Mechanics a School Course

Cover Mechanics a School Course
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However there is less kinetic energy after impact than before, owing to the loss already alluded to. If the kinetic energies before and after impact are E L, E 2, then E - E 2 is the lost energy. If e is the kinetic energy at the middle of the impact, E l e is the energy which ought to have been stored up as potential energy. The lost energy is a fraction of this which depends on the materials of the bodies. Let k be this fraction. Then E i -E, = k(E i -e], which gives E. 2 e = (l-k)(E l e).
No
...w EI = \ mi Uj 2 + 5 w 2 w a 2 E 2 = % nii v* + | ra 2 vj and, if F be the velocity of the two spheres at the middle of their contact, e = ^(m 1 + m 2 ) F 2 .
But mj UL + m 2 u 2 = m^ v t + m 2 v. 2 = (m^ + m 2 ) F (see 53), i 1 2 1 ' 2 Als This gives e = \/\-k.
(i) When the coefficient of restitution is -{g, what fraction of the kinetic energy is lost at impact?
(ii) If the loss of kinetic energy at impact is 10 per cent. , what is the ratio of the relative velocities before and after impact?
136.


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