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Collisions

Collisions

by Nitish Mittal -
Number of replies: 1

1.     On page no 149 of H.C.Verma (vol 1) it is written that in the case of elastic collision in 2 dimensions “ the final motion depends on the angle between the line of force during collision and direction of initial velocity. The momentum of each object must be individually conserved in the direction perpendicular to the force. ”

 

a)     What is this line of force?

b)    Why does the final motion depend on the angle between the line of force during collision and direction of initial velocity?

c)     Why the momentum of each object must be individually conserved in the direction perpendicular to the force?

In reply to Nitish Mittal

Re: Collisions

by Ankul Garg -
a) During elastic collision between two bodies, each body exerts an impulsive force on the other body at the point of contact. These pair of impulsive forces are equal and opposite in direction and act along the line joining the two centres of the two bodies and also the point of contact lies on this line only. Specifically, this line is known as Common Normal or line of Force.

b) Since the net force on the system along the common normal is zero (the two impulsive forces being equal and opp. cancel out when the system is taken as a whole), therefore, we can conserve the momentum of system along the common normal. Thus, the component of velocities  (that would bring the angle b/w common normal and direction of intitial velocity into consideration)  of the two bodies along the common normal will be taken into account. This means the final velocities will depend upon the above mentioned angle.

c) On each indiviadual body, the component of impulsive force along an axis perpendicular to line of force or common normal will be zero. Thus, the momentum of each individual body will remain conserved along this axis which is commonly known as common tangent.

I hope you must find my answer helpful in clearing your doubt.
- ANKUL GARG
  XIIth
  DELHI