A 2.0 g particle moving at 7.8 m/s makes a perfectly elastic head-on collision w

Question

A 2.0 g particle moving at 7.8 m/s makes a perfectly elastic head-on collision with a resting 1.0 g object. (a) Find the speed of each after the collision. 1.) A 2.0 g particle 2.) A 1.0 g particle (b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g. 1.) A 2.0 g particle. 2.) A 1.0 g particle m/s (c) Find the final kinetic energy of the incident 2.0 g particle in the situations described in (a) and (b). KE in part (a) KE in part (b) In which case does the incident particle lose more kinetic energy? case (b) case (a)

Explanation / Answer

a] By Conservation of Momentum

Before Vcg = 2 /3 * 7.8 m/s

V1 before = Vcg +1/2Vcg = 3/2 Vcg

V1 after = Vcg -1/2Vcg = 1/2 Vcg = 1/3 * 7.8 m/s = 2.6 m/s

V2 before =Vcg - Vcg = 0

V2 after = Vcg + Vcg = 2 Vcg = 4/3 *7.8 m/s = 10.4 m/s

b] Vcg = 1/6 * 7.8 m/sec

V1 = Vcg - 5 Vcg = -4Vcg = -4/6 *7.8 m/s = - 5.2 m/s

V2 = Vcg +Vcg = 2 Vcg = 2/6 * 7.8 m/sec = 2.6 m/s

c]
a. KE = 1/2 *0.002 * 7.8^2 = 0.06084 N, out KE = 0.06084 N/9 = 0.00676 N

b. KE in = 0.06084, KE out = (2/3)^2 * 0.06084 = 0.02704 N

In case a, incident particle loose more kinetic energy

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