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A steel ball strikes a steel plate at an angle with the vertical . If the coefficient of restitution is e, the angle at which the rebound will take place is

A steel ball strikes a steel plate at an angle with the vertical . If the coefficient of restitution is e, the angle at which the rebound will take place is

Grade:12

1 Answers

S PRASANTH
8 Points
12 years ago

Consider the steel plate to be lying on the floor. Let the coefficient of friction between the plate and ball be n. Let the vertical component of velocity be y & horizontal component be x. Let time of collision be t(tending to zero). Final vertical component of velocity after collision is ey.

If average (normal) force during collision is F,

Ft  =  m ( y + ey)            where m is mass of ball              

Average frictional force ffriction =   F=  m (y + ey) n  / t 

So    m (y + ey) =  m  (x - xfinal)

xfinal  x - n (y + ey

Let angle of rebound be a with vertical

tan a =  (   x - n (y + ey  )   /    ey  =  (tan b) / e   -   n/e     -  n            where b is angle of striking of steel ball with the vertical

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