ANALYSIS OF IMPACT FORCE VARIATION DURING COLLISION OF TWO BODIES USING A SINGLE-DEGREE-OF-FREEDOM SYSTEM MODEL

Abstract

In elementary dynamics, the concept of a large force acting for a short time is used to simplify the analysis of impulsive motion of two masses undergoing collision. When the duration of impact is known, the average force of impact can be estimated from the momentum exchange between the masses. Additional information on the impact force variation is extracted in the present analysis by using a linear spring–damper contact model. The analysis relates this force variation to the average force and the coefficient of restitution between the masses. The deviation of the coefficient of restitution from unity is the effect of the internal damping in the materials and this deviation increases with damping. As the damping increases, the maximum impact force decreases initially until it reaches its minimum as the coefficient of restitution approaches 0·49. Further increase in damping results in an increase in the maximum force at an increasing rate, which becomes significantly large when the coefficient of restitution falls below 0·3.