Overview
The primary purpose of the Collisions simulation is to provide students a realistic environment where they can explore and better understand the concepts in Newtonian mechanics using fundamental mechanics methods. In the Collisions simulation, experiments are performed in a framework consistent with the other virtual simulations; that is, students are put into a virtual environment where they are free to choose their objects and equipment, build a conceptual experiment of their own design, and then experience the resulting consequences. The focus in the simulation is to allow students the flexibility to perform many fundamental experiments to teach the basic concepts of Newton’s laws that are easier to model in a simulated situation rather than a real laboratory. The ability to control the frictions, forces, and physical parameters of motion allows students the ability to easily use equipment that can be found in most instructional laboratories and some equipment that would be less readily available. Students are able to measure speeds and distances, describe the motion of objects using graphs, interpret data and gain a foundation for concepts in physics. These results can then be used to validate Newton’s laws; demonstrate the interplay between force and motion and calculate conservation of momentum.
Simulation Assumptions and Equations
Basic Newtonian force equations were used to model the motion of the objects within these experiments. All force equations were solved using a Runge Kutta Fehlberg Forth-Fifth (RKF45) numerical method to solve the differential equations. The two second derivative equations were manipulated into four first order equations and then integrated through RKF45 to find the position and the velocity equations of motion of the objects. The assumptions and generalizations made are described below.
| Objects | We have not modeled the twisting, bending, compression, or other physical deformations that could occur throughout the experiments. The ball is assumed to be a point mass with a defined radius. |
| Gravity | In most cases the gravity is taken to be equal to one g on earth or 9.80665 m/s2. The various types are described below. There are four types of uniform gravity: up, down, left, and right. These create a gravitational field in the chosen direction whenever they are placed in the motion area. The limitation is one gravity can be chosen at a time, which implies that no gravity fields can be created in the diagonal direction. |
The assumptions and limitations of the force and friction are described below.
Forces. In the collisions laboratory there is only one type of force, a plunger force. The impulse force (plunger) hits the object with a chosen magnitude for a short period (default 0.05 seconds) of time thus giving the object an almost instantaneous initial velocity. The assumptions are those of an exact central hit from the plunger to prevent spin.
Frictions. A friction is considered something that opposes an object’s motion. In this laboratory there is only one type of friction available. Rolling friction is what is used to apply friction between a ball and the table. The simulation calculates the point at which perfect rolling without sliding occurs and applies sliding friction to the ball until that point. When the rotational velocity of the ball reaches the critical barrier to roll without slipping, then the ball just rolls with no frictional forces being applied. The assumption is taken that the perfectly round ball only comes in contact with the ground at exactly one spot and when perfectly rolling, the velocity of the ball at that point is zero, so no forces act upon it. For this reason, once a ball reaches perfect rolling conditions, it will roll without resistance.