Question

Blocks a and b are moving towards each other along the x-axis. A has a mass of 2 kg and a velocity of , while b has a mass of 4 kg and a velocity of . They suffer an elastic collision and move off along the x-axis. After the collision the velocities of both a and b, respectively are

Answer 1

2 answers · Physics

Best Answer

Let v₁ and v₂ be the final velocities of ball A and ball B respectively.

In an elastic collision, both momentum and kinetic energy is conserved. So, since momentum is conserved, we have:

(2.0)(50) + (4.0)(-25) = 2.0v₁ + 4.0v₂

==> 2v₁ + 4v₂ = 0

==> v₁ = -2v₂. . . . . . . . . . . . . . . . . . . . .(1)

Since kinetic energy is conserved:

(1/2)(2.0)(50)^2 + (1/2)(4.0)(-25)^2 = (1/2)(2.0)v₁^2 + (1/2)(4.0)v₂^2

==> v₁^2 + 2v₂^2 = 3750. . . . . . . . . . . . .(2)

Substituting (1) into (2) gives:

(-2v₂)^2 + 2v₂^2 = 3750

==> 6v₂^2 = 3750

==> v₂^2 = 625

==> v₂ = 25 m/s.

From (1), v₁ = -2(25) = -50 m/s.

Then, the kinetic energy transferred from A to B is the difference between the initial and final kinetic energies of A:

∆KE = (1/2)(2.0)(-50)^2 - (1/2)(2.0)(50)^2 = 0.