Elastic collisions in one dimension: A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s. If the collision is perfectly elastic, what is the final speed of the 2.3-kg object?

Question

Quizplus · Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved. The initial momentum of the system is zero, because the objects are moving in opposite directions. Therefore, the final momentum of the system must also be zero. Let us call the final speed of the 2.3-kg object v. Then, the final speed of the 3.5-kg object must be -v.

Using the conservation of momentum:
(2.3 kg)(6.1 m/s) + (3.5 kg)(-4.8 m/s) = 0
14.03 kg m/s = 16.8 kg m/s - 16.8 kg m/s
Therefore, the final momentum is conserved.

Using the conservation of kinetic energy:
(1/2)(2.3 kg)(6.1 m/s)^2 + (1/2)(3.5 kg)(4.8 m/s)^2 = (1/2)(2.3 kg + 3.5 kg)(v)^2
22.1435 J = 5.8 kg(v)^2
v = sqrt(22.1435 J / 5.8 kg) 
v = 7.1 m/s

Therefore, the final speed of the 2.3-kg object is 7.1 m/s.

Elastic Collisions in One Dimension: a 2