his lab is concerned with two situations that involve the conservation of PE and KE, PE = mgh and KE = m v2. The first is a skate ramp that is similar to a roller coaster, and the second is the Atwood's machine. In both cases, the PE is conserved and released as KE, This basically has height "h" being transformed into velocity "v". PE = mgh at the top, all becomes KE = m v2 at the bottom. Conversely the KE at the bottom allows it to climb, "losing its KE going into PE" as it climbs. g = 9.8 m/s2. We worked Example 6-6 PE Changes for a Roller Coaster in the lecture (see figure to the left). https://phet.colorado.edu/sims/html/energy-skate-park/latest/energy-skate-park_en.html Energy Skate Park Open the PhEt simulation, and click on Intro quick set up. Click on Energy + (upper left), Pie Chart and Speed (upper right), Grid (lower left) and Slow (bottom center). Now click the Stop symbol. With the simulation stopped, grab the skater and place their lower red dot exactly on the 5 m height grid line, on the right of the track. The simulation will appear as it is to the right. Grid lines are 0, 2, 4 and 6 m. Click start, and watch the skater cycle back and forth. Our concern is to watch the Speed dial, energy Pie Chart and bars, during the cycles back and forth, in terms of position on the track. The pie chart and bar energies are color-coded. 1. Watch the Speed dial, it cycles too, back and forth. Zero speed briefly at h = 5 m, and maximum speed at the bottom. a. Use conservation of PE = m g h and KE, to calculate the speed at the bottom (mass cancels), v = _____ m/s. (3 sig figs) Can you roughly verify this by stopping the simulation at the bottom? Yes/No. b. Stop the simulation several times on both sides of the track, do the energy bars and pie chart correspond? Yes/No. c. Is total energy = + KE + PE conserved at various points on the track? Yes/No. 2. Click on the Measure box at the bottom of the simulation. Do the same set up as above, having the simulation stopped and the skater at h = 5 m. Note the purple measuring device, reading out Kinetic, Potential, Thermal and Total energies. Click on run, and continue watching for several cycles. Then stop. The track has dots showing where measurements can be made. These are based on the skater's m = 60 kg and g = 9.8 m/s2. a. Calculate the skater's PE at maximum height h = 5 m. PE = ________ J. Pull the cross hairs on the measuring device over to an upper dot, and approximately verify you calculation. Yes/No. b. Pull the cross hairs down to the lowest dot (not exactly centered), and approximately verify the speed above in 5a. Yes/No. 3. What we are seeing is Conservation of Energy, between Kinetic and Potential energies. The total of both is completely conserved, throughout the skater's motion. "They always add up to a full pie". 4. Click on the lower-right Playground box. Do the above set up: Pie Chart, Speed, Grid and Slow. Create a "track" as follows. Grab the red barbell's center and pull it straight up to h = 4 m. Grab it down below again, and put this second one's center at h = 2 m, and displaced 3 m to the right. Pull the right hand ball on this second one, down to ground level one grid line to the left of the skater. Now on the first barbell, pull its right ball down to the second barbell's left one. Finally pull the first barbell's left hand dot up to h = 6 m. "Nice!", you have a slide as is shown.. Click on stop, and then put the skater on the track at h = 5 m. a. Click run, and even at slow motion, try to click stop just as the skater reaches ground level. This may take several tries. Here the skater impacts the ground just after this, the impact absorbs energy, and the Speed dial will be "too low". Continue trying, and you should be able to record a speed of 9.5 m/s or a bit faster. Record your best try, v = _____ m/s. b. Click stop, and now pull the left upper part of the track, all the "way to the left", and it's shallower. Pull all the other red balls similarly as is shown. You will need to pull the right hand two down several times, to get them to lay on the ground. Put the final two on the right at ground level. A long and shallow ramp. Put the skater at h = 5 m again, click run, and then stop once they're on the final part. Here you measure v = _____ m/s. c. Compare this value to that in 4.a. above. Same/different (nearest couple tenths). 5. Can we conclude that no matter the frictionless ramp's shape--only an object's height determines its final speed? Yes/No. Would the object have this same speed if it was dropped straight down (from h = 5 m)? Yes/No. Such is roller coaster design!

Atwood's Machine Energy Lab We have an Atwood Machine, where we analyze it using energy. There are two masses A and B, and gravity pulls B down. Through the string in the pulley, mass A moves to the right (see the arrows). B starts at an initial height, and drops. So B has energy PE = mB g h at the top, that goes to zero when h = 0. Both masses move while this occurs. So all the PE = mB g h becomes KE for both. This gives us mB g h = mA v2 + mB v2, when B fully drops to h = 0 and both have the same v. Algebra solves for v, v = ( 2 g h mB / (mA + mB) )^.5. Physlet Physics by Christian and Belloni: Problem 4.11 (compadre.org) Open the simulation, a Modified Atwood's Machine. Mathematician George Atwood invented it, in 1784 to show the physics of Newton's 2nd Law. We analyze it now (2021). Click run, and watch how the two masses move. Gravity pulls down on the hanging weight, it accelerates down, and pulls the mass on the lab track to the rightthey're connected by a string going over a pulley. Both same speed, and no friction. 6. Our data indicates an initial speed of zero and we need to measure the final speed from the plot of vx vs. t. Click on the half-red dot at the upper right end of the vx vs t graph and hold it downa yellow box appears. With two numbers. The left number is the time, .8 s, and the right number is the speed. This indicates a final speed of vy = _____ m/s 7. PE and KE do not have time as a variable, while the height is a variable. We need to measure the height change of mass B. Do this by clicking reset, and we can get an initial height from the circular hanger on the top of the mass B. We center on it, click and hold it down, again a yellow box with two numbers. And the right number is the initial value of height, y0. Measured y0 = _____ m. Click run, let it drop, and measure the final value of height, y = _____ m. The net change in height must be a positive number, and this is h = y0 - y = +_____ m (about 1 m). 8. We can use the height, the speed vy from 6, and the mass of mA = 1 kg, to calculate mB. This gives mB = ______ kg (3 sig figs, about .5 kg).