# Ball Toss. Vernier Motion Detector

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1 Experiment 6 When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time would show these changes. Is there a mathematical pattern to the changes in velocity? What is the accompanying pattern to the position vs. time graph? What would the acceleration vs. time graph look like? In this experiment, you will use a Motion Detector to collect position, velocity, and acceleration data for a ball thrown straight upward. Analysis of the graphs of this motion will answer the questions asked above. OBJECTIVES Collect position, velocity, and acceleration data as a ball travels straight up and down. Analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs. Determine the mean acceleration from the acceleration vs. time graph. MATERIALS computer Vernier computer interface Logger Pro Vernier Motion Detector dodge ball PRELIMINARY QUESTIONS (6 points) Think about the changes in motion a ball will undergo as it travels straight up and down. Sketch your predictions of the motion on the axes below. Make sure to line up specific points on each graph with the one above it. Physics with Computers 6-1

2 Experiment 6 PROCEDURE 1. Plug the Motion Detector into the DIG/SONIC Place the Motion Detector on the floor. 3. Open the file 06 Ball Toss from the Physics with Vernier folder. 4. In this step, you will toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector. Try to catch it about the same height you threw it. This step may require some practice. Repeat until you get a good set of graphs! Make sure your hands don t get in the way! 5. Examine the velocity vs. time graph. Repeat Step 4 if your velocity vs. time graph does not have a nice line with a negative slope. ANALYSIS 1. Print a copy of the graphs. (Please only print page 1.) Colored pencils or markers may help here. a) (1 point) Find the highest point on the position vs. time graph. Draw a vertical line from this graph down through all the other graphs. b) Identify the region when the ball was being tossed but was still being touched by your hands: (1 point) Examine the velocity vs. time graph and identify this region. Label this on the graph. (2 points) Examine the position vs. time and acceleration vs. time graphs and identify the same region. Label the graph. c) Identify the region where the ball is in free fall: upward. downward. d) Determine the position, velocity, and acceleration at specific points. Click the Examine button,, and move the mouse across any graph to answer the following questions. (1 point) On the velocity vs. time graph, decide where the ball had its maximum velocity, just as the ball was released from your hands after being thrown upward. Mark the spot and record the value on the graph. (1 point) On the position vs. time graph, locate the maximum height of the ball during free fall. Mark the spot and record the value on the graph. (1 point) Keeping the line from the Examine button through all the graphs, follow it down to the velocity vs. time graph. What was the velocity of the ball when it was at the top of its motion? Mark the spot on the velocity vs. time graph that shows this value. Record the value on the graph. (1 point) Keep following the line down to the acceleration vs. time graph. What was the value of acceleration when the ball was at the top of its motion? Mark the spot on the acceleration vs. time graph that shows this value. Record the value on the graph. 2. (2 points) The graph of acceleration vs. time should appear to be more or less constant. Click 6-2 Physics with Computers

3 and drag the mouse across the free-fall section of the acceleration vs. time graph and click the Statistics button,. Mean acceleration How closely does the mean acceleration value compare to the accepted value of g (9.8 m/s 2 )? 3. (1 point) Give one reason why your values for the ball s acceleration may be different from the accepted value for g. EXTENSIONS (EXTRA CREDIT) Instead of throwing a ball upward, drop a ball and have it bounce on the ground from a predetermined height. (Position the Motion Detector above the ball.) Print and analyze the resulting graphs. Label the point on each graph where the ball was let go. Label the point on each graph where the ball hit the floor. Identify the region(s) of the graph where the ball is in free fall. Label the velocity of the ball just the instant before it hit the ground. - Now, assume you did not know the velocity you just read recorded. Measure the height from which you dropped the ball. Use kinematics equations to calculate the speed that the ball should hit the floor. How does this value compare to the velocity measured by Logger Pro? Click and drag the mouse across a free-fall section of the motion on the acceleration vs. time graph and click the Statistics button,. Mean acceleration: How closely does the mean acceleration value compare to the accepted value of g (9.8 m/s 2 )?

4 Experiment 6 Physics Ball Toss Lab Answer Sheet PRELIMINARY QUESTIONS (6 points) Think about the changes in motion a ball will undergo as it travels straight up and down. Sketch your predictions of the motion on the axes below. Make sure to line up specific points on each graph with the one above it. ANALYSIS 1. Print a copy of the graphs. (Please only print page 1.) Colored pencils or markers may help here. a) (1 point) Find the highest point on the position vs. time graph. Draw a vertical line from this graph down through all the other graphs. b) Identify the region when the ball was being tossed but was still being touched by your hands: (1 point) Examine the velocity vs. time graph and identify this region. Label this on the graph. (2 points) Examine the position vs. time and acceleration vs. time graphs and identify the same region. Label the graph. c) Identify the region where the ball is in free fall: upward. downward. d) Determine the position, velocity, and acceleration at specific points. Click the Examine button,, and move the mouse across any graph to answer the following questions. (1 point) On the velocity vs. time graph, decide where the ball had its maximum velocity, just as the ball was released from your hands after being thrown upward. Mark the spot and record the value on the graph. 6-4 Physics with Computers

5 (1 point) On the position vs. time graph, locate the maximum height of the ball during free fall. Mark the spot and record the value on the graph. (1 point) Keeping the line from the Examine button through all the graphs, follow it down to the velocity vs. time graph. What was the velocity of the ball when it was at the top of its motion? Mark the spot on the velocity vs. time graph that shows this value. Record the value on the graph. (1 point) Keep following the line down to the acceleration vs. time graph. What was the value of acceleration when the ball was at the top of its motion? Mark the spot on the acceleration vs. time graph that shows this value. Record the value on the graph. 2. (2 points) The graph of acceleration vs. time should appear to be more or less constant. Click and drag the mouse across the free-fall section of the acceleration vs. time graph and click the Statistics button,. Mean acceleration How closely does the mean acceleration value compare to the accepted value of g (9.8 m/s 2 )? 3. (1 point) Give one reason why your values for the ball s acceleration may be different from the accepted value for g. EXTENSIONS (EXTRA CREDIT) Instead of throwing a ball upward, drop a ball and have it bounce on the ground from a predetermined height. (Position the Motion Detector above the ball.) Print and analyze the resulting graphs. Label the point on each graph where the ball was let go. Label the point on each graph where the ball hit the floor. Identify the region(s) of the graph where the ball is in free fall. Label the velocity of the ball just the instant before it hit the ground. - Now, assume you did not know the velocity you just read recorded. Measure the height from which you dropped the ball. Use kinematics equations to calculate the speed that the ball should hit the floor. How does this value compare to the velocity measured by Logger Pro? Click and drag the mouse across a free-fall section of the motion on the acceleration vs. time graph and click the Statistics button,. Mean acceleration: How closely does the mean acceleration value compare to the accepted value of g (9.8 m/s 2 )?

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