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
Explanation:
"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 = (v_2 - v_1) / (u_1 - u_2)
For perfectly elastic collision
1 = (v_2 - v_1)/ (6 - 0)
v _2 - v_1 = 6
Multiply both sides by
3v_2 - 3v_1 = 18 color(white)(...) ……(2)
Add equations
18 + 18 = 3v_1 + 8v_2 + 3v_2 - 3v_1
36 = 11v_2
v_2 = 36/11 = color(blue)"3.27 m/s"
Substitute