大学物理演示实验.doc

Bounce of a Balll AimThe aim of this experiment is to study inelastic collision. In this experiment, the momentum is conserved while the mechanical energy is no. In particular, we will determine the coefficients of restitution of the given basketball, football, tennis ball and ping-pong ball in the experiment when they collide with the force platform by using the data returned by the sensors. We will also compare the experimental values with the theoretical ones. l BackgroundThis experiment is about inelastic collision. Inelastic collision is very different from elastic collision. In elastic collision, the total mechanical energy is conserved. The energy of the system will not be transferred to its surroundings and the speed of the object will still remains the same. In inelastic collision, the speed of the object involved in the collision will become smaller due to the energy loss. The radio of the rebound speed and the initial speed is defined as the coefficient of restitution.e=v2v1In this equation, v1 is the initial speed of the object before collision. v2 is the rebound speed after the collision. If there is no air resistance, only gravity will act on the ball. So according to the equation that h=v2g. e=v2v1=h2h1h1 is the maximum height the ball can reach before the collision, h2 is the maximum height the ball can reach after the collision.To do this experiment, we need PASCO Motion Sensor PS-2103, PASCO Pasport USB Link PS-2100, PASCO Force Platform PS-2141 and basketball, football, tennis ball and ping-pong ball. We also need a computer with DataStudio to help us to plot the diagrams.l Experiment procedureA、 Preparation of the experimentSet up the equipments as Figure 1.Figure 11、 Make sure that motion sensor and force platform were properly connected to the USB Link and could be recognized by the computer operating system. 2、 Start DataStudio in the desktop computer and set the sampling rate of motion sensor to 50Hz. Adjust the height of the motion sensor to the ground as 1.655m and then calibrated the distance in DataStudio. 3、 Check the Position, Velocity and Acceleration option to make sure the sensor could return back all the data wanted. 4、 Set the sampling rate of the force platform to 1000Hz and calibrate it so that its reading could be zero when nothing was put on it. 5、 Make the motion sensor be horizontal and just point towards the center of the force platform. 6、 Conduct a trial run to examine whether the setting is properly done.B、 Procedure of the experiment1、 Hold the basketball a distance from the motion sensor. 2、 Press the start button on the computer3、 Release the basketball from the initial position and make sure it bounces at least three times on the platform. 4、 Click the stop button and remove the ball.5、 Use the Datastudio to plot the graph of position vs. time, velocity vs. time, acceleration vs. time, and vertical force vs. time.6、 Use the Datastudio and the graph of position vs. time to plot the graph of potential energy vs. time. sUse the Datastudio and the graph of velocity vs. time to plot the graph of kinetic energy vs. time.7、 Save the data in TXT files and the graph in JPEG.8、 Repeat the previous steps using football, tennis ball and ping-pong ball.9、 Calculate the coefficient of restitution and the impulse of the ball.l Result & Discussion1、 Result for basketballTo calculate the coefficient of restitution, we use the graph plotted by the DataStudio. Graph 1 is the graph of position vs. time of the basketball, which is the distance from the motion sensor to the basketball.Graph 1In the beginning, the data is not very good since the basketball bounce on the edge of the platform. So I choose the data from 3.5 second to 6.5 second. Use the data from the TXT file we can know that before it bounces at the first time during this period, the height is about 0.522m. And subsequently the heights are 0.445m, 0.395m, 0.357m and 0.329m. The statistics are shown in table 1.Collision No.Height before collisionHeight after collisioneFirst collision0.522m0.445m0.852Second collision0.445m0.395m0.888Third collision0.395m0.357m0.904Fourth collision0.357m0.329m0.922Table 1The average e is 0.903.Graph 2 We can also calculate the coefficient of restitution using the velocity. I also use the statistics from 3.5 second to 6.5 second. Use the data from the TXT file we can know that before it bounces at the first time during this period, the speed is about 2.06m/s. And subsequently the velocities are 1.69m/s, 1.51m/s and 1.29m/s and 1.07m/s. The statistics are shown in table 2.Collision No.Velocity before collisionVelocity after collisioneFirst collision2.06m/s1.69 m/s0.820Second collision1.69 m/s1.51 m/s0.893Third collision1.51 m/s1.29 m/s0.854Fourth collision1.29 m/s1.07 m/s0.829Table 2The average e is 0.849. The weight of the basketball is 5.9N. So mass of the basketball is about 0.6kg. So According to the equation I=-Mv, we can show the magnitude of impulse in the table 3, pointing upwards.Collision No.Velocity changeImpulseFirst collision3.65m/s2.19kg m/sSecond collision3.20m/s1.92kg m/sThird collision2.80 m/s1.68kg m/sFourth collision2.36 m/s1.42kg m/sTable 3 We can see from table 3 that the impulse of the ball is becoming smaller and smaller, which can also be seen in the graph of acceleration vs. time, Graph 3 and the graph of vertical force vs. time, Graph 4.Graph 3Graph 4 We can also see that there are energy loss in the graph of potential energy vs. time, Graph 5, and the graph of kinetic energy vs. time, Graph 6.Potential Energy (J)Graph 5Kinetic Energy (J)Graph 62、 Result for footballGraph 7 is the graph of position vs. time of the football, which is the distance from the motion sensor to the football.Graph 7From the data of the graph and the TXT file we can calculate the e. The statistics are shown in table 4.Collision No.Height before collisionHeight after collisioneFirst collision1.255m0.878m0.700Second collision0.878m0.641m0.730Third collision0.641m0.485m0.757Fourth collision0.485m0.396m0.816Table 4 The average e is 0.751.Graph 8 We can calculate the e using velocity shown in the Graph 8. The data is shown in table 5.Collision No.Velocity before collisionVelocity after collisioneFirst collision4.22m/s3.27 m/s0.775Second collision3.27 m/s2.56 m/s0.783Third collision2.56 m/s1.89 m/s0.738Fourth collision1.89 m/s1.60 m/s0.847Table 5 The average e is 0.786. Since the weight of the football is 4.1N, so the mass is 0.42kg. So according to I=-Mv, the magnitude of impulse is shown in table 6.Collision No.Velocity changeImpulseFirst collision7.49m/s3.15kg m/sSecond collision5.83m/s2.45kg m/sThird collision4.45 m/s1.87kg m/sFourth collision3.49 m/s1.47kg m/sTable 6We can see from table 6 that the impulse of the ball is becoming smaller and smaller, which can also be seen in the graph of acceleration vs. time, Graph 9 and the graph of vertical force vs. time, Graph 10.Graph 9Graph 10We can also see that there are energy loss in the graph of potential energy vs. time, Graph 11, and the graph of kinetic energy vs. time, Graph 12.Potential Energy (J)Graph 11Kinetic Energy (J)Graph 12For tennis ball and ping-pong ball, we could not get data that is good enough to show the tendency of the potential, velocity, vertical force and acceleration. So we cannot calculate the coefficient of restitution of the ball.According to the research, a leather basketball has a coefficient of restitution around 0.81-0.85.1 From table 1, the e is 0.903, which is 6% larger than the upper bound of the range. From table 2, the e is 0.849, which is in the range. For a football, the coefficient of restitution is about 0.8 2. From table 4, the e is 0.751, which is 6% smaller. From table 5, the e is 0.786, which is 2% smaller. The reason that the coefficient of restitution is different is that the material of the ground is different and the air resistance can influence the data.The influence of the air resistance can be shown in the table of the position. In the table, e will get larger after every collision. This is because that after every collision, the distance that the ball move