Free Fall. Objective. Materials. Part 1: Determining Gravitational Acceleration, g

Transcription

1 Free Fall Objective Students will work in groups to investigate free fall acceleration on the Earth. Students will measure the fundamental physical constant, g, and evaluate the dependence of free fall acceleration on the mass of the falling object. They will also investigate the effects of air resistance on the motion of a falling object. Analysis will include graphing, measuring the slope of a velocity versus time graph, analyzing a nonlinear velocity versus time graph, average and standard deviation. Materials Two balls of significantly different masses to drop. Tennis, soccer, basketballs work well. Large coffee filters, parachute, beach ball or some other object that has a large amount of air resistance IPad Mini with Vernier Video Physics software Logger Pro software, which is available in the lab rooms and SL 220 Meter stick or some other measuring device with metric markings Part 1: Determining Gravitational Acceleration, g Galileo is often referred to as the father of modern science because of his idea that our conclusions about how the world works must be based on experimental data we have collected about the actual world we live in, rather than our philosophical ideas about how we think the world is. Today you will get to perform measurements to determine a fundamental constant, the acceleration due to gravity on the surface of the Earth. This constant is often referred to as g and was first measured by Galileo about four hundred years ago. Just a quick reminder what acceleration means. Acceleration is a change in velocity, and has units of m/s per second or m/s 2. If an object starts at 10 m/s and undergoes an acceleration of 2 m/s 2 to speed it up, then after one second the object will be travelling at 12 m/s and after 2 seconds its speed will be 14 m/s and so on. You are going to drop an object from rest. As an object falls we say that it is in Free Fall, indicating that the only force acting on it is the Earth s gravity (we will neglect air resistance for now). The Earth s gravity will pull the object downward and as the object falls it will speed up, or accelerate. Pretend that you are Galileo, the first person EVER to measure how an object accelerates when it is dropped. You will be able to measure this in a way that was unimaginable to Galileo, using an IPad to actually video the falling object. Free Fall 1

2 1. You are going to drop an object from at least 3 m off the ground and video the object as it falls using the IPad Mini provided to you. Do not use a beach ball, balloon or any other object that has substantial air resistance. A few helpful hints that will help with taking the video: a. The more light you have, the less blurring there will be of the falling object. Take the video outside if you can to get plenty of light. b. The object will need to fall in a plane perpendicular to the line of sight of the camera. So, hold your IPad as upright/vertical as you can when you take the video. c. You will need an object of known vertical height in the same plane that the object falls, so that you can use this distance to calibrate the distance fallen. You can use the actual ball, but it is better to have something that is a bit larger. Some ideas would be to use the height of the person dropping the ball if you can see them from head to toe in the video. Another idea would be to have a meter stick a few inches to the right or left of the falling object (in the same plane). Answer question 1 in the report. 2. Open the Vernier Video Physics app on your IPad. The initial display for this app says Videos in the top center and lists all previous videos that have been recorded. If this is not what you see when you open the app push the top left buttons until you are returned to this initial page. Select the + in the top left corner to add a video, and select Take Video. You can choose whether or not you would like the software to access the microphone, which gives the video audio (we won t need it but it is fun to have it). a. Select a ball to drop. Have the partner that will drop the ball get positioned. Have the partner that will record the video be positioned so that they can see the entire fall of the object without moving. The person videoing should also be able to see the object of known height that will be used to calibrate distance in the video. If you cannot see the entire path the ball will follow as it falls, step backwards until the video will include the entire path without having to move the camera. The IPad must be kept stationary while you video the ball s fall and the IPad should be as close to vertical as possible. b. Push the red button on the right of the IPad display to start recording your video, the other partner then drops the ball from rest, and the large red button is pushed again to stop the recording. The IPad should be held as still as possible while videoing the falling object. c. Once the video has been recorded you can select Retake if you would like to record it again for some reason, or Use Video if you are happy with the video you took. d. After selecting Use Video you will be brought to a page that can be used to analyze the video. i. Using the slider at the bottom, advance the video until you find the frame just after the ball has begun to fall. Choose a position on the ball to track. This position should be easy to see; two possible suggestions would be to track the center of the ball or the top of the ball. You can mark the position of the ball in this frame by dragging the target shaped white circle to the position you wish to mark and then tapping the center of the circle with your finger. A red dot will Free Fall 2

