A 2.0-g particle moving at 7.4 m/s makes a perfectly elastic head-on collision w

Question

A 2.0-g particle moving at 7.4 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object.

(a) Find the speed of each particle after the collision.

2.0 g particle _______ m/s

1.0 g particle ________ m/s

(b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g.

2.0 g particle ________ m/s

10.0 g particle _______ m/s

(c) Find the final kinetic energy of the incident 2.0-g particle in the situations described in parts (a) and (b).

KE in part (a) ________ J

KE in part (b) _______ J

Explanation / Answer

part a )

after elastic collision

2g particle

v1f = (m1 - m2)*v1i/(m1+m2)

v1f = 1*10^-3 * 7.4 / 3 *10^-3 = 2.467 m/s

1g particle

v2f = 2m1*v1i/m1+m2

v2f = 2 * 2*7.4 / 3 = 9.867 m/s

part b )

2g particle

v1f = (2-10)*7.4 / 12 = -4.93 m/s

10 g particle

v2f = 2*2*7.4 / 12 = 2.467 m/s

part c )

KE in a ) = 1/2 * m*vf^2

KE = 1/2 * 2 x 10^-3 * (2.467)^2 = 6.086 x 10^-3 J

KE in b )

KE = 1/2 * 2 x 10^-3 * (-4.93)^2

KE = 0.024 J

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