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Simulation of Fan Cart Motion: Analyzing Constant Force Impact on Velocity and Time

This project involves a simulation of a fan cart's motion, emphasizing the relationship between net force and velocity over time. The scenario features a 0.057 kg tennis ball struck at 54 m/s, colliding with a wall and reversing direction. We aim to calculate the duration between impact and momentary halt, and determine the net force during the collision. The simulation uses the Euler-Cromer method for numerical integration under the assumption of constant net force and small time intervals. Proper initial conditions and assumptions will be stated clearly in the program.

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Simulation of Fan Cart Motion: Analyzing Constant Force Impact on Velocity and Time

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  1. CH02-1 Constant Net Force

  2. x-velocity vs. time graph Theory fan cart

  3. displacement Theory

  4. arithmetic mean velocity Theory assuming a constant velocity of vx,avg gives the same result.

  5. Fnet vs. time graph Theory fan cart

  6. Summary of Analytic Method Theory

  7. Analytic Method in 1-D Theory

  8. Example A tennis ball has a mass of 0.057 kg. A professional tennis player hits the ball hard enough to give it a speed of 54 m/s (about 121 miles per hour.) The ball moves toward the left, hits a wall and bounces straight back to the right with almost the same speed (54 m/s). As indicated in the diagram below, high-speed photography shows that the ball is crushed about 2 cm at the instant when its speed is momentarily zero, before rebounding. How much time elapses between first hitting the wall and momentarily stopping? What is the net force on the ball during the collision? video

  9. Numerical (computational) integration Computation Assumptions: constant net force, small ∆t

  10. Numerical error Computation Assumptions: constant net force, small ∆t Error can be decreased by using a smaller time interval. Also, using the mean velocity is clearly a better estimate than using the final velocity. Decide at this point to accept the error, but select a reasonable time interval to reduce the error. Error

  11. Summary of Numerical Method Computation Assumptions: constant net force, small ∆t At this point, you are using the Euler-Cromer Method (semi-implicit Euler Method) to solve the differential equations: with

  12. VPython Write a simulation that models the motion of a fan cart. Clearly state your assumptions and your initial conditions before starting your program.

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