\f\\l' O nergy and Work Purpose To understand the idea of \"energy\" and the idea of \"conservation of mechanical energy\". Connections to What You Already Know About in Life Energy is often dened as \"the ability to do work\". It is not a thing [although in the past it was thought of as a sort of uid that owed from place to place or from object to object]. It is not something you can pick up and hold, neither is it something you can see or always feel. It is more of a property than a thing. When you provide a value for the energy of an object, you are describing what that object could do. And what can it do? It can do work. That \"energized\" object can provide a force that contributes, either directly or indirectly, to the motion of some mass. Consider \"kinetic g; a pitched baseball, for instance. We would say that a baseball pitched at 100 mph has signicant kinetic energy. But does it really \"have\" something? How does that baseball differ from the baseball resting in the umpire's pocket? The answer? It doesn't differ at all. That moving baseball doesn't \"contain\" something more than the stationary ball does [even though we would say that the moving ball has kinetic energy while the stationary ball does not). There is no \"stuff\" stored in that moving baseball merely because it is moving. In fact, a mite living in the stitching of that moving baseball would say that the baseball is NOT moving (remember relative velocity). Therefore, that mite would say, \"This ball has no kinetic energy!\" Is the mite wrong? Nope. It is the same ball, but two different observers would make different proclamations about how much energy that ball has. Therefore, this \"energy\" idea can't really have anything to do with the ball itself. The moving ball is not intrinsically different from the stationary one, even though we who see a moving ball would say it "Has more energy\" than the resting ball. In other words, we who see a moving ball would say, "Hey! That ball can do some work!\effects of some outside forces doing work on the system. For so-called \"Conservative Forces\Procedures and Questions: PART 1 - Static Stretching of Rubber Band (Determining k and N] 1. Choose a rubber band and attach it to the force probe that is screwed onto the track [the force probe should have a hook on it to attach one end of the rubber band. 2. Attach the other end of the rubber band to one end of a cart on the track [you may need to use a paper clip for this] 3. Attach to the other end of the cart a string that is long enough to ride over the smart pulley at the end of the track [you may need a paper clip for this). Attach the mass hanger to the hanging end of the string and add 100 grams to the hanger for a total of 150g of initia.l mass. This initial mass is to give the rubber band a little beginning tension. Starting with an WW rubber band will skew the initial readings. 6. Locate either the front edge or back edge of the cart and make a precise measurement of its location [using the tape measure that is permanently affixed to the track). 7. Copy this table [Table #1] into an Excel document 5-\"? Hanging . Displacement Mass (g) 03$ (m) Force (N) 108. 6 0. 321 5. 39 600 450 110.5 0.369 5.88 650 500 113.1 0.432 6.37 700 550 115.3 0.479 6.86 750 600 117.2 0.533 7.35 800 650 119.1 0.601 7.84 850 700 120.9 0.663 8.33 900 750 122.5 0.712 8.82 950 800 124.3 0.794 9.31 1000 850 126.3 0.858 9.8 1050 900 128.2 0.921 10.29 1100 950 129.8 0.983 10.78 10. 11. Record both the initial hanging mass and the initial location measurement of the cart end in the Excel Table #1 [be sure to use the same end of the cart for every subsequent measurement). Make sure that the bottom of the mass hanger [with the 150 grams attached] hangs between 35- 50 cm. from the oor. In the Excel table, you should insert the correct formulas in the \"Added Mass" column, in the \"Displacement" column, and in the \"Force" column to correctly evaluate those values. The \"Added Mass\" means how much mass beyond the initial 150 3 you have added to the hanging mass. The "Displacement\" is how Ethe cart has moved beyond the initial Cart End Location. The \"Force\" is the weight [in Newtons] of the \"Added Mass\". Start added masses in increments according to the table. After each added mass, measure and record the \"Cart End Location" on the tape measure. The table has you add mass until you have added 500 grams. This may or may not be too much mass. Add mass, in increments according to the table, until the mass hanger nearly touches the oor. I. To find a relationship, plot a graph of Force vs. Stretch. Fit a trendline to a \"Power\" relation: F=k[AxJ; Be sure to show trendline, the equation, and the correlation coefficient on the graph. Show the graph below: 13. 