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Cultivating Your Inner Scientist Modeling Emmona, and E and exploring Ethermal kinetic Exploring Gravitational Potential Energy, E9: While we use the triangle as illustrated in Figure 1,we now want to expand our toolbox and explore what is illustrated in Figure 2. Let us cultivate our inner scientist by using the scientic practice of Mathematical Thinking and discussing in our small groups: 1. What is an easy concrete example of something that has a little gravitational potential energy, Eg, and something that has a lot of E5? Figure 1 2. What quanties make something have more E5? For example, we know the strength of the earth's gravity, g, is one of them. What are two other things? :ll:l:l 3. Then taking these quanties one at a time, what happens when we double the quantity? After playing with these questions can you start to imagine the mathematical model for E3? Put a possible one below. Figure 2 Activity: Embracing Mathematical Thinking Find four identical pens, pencils, or other objects and then take two of the four and tape them together as shown below. Then stack two books and offset them to make a set of stairs as shown in Drawing 1 below. Complete the mathematical model of Es as you go. Now let's be playful when you lift one pen up one step it now has some gravitational potential energy due to gravity, say 1 ]. Now, if you then lift the second pen up to the same step, complete the table on the next page to communicate how much E, it would have. Next, can you creatively think through what E, next page to communicate how much E, it would have. Next, can you creatively think through what E would be of the two pens that are taped and lifted together?Now walk the triangle as in Figure 2, what does that mean about how mass, m, will show up in the mathematical model, the equation for Eg? Drawing 1 Then also we know from the previous lesson, that the strength of gravity here on the surface of the earth, g, will in part determine how much gravitational potential energy an object has so now would be a good time to add that to our mathematical model. Additionally, we have one more factor to integrate into our model. We know the higher you are the more gravitational potential energy you have and it can get scary when you fall the Es transforms into motion energy, Ek, because you eventually have to stop. Let's return to our practice of mathematical thinking and treat the variable height systematically. lfyou lift one pen up one step it had about 1] of Es' Now if you repeat that same process and lift that same pen up one more step what would happen to the pen's Eg? Complete the table above and reason how this result would show up in the mathematical model, the equation for Es? Crude-In with Teacher E Teacher Initials Exploring the Energy of Motion, Kinetic Energy, Ek: Let us continue to grow our skills and thinklike a theoretical physicist as illustrated in Figure 3. Activity: Think Like a Theoretical Physicist Let us again start with: 1. What is an easy concrete example of something that has a little kinetic energy, Em: and something that has a lot of E1? 2. What two main quantities make something have more Ek? Figure,I 3 . DD 3. Now knowing the two quanties above should, therefore, be in the mathematical model for E, and that the model for Ek is one of our four patterns, let us eliminate two of our four patterns below because they are nonsensical: Ek=n1v Ek=mv2 En: A Er At this point, we may need an experimental physicist to get us some data to determine which of these models! actually models what happens in reality. 4-. Two students did collect the raw data for mass, height, and velocity as shown in this video: I! 3Lactivity - Modeling Kinetic Energy 5. Using Energy Analysis and the data shown in the video, complete this data table and copy and 6. Now as an experimental physicist you can graph with this Desmos link the velocity vs E, and determine if the model is proportional or quadratic. insert_Desmos_here7. Look carefully, the constant (c-Value) is not exactly mass but rather some fraction of the object's mass, so what is E, in all words? =Copy of 3Lactivity - Spreadsheet for Modeling Ek File Edit View Insert Format Data Tools Extensions Help Last edit was 1 hour ago 100% % .0 .00 123- Arial 10 . BISA fx A B C D E F G System Component: Jumper Total System How will we get this? Controls: Mass = Position 1: kg (Initial) Etotal = E. star g start = mgh start Gravity = m/s /s E. E ETotal Data Table Position 2: (4 Initial Height) Ex = Etotal - Es To be graphed on To be graphed on the the X - Axis Y - Axis Total E. E Height Gravitational Total (get from video analysis) Kinetic Energy Energy Energy Velocity (m) +/- 0.05 (you need to code this using ( E Total = m * g * starting Eg = m * g * current h (get from video analysis) the system analysis) Position 3: h) (J) +/- 0.2 (m/s) +/- 0.2 (4 Initial Height) (J) +/- 0.2 (J) +/- 0.4 0 0 Code Here E Total 0 10 0 Position 4: O O Ground Final Height) 0 O ust before the ball hits the ground E3Lactivity - Modeling Ek desmos Log In | or Sign Up ? + #