3 appear indicating the position you marked and the video will then advance to the next frame. In each frame mark the same position on the ball. Continue marking the path of the ball until you have at least data points; do not mark when it strikes or any subsequent bounces. ii. Next select Origin & Scale at the top. This will add an XY origin that you can drag to indicate where you would like the (0, 0) coordinate to be located. Putut x=0, y=0 to be approximately where the ball hits the ground. This tab also shows a scale (two circles with a line drawn between them). Drag each of the two circles to opposite ends of the object of known vertical height and enter the corresponding height for that object in units of meters (m). iii. If you select the little icon in the top right corner that looks like a miniature graph you will see several pages of graphs using the data points you selected. You can slide through the pages by swiping your finger across the page. Your graph of vertical (y) velocity versus time should be roughly linear. We will send the data to a computer that will make further analysis easier. e. Select the sharing icon that looks like an arrow shaped into a U (top right). Select Data File and Mail, and enter an address to send the data to. 3. Before going to a computer to analyze your data further and see how the ball accelerated as it fell, repeat step 2 at least two more times. That is, collect at least three videos total of the ball as it falls, enter the points to track the ball as it falls, set the origin and scale, and the three sets of files to an address. It doesn t matter if you drop it from the exact height each time the experiment is repeated but the ball should be dropped from rest each time. 4. Go to a computer that has the Logger Pro software. The computers in all of the introductory physics labs have it, as well as the computer lab in SL 220. Once again, this is just being done to make the analysis a bit easier than it would be on a small IPad screen. You should have three pairs of files in your inbox. Each will have two files the actual video file and an accompanying Logger Pro file, that has extension.cmbl. a. Open the and save the two files (video and.cmbl) to the Desktop. b. Open the Logger Pro software by selecting Basic, Applications, Logger Pro and opening the Logger Pro launch file. Select Open, second icon from the top left, and open one of the.cmbl files that you saved to the Desktop. The Logger Pro software allows users to open a number of objects to be displayed on a single page, or to have several pages showing various data. In this.cmbl file there are four objects on your page. The top left corner should be the video you took. Below that is a data table for time, position and velocity. On the right are two graphs the top is position versus time and the bottom is velocity versus time. Each of these four objects can be moved, enlarged, deleted, etc. New objects could also be inserted, but we will not be doing that. You may have to move the video to see the data table if it is positioned on top of the table. Free Fall 3

4 c. Click on the video. You can enlarge the video to see it better by left clicking and dragging the bottom right corner of the object, if you like. You can push the play button in the bottom left corner to watch the video. There are several buttons along the right side of the video that can be used to analyze the object in the video. You have already selected the data points, set the origin and scale, so you will not need to use those buttons. d. The software has automatically populated the data table and two graphs based on the data points you selected for the ball s position as it fell. Wow! Your computer just did a ton of work generating data that Galileo would have had a much harder time measuring. Take a few minutes to look at the data table and the graphs. The x-direction is the horizontal direction. The y-direction is the vertical direction. In the data table, the first column lists the time at which each of your data points was selected, with 0s being the time that the video was started. Then using the origin you provided and the object of known length, the data table for the x and y position of the ball at each data point is filled in. The calculation of the velocity of the ball at each data point is a little more complicated. Basically the computer determines how the position has changed from one frame to the next and divides this by the time between frames, giving distance/time or velocity. Answer question 2 of the report. e. The first graph on the right depicts Position versus Time. The horizontal, x position is shown in red and the vertical, y position is shown in blue as a function of time along the bottom axis. The software shows the scaling for the two on two different scales, with the horizontal position being along the left vertical axis and the vertical position along the right vertical axis. Confused yet? Let s fix that, and remove the horizontal data since the ball is not really moving in the horizontal direction very much. Right click on the graph and select Graph Options which will open a window. Select Graph Options along the top of the window and type Vertical Position versus Time as the graph title. Click off Connect Points under Appearance which will remove the lines connecting the data points on the graph. Now select Axes Options on the top of this window and click off Right Y-Axis. This will remove the second scale on the right of the graph. Under Y Axis type Position (m) as the Label, and click off X (m) and select Y (m) beneath the Y Axis Column so that only the Y position data will be shown on the left of the graph. Select Done. You should now have a graph with a title and a single set of data that illustrates the vertical position as a function of time. If your graph shows no data (is empty), right click it again to go the Graph Options window and make sure that Y(m) is selected for the Y Axis. Answer question 3 in the report. f. The lower graph on the right depicts Velocity versus Time. Make the same changes that you made to the Position versus Time graph. Title this graph Vertical Velocity versus Time, remove the lines that connect the data points, remove the scaling on the right vertical axis and put just the vertical (y) velocity data on the left of the graph and label this axis Velocity (m/s). Answer question 4 in the report. g. Acceleration is a change in velocity. If acceleration is constant, the velocity changes at a constant rate. Answer questions 5, 6 and 7 in the report. Free Fall 4