14. 15. Determine the constants k and N [F = k [w for the rubber band, and record them below: k: 21 N: 7.55 PART II - Dynamic Motion of Cart and Rubber Band Remove the hanging mass from the rubber band [keep the hanger and 100 g attached... this will be the initial mass Mo). Again, locate where the end of the cart rests and remember where that is [we will call this X0). Then, by trial and error, start detenminethe added (driving) mass that, when applied to the weight hanger, drives the hanger closest to the oor without hitting it [do not stretch the rubber band to the oor!). Do this by adding some mass [maybe another 100 g). Then bring the cart back to X9 and then release it. If the hanger does not hit the oor, add some more mass. If the hanger does hit the oor, remove some mass. Keep adjusting (tuning) the mass until a w additional mass will cause the hanger to hit the oor, whereas removing that 5 grams stops the hanger from hitting the oor. 16. Once you have tuned to the correct mass, bring the cart back to Xn, record the initial height h0 [from the oor to the bottom of the hanger when the cart is held at X0), the initial mass M, the added mass M, [how much mass had to be added to the initial mass to tune it to fall correctly), and the cart mass Mo. Fill in the table below: 17. Use the Capstone software and open the le \"Energy\" [found in G:\\Phy\\DiFranzo\\Physics\\150\\Energy). 18. Place the Mad\" onto hanger but hold onto the hanger or string to keep it at the same initial position, ho [this is most easily done by bringing the cart back to X0). Start the program and then release the cart [Make sure you don't inadvertently push the cart. This may be most easily done by placing one of the auxiliary masses in front of the cart to hold the cart in place, and then just pulling the auxiliary mass away to start the movement). 19. Copy and paste your data of velocity versus position into Excel. Delete any rows before and after the relevant data. PART III - Calculation and Plotting of Energies 20. Load your data [velocity v[m/s) vs. position x[m)) into a blank spreadsheet and into a table with the headings given below. For graphing purposes, you may want to move the position columnso it is to the right of the speed column. Also add a row so at x = 0, v = 0. 21. For each position, x, calculate the total Kinetic energy, K, the Gravitational Potential energy, Ug, the Spring Potential energy, LL59, and the total mechanical Energy, E. [Since the position and speed are in meters 8: m/s respectively, use 5.1. units for mass (kg) and for g use 9.8 m/sz.) K: '26 Mural,\" Where MJWF Mo + Madm+ Mam Gravitational Potential: Us = Wu - x) Spring Potential: U51: = k xN+1f [N+ 1) and total mechanical energy E1- : K + Us + ng 22. Plot the 4 energy curves on one graph [Energies vs. Position). Label each curve and include a legend for the graph. Just select all five columns [not including v) and click the graph wizard. 23. Below, show the graph of_\"Energy vs Position" that you made in lab. 24-. From the graph, record the final Total Energy [in Ioules] and the initial Total Energy, as well as the percent loss [if any] of that Total Energy [the % Loss would be the [Final-Initial] / Initial x 100]. 25. Dening your \"system\" as the \"Cart/ Hanging Mass/ Rubber Band\27. Describe the movement of energy as the cart slid along the track while the hanging mass fell and as the rubber band stretched. To give this a somewhat quantitative/ qualitative aspect, we will use plus signs to represent energy amounts. Ten plus signs represents the total energy. We are going to look at 5 different positions along the motion at the initial point, at the % point, at the 11% point, at the 3A; point, and at the nal point. I have lled in the Initial and Final positions for you. These plus signs won't represent \"exact\" amounts, but they should represent your best estimate of where the energy is found in the system at these various points. Kinetic Ene a ++++++++++ ++++++++++ 28. In question #2 you noted a loss in energy. What non-conservative force do you think is responsible for this loss in energy from the system? 29. Where do you think this energy went