Overview
Physics 201
Lab 8: Inelastic Collisions What to turn in Photo + description of your ball and surface (please paste into google doc or attach separately) Answers to the questions Dataset (labeled) you can submit these as a pdf or google sheet 2 Graphs (labeled) you can submit these as a pdf or google doc Group Roles Team Roles Please choose roles in your lab group and indicate who will be doing each task. If your group has less than 4 people you can have more than one role. Role Name Director - Coordinates the lab, makes sure all instructions are followed. Technician - Sets up the experiment, records the data and distributes it to the group Graph Creator - Creates and labels the graph Explainer - This person writes the responses to the questions after discussing with the team. 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 a basketball Designed by Miriam Simpson 1
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... , 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 = 𝑣𝑓 𝑣𝑖 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 it 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 < e < 1, the collision that occurs is partially inelastic. Think: Some questions before you take your data: 1. What 2 things are colliding? 2. Is energy conserved? Why or why not? 3. Is momentum conserved? Why or why not? 4. Estimate what the coefficient of restitution will be for your ball. 2
Taking Data Check/Calibrate: You should use these results for calibration: make sure that you set up your experiment in such a way that phyphox correctly determines (within a small error) the initial height, which you should measure with a ruler or meter stick. Things to watch out for are: ● Make sure you set the threshold for sound detection of the app appropriately, as shown in the video. ● Make sure that the ball is falling straight down, without any sideways velocity. ● Make sure you drop the ball with initial zero velocity; that is to say, that you do not accidentally give it a small push up or down upon releasing it. ● The app has no way of knowing how big your ball is, so you should measure heights from the bottom of the ball to the floor. ● This just gives all your potential energies (which typically would be measured from the center of the ball) a constant offset that does not affect the calculations that follow. When you are satisfied that your setup is giving you reliable results, you can move on to the actual data gathering phase. Record Data: Open the phyphox app. Scroll through the list of sensors and select “(In)elastic collision.” ● Place your phone on the floor and tap record. ● Hold the ball above the floor at a height equivalent to the height of a table or countertop. Some height you can measure. ● Drop the ball. DO NOT DROP THE BALL ONTO YOUR PHONE. ● Allow the ball to bounce about 6 to 8 times. ● Tap to stop recording. 1. Measure the initial height (table or countertop) you dropped the ball. Record it here: Initial Height (cm): __________ 2. Open a blank Google Sheet in your Google Drive (you can also use excel) ● In cell A1 type the header “Bounce.” ● In cells A2 through A6 enter the bounce number 0-5. ● In cell B1 type the header “Height (cm).” ● In cells B2 through B6 enter the values of the heights for the corresponding bounce. 3. Does the phyphox app Height 0 agree with your measured height of the ball initially dropped? 3
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 Ctrl 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 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.) 4