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
Apr 7, 2018

-"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")