law of conservation of energy states that energy cannot be created or destroyed – it can only be transformed. Conservation of Energy applies to the sum of all energies in a system, but in this experiment we consider only two forms of mechanical energy: TotalMechanical Energy=KE + PE (Eq. 4) In this experiment, we will observe how this occurs in a system without nonconservative forces (forces that can dissipate mechanical energy) as well as in a system that includes friction, which is a nonconservative force. Although the system with friction will not conserve total mechanical energy, it will be shown that total energy is still conserved in this case. In this case, we can expand our calculation of total energy to include the energy dissipated as heat as a result of friction: TotalEnergy =KE+ PE +(ThermalEnergy) (Eq. 4) Conservation of Energy – Lab Report GOAL: (briefly state what experiment(s) will be performed and with what purpose) The simulation used will be a pendulum, in order to understand the law of conservation of energy. The law states that energy can only be transferred, not destroyed nor created. The simulation will be observed to see how the energy is transferred from potential to kinetic energy, with and without friction. The equations provided will also be used to determine values needed to calculate the KE and PE energy. PROCEDURE 1: Calculating Total Mechanical Energy 1. Navigate to the website, into the “Energy” tab. 2. Use the following initial conditions for the simulation: Length: 0.7 m Mass: 1.0 kg Friction: None Angle: 0 degrees Speed is set to “Slow” 3. Click and drag the mass on the end of the pendulum up to an angle of 50 degrees and release. 4. Observe the KE, PE, Ethermal and Etotal energies in the graph on the left of the simulation as the mass oscillates. 5. Use Equation 3 from theory to determine the height of the mass at 50 degrees. 6. Use Equation 2 to determine the potential energy of the mass at this height (PEmax). 7. You can see from the energy graph that at the bottom of the pendulum path, 100% of the potential energy is converted into Kinetic Energy. Use this information to fill in the maximum kinetic energy (KEmax) of the mass at the bottom of the pendulum’s path. 8. Use Equation 1 to determine the speed (v) of the pendulum at the bottom of the pendulum’s path 9. You can use Equation 4 at any point in the swing to determine the Total Mechanical Energy of the mass. Hint: Do not use PEmax + KEmax. Adding together the energies must be from the same point on the pendulum’s path. Use your observation of Etotal in the energy graph to fill in your answer. 10. Repeat this process to fill the values for 30 degrees and 10 degrees in Table 1 below Table 1: Mass (kg) 1.0 1.0 1.0 Length (m) 0.7 0.7 0.7 Angle (degrees) 50 30 10 Height of mass (at top) 0.25 0.09 0.01 PEmax (at top) 2.45 0.88 0.09 KEmax (at bottom) 2.45 0.88 0.09 Speed of mass (at bottom) 2.21 m/s 1.33 m/s 0.42 m/s Total Energy (KE+PE) 4.90 1.74 0.18 CONCLUSION (Part I) Explain your results. Describe your observations in KE, PE and Etotal of the system. Does anything change over time? Nothing changes over time since there is no friction, the pendulum does not stop. The potential and kinetic energy continue to be transferred at different heights of the pendulum. How does changing the angle affect the energy in the system and the motion overall? Yes, the less of an angle, the less kinetic and potential energy overall. PROCEDURE 2: Conservation of Energy (with Friction) In this procedure, you will include friction in your simulation in order to show how conservation of energy still holds when nonconservative forces act in a system 1. Using the same “Energy” tab simulation, move the “Friction” slider away from “None”, midway toward “Lots” 2. Use the following initial settings Length: 0.7 m Mass: 1.0 kg Angle: 0 degrees Speed is set to “Slow” 3. Click and drag the mass on the end of the pendulum up to an angle of 50 degrees and release. 4. Observe the KE, PE, Ethermal and Etotal energies in the graph on the left of the simulation as the mass oscillates. 5. Use Equation 3 from theory to determine the height of the mass at 50 degrees. 6. Use Equation 2 to determine the potential energy of the mass at this height (PEmax)1. 7. Just as in procedure 1, the initial total mechanical energy is equal to the PE at the maximum height. Input the calculated PEmax as the Initial Total Mechanical Energy. 8. Let the mass swing through 5 oscillations and then use the PAUSE button to pause the simulation when the mass is at the top of its 5th swing. Record the angle at this point. 9. Use Equation 3 from theory to determine the height of the mass at this new angle. 10. Use Equation 2 to determine the potential energy of the mass at this new height (PEmax)2. 11. Input the new calculated PEmax as the Final Total Mechanical Energy. 12. As you can see from the energy graphs, the total energy is still equivalent to the initial value, but now there is thermal energy present. Find the amount of thermal energy by Using the formula (PEmax)1 = (PEmax)2 + Ethermal. 13. Repeat this process for 30 degrees and 10 degrees to fill Table 2 below. Table 2: Angle ,  (degrees) 50 30 10 Height of mass (at top) 0.25 0.09 0.01 Initial Total Mechanical Energy (J) 2.45 0.88 0.09 Angle (after 5 oscillations) 44o 27o 9o Height of mass (after 5 oscillations) 0.20 0.08 0.009 Final Total Mechanical Energy 1.96 0.79 0.09 Final Thermal Energy 0.49 .09 0 CONCLUSION (Part II) Evaluate your results and discuss the difference between the system without friction and with friction included. When friction is present, the amount of kinetic and potential energy decreases. Thermal energy increases as the oscillations begin to slow down and come to a stop. Another observation is that the angle gets smaller and smaller as the oscillations come to a stop. When friction is not present, none of the above happens. Thermal energy is not present and the pendulum continues to swing as it transfers its PE and KE energy. Does Friction violate Conservation of Energy? No, because the friction will turn into thermal energy and will be spread to its surroundings. Energy cannot be created nor destroyed, only transferred. Friction can be transferred to a different energy, depending on the situation. QUESTIONS: The length of a pendulum is 25 cm, and the mass of the bob is 300 g. It is displaced from the equilibrium position and released. At the lowest point of the trajectory the KE of the pendulum is 0.265 J. A. How fast is the pendulum moving when at the lowest point? 0.265J is the lowest KE. Formula used is v= square root 2(KE)/m Convert 300 g to kg = square root 2(0.265)/.3 = 1.33 m/s B. From what height (above the lowest point of the trajectory) was it released? PE=KE Formula used for height is h= 0.265/.3(9.8) Mgh= 1/2 mv2 = 0.09 m =0.265 J C. What is the total mechanical energy of the pendulum? 0.265 J D. The pendulum is passing through a point 5 cm above its equilibrium position (its lowest point). - find its PE PE=mgh So the formula used will be PE= (0.3kg)(9.8 m/s2)(0.05 m) = 0.147J - find its KE KE=0.265-0.147 = 0.118 J Once you have completed the assignment, save your report as a PDF and upload using the blackboard submission on the lab course page (found under “Lab Online Submissions”):