A ball with a mass of $3 kg$ is rolling at $6 m/s$ and elastically collides with a resting ball with a mass of $8 kg$ . What are the post-collision velocities of the balls?

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A ball with a mass of $3 kg$ is rolling at $6 m/s$ and elastically collides with a resting ball with a mass of $8 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2018-04-07T02:44:19

$-"2.72 m/s"$ and $"3.27 m/s"$

Explanation:

From conservation of momentum

$"Initial total momentum = Final total momentum"$

$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

$("3 kg × 6 m/s") + ("8 kg × 0 m/s") = ("3 kg" × v_1) + ("8 kg" × v_2)$

$18 = 3v_1 + 8v_2 color(white)(...)……(1)$

Coefficient of restitution $(e)$ is given by

$e = (v_2 - v_1) / (u_1 - u_2)$

For perfectly elastic collision $e = 1$

$1 = (v_2 - v_1)/ (6 - 0)$

$v _2 - v_1 = 6$

Multiply both sides by $3$

$3v_2 - 3v_1 = 18 color(white)(...) ……(2)$

Add equations $(1)$ and $(2)$

$18 + 18 = 3v_1 + 8v_2 + 3v_2 - 3v_1$

$36 = 11v_2$

$v_2 = 36/11 = color(blue)"3.27 m/s"$

Substitute $v_2 = 3.27$ in equation $(1)$

$18 = 3v_1 + (8 × 3.27)$

$v_1 = (18 - (8 × 3.27))/3 = color(blue)(-"2.72 m/s")$

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A ball with a mass of $3 kg$ is rolling at $6 m/s$ and elastically collides with a resting ball with a mass of $8 kg$ . What are the post-collision velocities of the balls?

1 Answer

Explanation:

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Science

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A ball with a mass of 3 kg 3 kg is rolling at 6 m/s6 m/s and elastically collides with a resting ball with a mass of 8 kg 8 kg. What are the post-collision velocities of the balls?

1 Answer

Explanation:

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A ball with a mass of $3 kg$ is rolling at $6 m/s$ and elastically collides with a resting ball with a mass of $8 kg$ . What are the post-collision velocities of the balls?