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Lab 8 “Energy of a Tossed Ball.” Motion Detector In this experiment, we will study energy changes using a Motion Detector. OBJECTIVES: • • Measure the change in the kinetic and potential energies as a ball moves in free fall. See how the total energy of the ball changes during free fall. MATERIALS: Computer Lab Pro Logger Pro Vernier Motion Detector Basketball; PRELIMINARY QUESTIONS: For each question, consider the free-fall portion of the motion of a ball tossed straight upward, starting just as the ball is released to just before it is caught. Assume that there is very little air resistance. 1. What form or forms of energy does the ball have while momentarily at rest at the top of the path? _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ 2. What form or forms of energy does the ball have while in motion near the bottom of the path? _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ 3. Sketch a graph of velocity vs. time for the ball, kinetic energy vs. time for the ball, and potential energy vs. time for the ball. 1 PROCEDURE: 1. Measure and record the mass of the ball you plan to use in this experiment. 2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. Place the Motion Detector on the floor and protect it by placing a wire basket over it. 3. Hold the ball directly above the Motion Detector. Have your partner click to begin data collection. Toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector catch the ball before it hits the detector. Note: Use two hands, be sure to pull your hands away from the ball after it starts moving so they are not picked up by the Motion Detector. Throw the ball so it moves vertically above the detector. Verify that the position vs. time graph corresponding to the free-fall motion is parabolic in shape, without spikes or flat regions, before you continue. This step may require some practice. If necessary, repeat the toss, until you get a good graph. When you have good data on the screen, proceed to the Analysis section. 4. Click on the Examine button, , and move the mouse across the position or velocity graphs of the motion of the ball to answer these questions. a. Identify the portion of each graph where the ball had just left your hands and was in free fall. Determine the position and velocity of the ball at this time. Enter your values in your data table. (after release) b. Identify the point on each graph where the ball was at the top of its path. Determine the time, position, and velocity of the ball at this point. Enter your values in your data table. (top path) c. Identify the point where the ball is moving downward, but a short time before it was caught. Measure and record time, position, and velocity of the ball at that time. (before catch) d. Collect two more times on the way up and on the way down for a total of seven data points. e. For each of the seven points in your data table, calculate the Gravitational Potential Energy (GPE), Kinetic Energy (KE), and Total Energy (TE). Use the position of the Motion Detector as the zero of your gravitational potential energy. Theory. A ball is toss straight upward with initial velocity without friction, we can describe the position and velocity using the kinematics equations of UAM. The velocity is 𝑣 = 𝑣0 − 𝑔𝑡 (1) The position y is 𝑦 = 𝑦0 + 𝑣0 𝑡 − 1/2 𝑔𝑡^2 (2) The kinetic energy is 𝐾 = 1/2 𝑚𝑣^2 (3) The potential energy is PE=mgy (4) The total mechanical energy is E=K+PE (5) 2 Mass of the ball (kg) 0.5 Position Time (s) position (m) Velocity (m/s) After release 0 0.03 4.85 On the way up 0.11 0.44 3.82 On the way up 0.23 0.85 2.56 On the way up 0.35 1.06 1.37 Before the Top 0.45 1.15 0.38 Top of path 0.49 1.21 0.01 After the Top 0.56 1.12 -0.07 going down 0.67 1.03 -1.72 going down 0.75 0.82 -2.46 going down 0.84 0.55 -3.51 Before catch 1.02 0.05 -4.95 GPE (J) KE (J) TE (J) 3 ANALYSIS: 1.Complete the data table with the received information and the given formulas. Show your calculations 2.Use Logger Pro and graph V vs time t. Identify the slope. Using slope calculate g experimental. 3.Use Logger Pro graph Y vs time t. 4.Use Logger Pro graph PE vs t. 5.Use Logger Pro Graph K vs t. Inspect your gravitational potential energy vs. time graph for the free-fall flight of the ball. Explain its shape 6.Use Logger Pro Graph E vs t. Inspect your Total energy vs. time graph for the free-fall flight of the ball. Explain its shape 7. What do you conclude from this graph about the total energy of the ball as it moved up and down in free fall? Does the total energy remain constant? Should the total energy remain constant? Why? If it does not, what sources of extra energy are there or where could the missing energy have gone? 8. What would change in this experiment if you used a very light ball, like a beach ball? Why? 9. What would happen to your experimental results if you entered the wrong mass for the ball in this experiment? 10. Write a statement of the Law of Conservation of Energy and its mathematical representation. 11. What was the principal force acting in this experiment? Does the force Conservative or nonconservative forces? Explain. Write the goal and the conclusions. 4
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