When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. A variety of answers are possible. Encourage them to explain their ideas so you can better understand the answer they chose. Remind the students that friction is not a consideration. Water slides are not truly frictionless, so they might want to imagine an air hockey table as a slide. Students will find out later in the lesson that, in the absence of friction, the speeds would be the same. The only difference would be the direction each is traveling at impact.
Students may be familiar with conservation of mass as a conservation law. Try to get them to explain what it means for something to be “conserved.” There are many ways to describe conservation but students often struggle. They may say that they know what it means but they can’t figure out how to say it or write it. These questions should be a good exercise for them to express their ideas in writing. Conservation may be expressed as “no change in the quantity” or “before = after” or “the total always stays the same.”
Discuss ME as a useful tool for studying motion. Do not tell students yet that ME is conserved. They will determine this from the coming slides and calculations. As an example. toss a ball in the air and talk about the potential energy and kinetic energy as it rises and falls. As another example. show students a pendulum and talk about the PE and the KE changing as it swings.
Students should use PE = mgh to get the PE at each point. To calculate the KE they need to first find the velocity. The easiest way to get v 2 is using v f 2 = 2 g y. (Note that the initial velocity is zero, so it was eliminated from the equation). After getting the velocity, use the equation KE = 1/2 mv 2 . After making these calculations, show students the chart on the next slide.
Mention the following to the students: (1) KE and PE change during the fall but ME remains the same (it is conserved). (2) You might ask students what values would change if air resistance was considered. The KE values would be smaller and the ME would gradually decrease, so ME would not be conserved. (3) No consideration was given to the path the book took to the floor, only its position. Therefore, the result would be the same even if it slid down a ramp (as long as the ramp was frictionless).
Conservation of energy provides an easier method of solving some problems. For example, go back to the table created for the falling book, and point out the fact that they never needed to calculate the velocity. If they know the PE , then the KE is simply (19.6 J - PE ).
Previously, in Chapter 2, the equations developed required that acceleration be constant. That is not the case for conservation of ME . The example with friction provides an opportunity to point out that even though ME may not be conserved, energy in general is conserved. With friction, the material becomes warmer due to the contact between the surfaces, which causes the speed of the vibrating molecules to increase.
Remind students that J require the use of kg and m (not g and cm). Answer 1: 0.36 J. Students should use PE = 1/2 kx 2 to determine the energy stored in the rubber band. Answer 2: 0.36 J. Students should use conservation of mechanical energy. PE lost = KE gained Answer 3: 8.5 m/s. Students should use the KE from the last question and KE = 1/2 mv 2 to determine v Answer 4: 3.7 m. Students may revert to equations from Chapter 2. but this is most easily solved using conservation of ME . They only need to find the height required for KE lost = Pe g gained = 0.36 J = mgh .
Both strike at the same speed. One hits the water vertically, while the other slides in nearly horizontally. The PE lost is the same for both and, therefore, the KE gained is the same as well. With friction, the student falling straight down would be moving faster, because energy is not conserved for the student on the slide. Some of the lost PE is converted into thermal energy
Conserved means that the quantity does not change. The quantity neither increases nor decreases. Common examples are the conservation of mass and the conservation of energy. Mechanical energy is considered to be conserved in cases where friction is negligible. If friction is significant, mechanical energy is not conserved.