Abstract
Simple experiments for which differential equations cannot be solved analytically can be addressed using an effective model that satisfactorily reproduces the experimental data. In this work, the 1D kinematics of a remote-control model (toy) car was studied experimentally and its dynamical equation modelled. In the experiment, maximum power was applied to the car, initially at rest, until it reached its terminal velocity. Digital video recording was used to obtain the relevant kinematic variables that enabled to plot trajectories in the phase space. A dynamical equation of motion was proposed in which the overall frictional force was modelled as an effective force proportional to the velocity raised to the power of a real number. Since such an equation could not be solved analytically, a dynamical model was developed, and the system parameters were calculated by non-linear fitting. Finally, the resulting values were substituted in the motion equation and the numerical results thus obtained were compared with the experimental data, corroborating the accuracy of the model.
Highlights
The kinematic and dynamic aspects associated with the motion of remote-control model cars and the electromagnetic aspects associated with the operation and the efficiency of their small built-in electric motor as well as with the transmission and reception of electromagnetic waves for controlling their motion deserve the attention of researchers and teachers of physics
Trajectories in the phase space are abstract constructs whose interpretation can prove conceptually very valuable as it allows students to qualitatively understand the temporal evolution of a system governed by a first-order differential equation, as would be the case of a falling object subjected to a velocity-dependent drag force or a variable-mass system
Use of readily available computer tools like Tracker enables the analysis of experimental kinematic data in a phase space and the development of a dynamical model based on the numerical solution to the system’s motion equation
Summary
Wick and Ramsdell [1, 2] modelled the motion of toy cars rolling down an arbitrarily defined track. In their experiment, turning points were expressed in terms of height loss relative to a hypothetical frictionless situation based on the static friction coefficient between the car and the track. Unlike the remote-control cars of our study, the cars used by Wick and Ramsdell were not driven by a built-in motor but rolled by the effect of gravity. Unlike the case with remote-control cars, the power input of a train can be changed arbitrarily by accurately adjusting the voltage delivered by an external regulated source of direct current
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