GROUND REACTION FORCE

Ground Reaction Force

Ground Reaction Force

Introduction

A force platform can be an excellent teaching aid in undergraduate physics classes and laboratories. Recently, Cross1 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.

Force, Acceleration, Velocity, and Displacement

During a vertical jump, the jumper must overcome body weight, and the resultant force acting on the jumper's center of mass (c.m).! is F GRF -mg, where F GRF is the ground reaction force acting on the jumper, m is the jumper's mass, and g is the acceleration due to gravity. Curves of force-time, acceleration-time, velocity-time, displacement-time, and force-displacement are calculated from the ground reaction force record obtained from the force platform. The time record of the resultant force acting on the jumper's c.m. is calculated by subtracting the jumper's body weight from the ground reaction force record.

The velocity-time record is obtained by dividing the resultant force-time record by the jumper's body mass to give the acceleration-time record, and then numerically integrating with respect to time using the trapezoid rule. The displacement-time record is obtained by numerically integrating the velocity-time record, again using the trapezoid rule. Higher order integration procedures such as Simpson's rule do not improve the precision of the calculated parameters signi?cantly.

The integration calculations require that the velocity and vertical height of the jumper's c.m. be known at some instant. I use the start position of the jump, where the velocity of the jumper's c.m. is zero and the vertical height is set to zero. In the JUMP ANALYSIS program, the start of the jump is selected by moving a cursor along the force-time curve. It must be stressed that the velocity and displacement calculations are very sensitive to the initial ...