Analysis of standing vertical jumps using a force platform

A force platform can be an excellent teaching aid in undergraduate physics classes and laboratories. Recently, Cross showed how to increase student interest and understanding of elementary mechanics by using a force platform to study everyday human movement such as walking, running, and jumping. My experiences with using a force platform in undergraduate classes have also been highly favorable. The aim of this article is to show how a force platform analysis of the standing vertical jump may be used in teaching the kinematics and dynamics of one-dimensional motion. I use computer software that produces curves of velocity and displacement of the jumper’s center of mass by numerical integration of the force–time record from a force platform. A simultaneous examination of these curves gives an effective illustration of the relations between the forces acting on a body and the resulting acceleration, velocity, and displacement of the body. The curves obtained from the force platform may also be used to calculate the height of the jump, and three methods are presented here. The most straightforward method is to determine the time spent in the airborne phase and then use the kinematic equations for one-dimensional motion under constant acceleration. A more accurate method of determining the jump height is to apply the impluse–momentum theorem to the force–time record, and this provides an interesting example of numerical integration. The jump height may also be calculated by applying the work–energy theorem to the force–displacement curve, again using numerical integration.