momentum elastic collion

2012-02-07 9:45 pm

1) a 5.0 kg ball traveling east with a speed of 5.0 m/s makes an elastic collision with a 3.0 kg ball which is traveling in the same direction with a speed of 1.5 m/s. what are the velocities of the balls immediately after the collision?

2) a pool ball moving with a speed of 2.5 m/s makes an elastic head-on collision with an identical ball traveling in the opposite direction with a speed of 5.9 m/s. find the velocities of the balls after the collision.

please list all formulas the steps!
thanks!

回答 (1)

天同

2012-02-07 10:39 pm

✔ 最佳答案

1. Using conservation of momentum,
5 x 5 + 3 x 1.5 = 5(v1) + 3(v2)
where v1 and v2 are the velocities of the 5 kg ball and 3 kg ball respectively after collision
i.e. 5(v1) + 3(v2) = 29.5 --------------------- (1)

Since the collision is elastic, kinetic energy is conserved.
(1/2).(5).(5^2) + (1/2).(3).(1.5)^2 = (1/2).(5).(v1)^2 + (1/2).(3).(v2)^2
i.e. 5(v1)^2 + 3(v2)^2 = 131.75 ----------------- (2)
solve equations (1) and (2) gives v1 = 2.375 m/s and v2 = 5.875 m/s

2. Using conservation of momentum,
2.5m + (-5.9m) = m(v1) + m(v2)
where m is the mass of each ball, and v1 and v2 are their respective velocities after collision
i.e. (v1) + (v2) = -3.4 --------------------- (1)

Since the collision is elastic, kinetic energy is conserved.
(1/2).m.(2.5^2) + (1/2).m.(-5.9)^2 = (1/2).m.(v1)^2 + (1/2).m.(v2)^2
i.e. (v1)^2 + (v2)^2 = 41.06 ----------------- (2)
solve equations (1) and (2) gives v1 = -5.9 m/s and v2 = 2.5 m/s

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