Theory question 107
Dynamics(a) A boy of mass 3 kg moves with a velocity of 8 ms−1. It collides with a second body moving in the same direction with velocity of 5 ms−1. After collision the bodies move together with a velocity of 6 ms−1. Find the mass of the second body.
(b) If the second body in 7(a) moves with a velocity of 5 ms−1 in the opposite direction as that of the 3 kg body with a velocity of 8 ms−1, find, correct to two decimal places, the common velocity of the two bodies if they move together after collision.
Show the model answer
Model answer
(a) 3(8) + m(5) = (3 + m)(6), so 24 + 5m = 18 + 6m and m = 6 kg.
(b) 3(8) + 6(−5) = 9v, so v = −6/9 ≈ −0.67 ms⁻¹: 0.67 ms⁻¹ in the direction the second body was moving.
Explanation
Momentum is conserved; opposite directions get opposite signs.