Setting Up Objectives: Use Energy Conservation and Impulse-Momentum Theorem to investigate a bouncing ball Review free fall motion Practice good measurement techniques including calibration/validation of equipment . Practice data analysis (graphing) Equipment: For this activity you will need 1. A smartphone or tablet 2. The phyphox app, available for free for both Apple and Android phones, from their respective online stores. 3. A ball that bounces well (you need to be able to get at least four bounces out of it). Other than that, size does not matter: it could be a marble or ping-pong ball bouncing on a counter, or abasketball bouncing on a concrete floor. You may be able to get for cheap a small, bouncy rubber ball in the toy section of Walmart or Target, or even a pharmacy. 4. A ruler or tape measure of some sort. The measure app on phones will do in a pinch, just make sure you mark measurements on a piece of paper or wall or something. 5. A timer or stopwatch. A clock on the wall with seconds is fine, or the one on your phone works, or you can google one on your computer. Prepare: Watch the short (3:40) video before you start on this activity to get the basic idea: https://phyphox.org/experiment/inelastic-collision/ Play: Have everyone in the group (that can) install the phyphox app on their phone, and do a couple of trial runs dropping any ball you can find and having the "(In)elastic collision" module of the app tell you what the initial height and the height of the subsequent bounces were. Look at the times and distance and make sure that they make sense (we will check this more formally later). Look at the energy tab too and compare percentage losses. Try to pick the person whose phone/ball combo is working best to do the actual experiment. The coefficient of restitution e: e = = v .The coefficient of restitution (e) is expressed as the ratio of the relative speed of two objects before and after collision. The value of the coefficient of restitution is between 0 and 1. Perfectly elastic collisions lose no energy, therefore they have a coefficient of restitution equal to 1, meaning the ball would bounce to the same height from which is was dropped. Perfectly inelastic collisions would have a value of zero meaning the ball would stop on the floor in this case. If the coefficient of restitution is in the range 0 Scatter Chart, Make sure X-axis indicates Bounce Analyze/Graph Data: 1. Make a scatter plot of the Height vs. Bounce. Click on the top of the column with the Bounce values, Click and hold the Ctri key and click on the top of the column with Height (cm) values, Release Ctrl key and open the Insert menu and select Chart, The Charter Editor will open. In Setup choose Chart Type > Scatter Chart, Make sure X-axis indicates Bounce Make sure Series indicates Height (cm) In Customize > Chart & axis titles add axes titles with units to your graph. Fit the data to an equation and display the equation on the chart 2. Make a scatter plot of height vs next height. In the cell, C1 type the header "Next Height" Starting from the second value (n=1) copy the B3 into C2, and then repeat. Using the technique you used for the previous graph, plot "Next Height" on the x axis and "height" on y In Customize > Chart & axis titles add axes titles with units to your graph. . Fit the data to an equation and display the equation on the chart2. Make a scatter plot of height vs next height. . In the cell, C1 type the header "Next Height" Starting from the second value (n=1) copy the B3 into C2, and then repeat. . Using the technique you used for the previous graph, plot "Next Height" on the x axis and "height" on y In Customize > Chart & axis titles add axes titles with units to your graph. . Fit the data to an equation and display the equation on the chart Questions 1. What equation fits the data for your height vs bounce graph? 2. What equation fits the data for your height vs previous height graph? How is the slope related to your coefficient of restitution? 3. What is the impulse J, from the table on the first bounce? Show your work, 4. If work transfers energy away from the bouncing ball, where does the energy go? Hint: do you hear the ball bouncing? What do you feel when the ball hits the floor? 5. Do you expect e to change very much if you change the surface on which you bounce the ball? Explain. (Some quick experiments here would be useful. Note that you don't need to do all the plotting and tables again-you can use phyphox's estimate of the rate of energy loss as a proxy for the coefficient of restitution.)