Springbok: The physics of jumping

Abstract

The physics of jumping is explored for a simple spring-loaded toy. The toy is easy to make and easy to analyze using an elementary Hooke’s law model. Possible uses in introductory physics are described. Conceptual and pedagogical issues are discussed

From mechanics to thermodynamics—analysis of selected examples

“…We stress that the second equation is not an expression of an 'energy-work' theorem since the external normal force exerted by the wall does not produce any work [21]. If the force does no work, where is the source of energy responsible for the increase of the centre-of-mass kinetic energy?…”

Simple model of a standing vertical jump

“…Accurate biomechanical models of humans can go as far as having 16 rigid bodies joined together comprising 38 degrees of freedom [13], which resists any attempts at an analytic solution. Analytic solutions for the jumping motion of springs [14,15] have been made, but as the forces are not constant, they require the solving of differential equations. The simple, torqueless, algebraic model presented here can serve as a budget model against which more sophisticated models [16] can be compared.…”

Simple Model of a Standing Vertical Jump

“…Accurate biomechanical models of humans can go as far as having 16 rigid bodies joined together comprising 38 degrees of freedom [8], which resists any attempts at an analytic solution. Analytic solutions for the jumping motion of springs [9,10] have been made, but as the forces are not constant, they require the solving of differential equations. In theory at least, students who know the principles of physics but lack knowledge of calculus can model a varying force by partitioning the force over many small intervals and assuming the force is constant within each interval.…”