5 h. Since acceleration is a change in velocity, the slope of a velocity versus time graph can be used to measure the acceleration. Logger Pro can calculate the average slope of your velocity versus time graph. Select the velocity versus time graph and the select the icon that looks like a straight line (Linear Fit) on the icon toolbar at the top of the Logger Pro window. A black line will be added to your velocity graph (lower graph) representing the best fit line for your data and a text box on the graph will give the values for this fit. Answer question 8 in the report. You have just measured the acceleration due to gravity on the surface of the Earth! This is a very important number, and simply by videoing an object as it falls and analyzing how its position (and thus its velocity) changes in time, you were able to determine a super fundamental physics constant, g. i. Print a copy of your Logger Pro file for each group member to hand in with the report by selecting the Print icon. 5. Repeat step 4 for your remaining two Logger Pro (+video) files. Record your data in Table 1 of the report, computing the average and standard deviation for your measured value of g. Part 2: Dependence of Free Fall Acceleration on the Mass of the Object 1. Drop a different ball that has a significantly different mass than the mass of the first ball you dropped. Use Video Physics to video the object as it falls, select the data points for the position of the falling ball, and set the origin and scale for the video. the data files (video file + Logger Pro file) to an address. On a computer that has the Logger Pro software, open the Logger Pro file (.cmbl). Adjust the graphs to be y-position versus time and y-velocity versus time, and determine the slope of the y-velocity versus time graph to measure the object s vertical acceleration. Print the Logger Pro file for each group member to turn in with the lab report. 2. Answer questions 9 and 10 in the lab report. Part 3: Free Fall and Air Resistance Up to this point, we have assumed that as an object falls the only force that acts on the object is the Earth s gravity pulling it down. This assumption works well for many objects, including the balls you have dropped in parts I and 2. This assumption works reasonably well most of the time. As long as gravity is MUCH greater than air resistance, then it is okay to neglect air resistance all together. If air resistance is comparable in magnitude to the force of gravity acting on the object, then air resistance becomes important. If the surface area of an object is large then air resistance is large, and if the mass of the object is small then gravity is small. So, air resistance must be included for large surface area Free Fall 5

6 objects that don t have very much mass, such as a parachute, or perhaps easier to find, a coffee filter or beach ball. 1. Drop an object for which you think air resistance is significant. Go through the same steps of videoing the object, selecting data points to track the position of the object, ing the file, opening the file in Logger Pro, and adjusting the graphs to be y-position versus time and y- velocity versus time. You do not need to do a linear fit on the velocity versus time graph. Print the Logger Pro file for each group member to hand in with the report. 2. Answer questions 11, 12, 13 Free Fall 6

7 Report: Free Fall Name: Partner: Date: Part 1: Determining Gravitational Acceleration, g 1. What object will you use to calibrate the vertical distance? This object should roughly be in the same plane as the dropped ball. Object: Vertical height: 2. What was the time for your first data point? Does this make sense? 3. Describe in your own words, the vertical position of the ball as a function of time. Are the values for the position positive or negative? What does this indicate about the position? Is it increasing, decreasing or constant? Is it linear (a straight line) which would indicate the vertical position changes at the same rate as time passes? If it is not linear, does the vertical position change more quickly at the beginning of the fall or at the end? Free Fall 7

8 4. Describe in your own words, the vertical velocity of the ball as a function of time. Are the values for the velocity positive or negative? What does this indicate about the velcoity? Is the object speeding up, slowing down or is it s speed remaining constant? Is it linear (a straight line) which would indicate the vertical velocity changes at the same rate as time passes? If it is not linear, does the vertical velocity change more quickly at the beginning of the fall or at the end? 5. By looking only at the vertical position versus time data, can you determine if the ball has a constant acceleration? Explain. 6. By looking only at the vertical velocity versus time data, can you determine if the ball has a constant acceleration? Explain. 7. As your ball fell, was its acceleration constant? Explain how you came to this conclusion. Free Fall 8

9 8. What is the value of the slope of your velocity versus time graph? What physical quantity does the slope represent? Does this value seem reasonable? Explain Table 1 Trial g (m/s 2 ) Average value for g: Standard Deviation for g: Part 2: Dependence of Free Fall Acceleration on the Mass of the Object First Ball dropped in part 1: Free fall acceleration, g: (average +/- std. dev.) + / - Second Ball dropped in part 2: Free fall acceleration, g: 9. Did the free fall acceleration of the second ball fall within one standard deviation of the free fall acceleration you measured in part 1? (yes or no) Free Fall 9

10 10. Prior to Galileo, people believed that heavier objects fell faster than lighter objects. Galileo experimentally measured this by dropping bricks of different sizes and concluded that all objects fall at the same rate, no matter what the mass was. Based on your experimental measurements, describe what you observe for the relationship between free fall acceleration and the mass of the falling object. Part 3: Free Fall and Air Resistance Object dropped: 11. Look at your graph of vertical (y) velocity as a function of time. If your object has significant air resistance as it falls, this graph should look different than the velocity versus time graphs you had in parts 1 and 2. Describe the differences between this graph and your previous velocity versus time graphs. 12. Does this object have constant acceleration as it falls? Explain your answer. If the acceleration is not constant, is it increasing or decreasing as the object falls? 13. As the object falls it has two forces acting on it gravity pulling down and air resistance pushing up. The force of gravity on the object does not change as it falls. Does the force of air resistance acting on the object change as it falls or is it constant? If it is not constant, is it increasing or decreasing? Attach printouts of the 5 Logger Pro files (3 from part 1, 1 from part 2 and 1 from part 3). Free Fall 10