242 MOTION OF SYSTEMS OF PARTICLES 



Thus there is a normal impulse of amount emv, and this gener- 

 ates a velocity ev in the particle. There is no tangential impulse, 

 for there is no sliding of the surfaces past one another. Thus the 

 velocity of rebound is a velocity ev normal to the surface. 



Oblique Impact : Smooth Contact 



199. If the impact is oblique, let us suppose that the components 

 of velocity along the tangent plane and along the normal before 

 impact are u, v. As before, w"e find 



/= mv, I 1 = emv, 



so that the normal velocity after impact, say v', is 



v' = ev. 



If the contact is supposed smooth, there can be no force in the 

 tangent plane, so that the momentum in the tangent plane remains 

 unaltered. Thus the velocity in the tangent plane remains equal 

 to u, and the velocity after impact will be one of components u, ev. 

 Let 6 be the angle which the velocity before 

 impact makes with the normal, and let </> be the 

 corresponding angle after impact. Then 



tan 6 = > 



v 



u 

 tan (b y 



ev 



so that tan e tan <f>. 



If the bodies are perfectly elastic, e = 1, so that 

 = (f> i.e. the particle rebounds at an angle equal 

 to the angle of incidence. Its reflexion obeys the same law as 

 that of a ray of light. 



If the bodies are imperfectly elastic, is less than </>, so that 

 the path is bent away from the normal. 



If the bodies are perfectly inelastic, e = 0, so that <f> = ; the 



2 



particle simply slides along the plane, as of course it obviously 

 must since /'= 0. 



