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Big Ideas About the Conservation of Energy By Laura Zinszer 2011 Columbia Public Schools & Physics First Now that we know the types of Energy . . . Let’s analyze the total energy in a system. . . All Energy is measured in a unit called a Joule (J) or kilo-joule (kj). Total Energy is the all of the potential (usually Eg) and all of the kinetic energy. TE = Ep + Ek To determine the total energy, we will need to calculate the Ep and Ek, and then add all the energy together. Gravitational Potential Energy (Eg) Eg = m * g * h m = mass (Kg or g) g = 9.8 (m/s2) h = height (m or cm) Joules (Kg and m) Kilo-joules (g and cm) Gravitational Potential Energy (Eg). Why would a ball on the ground, have no gravitational potential energy? (Eg) Why is this true? The higher that an object is elevated, the greater the Eg … Gravitational Potential Energy (Eg) For example, a 3.5 kg ball held at a vertical position of 20 meters above the ground has gravitational potential energy. (What is the Eg) Gravitational Potential Energy (Eg) Eg = m * g * h Eg = 3.5kg * 9.8 Eg = 686 J m/s2 . * 20m Kinetic Energy (Ek) Ek = ½ m 2 *V m = mass (Kg or g) V = velocity (m/s or cm/s) Kinetic Energy (Ek) The amount of Ek depends on the mass and velocity of the object. Therefore . . . The greater the velocity or speed of an object, then the greater the Ek! Kinetic Energy (Ek) If the car has a mass of 2000 kg, and travels at a velocity of 15 m/s, then the Kinetic Energy equals… Kinetic Energy (Ek) 2 Ek= ½ m * V 2 Ek= ½ 2000kg * (15 m/s) 2 2 Ek= 1000 kg * 225 m /s Ek= 225,000 J How do Eg and Ek relate in an energy system? As the car moves down the track, Why does the Eg decreases and Ek increase? As the height is lower, the Eg becomes less. The car speeds up, so Ek increases!!! What is the car’s position on the track when the Eg = Ek? One-half of the distance down the track. Why does the Total Energy (TE) remains constant? Total Energy (TE) TE = Eg + Ek The TE will always remain constant!! As the pendulum swings, the Eg is transformed into Ek … but the Total Energy (TE) remains constant. What is the position of the pendulum when all of the energy is Eg? The pendulum is at the top on either side where it is stopped. What is the position of the pendulum when all of the energy is Ek? The pendulum is at the bottom of the swing…and is at its fastest!! What is the position of the pendulum when Eg = Ek? The pendulum is ½ way through the drop. As the coaster travels on the track, the Eg is exchanged for the Ek. but the Total Energy (TE) remains constant. The BIG IDEA for energy is Total Energy in the system is equal to the Eg + Ek …. The Total Energy in the system will always remain constant. Conservation of Energy! Energy can not be created or destroyed; it can only be transformed from one type of energy form to another. Let’s Look at some Energy Graphs As the swinging pendulum falls… Eg Ek TE Eg Ek TE Eg Ek TE Eg Ek TE Eg Ek TE The Eg is transformed into Ek Eg Ek TE Eg Ek TE Eg Ek TE but the Total Energy in the system at each position remains constant. Eg Ek TE Eg Ek TE Eg Ek TE Eg Ek TE As the kids on the sled go down the hill… the energy graph would look like this… Eg Ek TE Eg Ek TE Eg Ek TE Eg Ek TE Eg Ek TE But the Total Energy in this system remains constant as the sled goes down the hill! Practice Problem #1 Formula Work Answer Units A 5 kg ball is held at a vertical height of 32 meters. How much Gravitational Potential Energy does the ball have? (Show all math formulas, calculations, and units) Problem #3 A car has a mass of 1300kg and is traveling at a velocity of 31m/s. How much Kinetic Energy does the car have? Energy Efficiency A toy car was going down a track. It hit a rubberband but only bounced part of the way up. Energy Efficiency final Eg / beginning Eg l 100 = Efficiency (%) Energy Efficiency The car had a final Eg of 28 J when it bounced up after hitting the rubberband. The car had a beginning Eg of 32 J. Eg (initial) of 32 J Eg (final) of 28 J Energy Efficiency 28 J = .875 x 100 32 J Energy Efficiency = 87.5% Eg of 32 J Eg of 28 J Energy Efficiency If only 87.5% went back to the final Eg, what happened to 12.5% of the energy that disappeared? Eg of 32 J Eg of 28 J It became thermal energy due to the friction when the car hit the rubberband. How does the amount of work done compare to Eg of an object? (Bucket of Lead) Eg = m * g * h W=f*d Work & Gravitational Potential Energy (Eg) Eg = 1.74 kg * 9.8 * 1.5 m W = 16.8 N * 1.5 m Bucket of Lead Work & Gravitational Potential Energy (Eg) Eg = 1.74 kg * 9.8 * 1.5 m Eg = 25.6 J W = 16.8 N * 1.5 m W = 25.2 J Remember that work does not have to be vertical. We could pull the bucket of lead across the floor and there would be work done without any Eg. Work = 2.3 N * 1.5 m = 0.45 J Why is less work done? Same distance moved?