Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary.

Question

Question

A. If the collision is perfectly elastic, what are the final velocities v1 and v2 of objects 1 and 2?

Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express each velocity in terms of v.

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Physics Thái Dương 4 years 2021-08-19T19:08:28+00:00 2021-08-19T19:08:28+00:00 1 Answers 17 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

Answer*

Farah · Answer 1 · 2021-08-19T19:10:26+00:00

Answer:

(v, 0) or (0, v)

Explanation:

The law of conservation of linear momentum states total initial momentum equal total final momentum.

Total initial momentum = $mv + m\times 0 = mv$

Total final momentum = $mv_1 + mv_2 = m(v_1+v_2)$

Equating both,

$mv = m(v_1+v_2)$

$v = v_1+v_2$

For an elastic collision, kinetic energy is conserved i.e. total initial kinetic energy = total final kinetic energy

$\frac{1}{2}mv^2 + \frac{1}{2}m\times0^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2$

$v^2 = v_1^2+v_2^2$

From the first equation, $v_1 = v-v_2$ .

Substituting this in the second equation,

$v^2 = (v-v_2)^2+v_2^2$

$v^2 = v^2-2vv_2 +v_2^2+v_2^2$

$0 = 2v_2^2-2vv_2$

$v_2(v_2-v) = 0$

$v_2 = 0$ or $v_2 = v$

From $v_1 = v-v_2$ ,

$v_1 = v-v = 0$

OR

$v_1 = v-0 = v$