Motion of Whiplash

Abstract

We propose to study the wave motions on a whip using numerical study of associated partial differential equations with specific goals of explaining the supersonic speeds of the tip, under various boundary conditions and structural parameters, which is responsible for the crack and concentrated damaging power associated with a whip lash. In light of above, the problem for us is to study the wave motion of the whip and construct a suitable mechanical model which can explain the main distinguishing feature of the whip i.e., high speed of the tip as well as study the motion of wave on the whip and study its general characteristics. We have found that the factors which are important in the crack of a whiplash are varying thickness of the lash, stiffness of the whip, and jerk applied to the whip. The mass of the whiplash plays very vital role in the motion of the whip. Usually the whip is thicker from the end which is attached to the handle and becomes thinner as we move along the lash towards the tip. The density will decreases as the square of the length across the lash for a linear decrease in the thickness of the lash. We find that this tapering of the thickness is crucial for the speed gain of the tip and higher variation cause higher speed gain and crack. It is also confirmed that a whip having some stiffness in its lash is more effective in producing higher speeds of the tip.In modeling an actual whip, we have also found that jerk plays very important role. The speed of the tip depends on the jerk given to the lash for wave motion. For the sudden jerk, the increase in tip speed is dramatic which has that cracking sound and the painful effect which we need.For out model the tip speed dramatically increase upto about 30-40 times than the speed at the starting point. This tip speed is on the top of overall motion of the whip. This speed crosses the speed of sound easily. Speed gain is 30-40 times at the tip. It is moving with very high speed that it can cross speed of sound, this is also called sonic boom. This high speed of the tip cause that excessive pain which we need to drive an animal