Download Mechanical Energy ME Example

Directions: Read and highlight the following assignment. You have been taught how to properly highlight. Please use these skills in highlighting all new and important information. Mechanical Energy Imagine a skateboarder in a skate park. He is speeding up and slowing down as he glides through the half pipe. As he speeds up going down the pipe, his potential energy drops while his kinetic energy increases. As he slows down heading back up the pipe, his kinetic energy drops as his potential energy increases. This is a back and forth process that happens as the skater moves up and down the pipe. This is very similar to a baseball being thrown into the air. As the baseball goes higher and higher, the potential energy is increasing as the ball slows to almost a stop (thank goodness since without gravity it would fly away from earth and into outer space). When the ball turns and starts falling to earth again, the potential energy is converted back to kinetic energy as the ball speeds back towards your glove. This process is completed countless times as objects go up and down increasing potential energy as kinetic energy decreases and back again as the potential energy turns into kinetic energy. When we look at a specific example such as the baseball being thrown into the air or the skater in the skate park, we can add the potential energy to the kinetic energy and create the total energy of a system called the mechanical energy. Mechanical energy (ME) is the energy of an object due to its motion (KE) and due to its position (PE). Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position) or both. Since mechanical energy is the combination of kinetic and potential energy, the actual value is easy to calculate by adding together the KE and PE. The formula for mechanical energy is: mechanical energy = potential energy + kinetic energy An object that possesses mechanical energy is able to do work. In fact, mechanical energy is often defined as the ability to do work. Any object that possesses mechanical energy ‐ whether it is in the form of potential energy or kinetic energy ‐ is able to do work. ME Example Let’s work through an example of calculating mechanical energy using a pendulum. The formula to calculate the potential energy is: PE = mgh Substitute the values into the formula and you get: PE = 10 kg x 0.2 m x 9.8 m/s2 = 19.6 J Whenever the ball is at the ends, the Potential Energy (PE) = 19.6 J. Since the speed is 0 at the end (remember the ball stops at each end), the Kinetic Energy (KE) = 0 J. The total mechanical energy, ME, of the pendulum at either end would be: ME = KE + PE = 0 J + 19.6 J = 19.6 J mass of the ball = 10 kg height at each end, h = 0.2 m g = 9.8 m/s2 As the ball approaches the middle position, the PE is decreasing while the KE is increasing. At exactly halfway, the height of the ball will drop to zero. This would mean that PE would also equal zero. At this point, theoretically, all PE has transformed (turned) into KE. This would make the KE = 19.6 J while the PE = 0 J. The mechanical energy would be similar to the ends equaling 19.6 J: ME = KE + PE = 19.6 J + 0 J = 19.6 J The key word in the last paragraph was “theoretically.” In a perfect closed system, as the PE decreases, it all turns into KE. As KE decreases, it all turns back into PE. A closed system is very similar to the closed system we discussed in chemical and physical changes. In this case, a closed system refers to a group of objects that transfer energy only to each other. Conservation of Energy In a perfect world, we say that the energy transfers back and forth between KE and PE. When the PE equals 0, it has all been turned into KE. As the KE begins to decrease back towards 0 (as the object slows down), it all turns back into PE. Unfortunately, life isn’t so perfect. If you’ve ever watched a pendulum swing back and forth, you probably noticed it eventually stops if you don’t add additional energy. For example, think of playing on swing. You have to continue kicking your legs in order to provide energy to make the swing go back and forth. If you stop kicking, you lose energy making the swing stop. So where is the energy going? Why can’t it go on forever? Whenever you hear a sound (sound energy) or feel heat from friction (thermal energy), energy is turning into a different form of energy. One thing we can say though is that we can account for all of the energy in our closed system. Whether it is KE, PE, sound energy, thermal energy, or any other type of energy (light, electrical, nuclear, and chemical), the total energy of our closed system is always conserved. Because no exception to this rule has ever been found, we refer to this as a law. The law of conservation of energy states that in a closed system, energy cannot be created or destroyed. It can only be transferred from one form to another. We’ve seen a similar law to this when we discussed matter. The law of conservation of mass (or matter) states that matter cannot be created or destroyed. It can only change states. So energy and matter are very similar in that they can never be created or destroyed, they can only change forms or states. Where did the Energy Go? Is it easy to see that energy is conserved? Not really. Take the free fall experiment we’ve been working on in class. When we dropped the steel marble from the railing, the PE was 1.023 J (PE = 0.018 x 9.8 x 5). The speed of the marble topped out at 5 m/s giving us a KE of 0.229 J (0.5 x 0.018 x 52). In a perfect world, based on the law of conservation of energy, all of the PE should have become KE. That didn’t happen in our lab, though. It appears like we may have lost energy because the energy dropped from 1.023 J to 0.229 J. So where did it go? Just like the pendulum example above, the energy turned into other forms of energy such as thermal and sound. Perfection? So is anything ever perfect when transferring energy back and forth between KE and PE? Unfortunately, no. If anyone ever tells you they have created a perfect system that transfers all PE to KE and back again, you should be skeptical. These perfect systems, although impossible to make, are called perpetual motion machines. This fictional machine transfers all PE into KE and back again never losing a drop of energy. This isn’t possible. Because some waste thermal energy (heat) always results when KE and PE transfer back and forth, nothing can ever be perfect. But that doesn’t stop scientists from trying to achieve perfection. Engineers are always working on machines to make them more and more efficient. They do this by trying to minimize the amount of energy turning into thermal energy (heat). You might be surprised to hear that a car is one of the least efficient machines on earth coming in at around 20% efficiency. That poor efficiency doesn’t stop the automakers from saying they are making a more efficient car. Keep in mind that in the last several years they have improved efficiency about 1%. That qualifies as making a more efficient car even if it is still horrible. So if a car is that inefficient, what is the most efficient machine on earth? Good luck finding that answer. Opinions vary. If we are just turning something into heat, that’s a pretty simple process. That’s why you will hear your parents talk about how efficient the furnace in your house is. Many newer furnaces are in the 90+% efficiency range. That’s pretty good compared to the 20% efficiency of a car. As for a machine with the best efficiency, many sites list the bicycle as the most efficient machine topping out in the high 90% range. So the next time you need a ride somewhere, try to be more efficient and ride a bike ☺ Guided Notes for Conservation of Energy Directions: Answer the following questions found in your reading. 1. Define mechanical energy. 2. What is the formula for finding the value of mechanical energy? 3. What is a closed system? 4. Define the law of conservation of energy. 5. How are the law of conservation of mass and conservation of energy similar? 6. Why is perpetual motion impossible? 7. A 0.3 kg machine has a starting height of 8 m and slides down a 10 m long ramp in 2 seconds. Calculate the ME for this system. Show your work! 8. Could the system in question #6 be a perpetual motion machine? Why or why not?