Question

Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary. Now suppose that the collision is perfectly inelastic. What are the velocities v1 and v2 of the two objects after the collision?

Answer 1

Answer:

v₁ = v₂ = v/2

Explanation:

• Assuming no external forces acting during the collision, total momentum must be conserved, as follows:

        $m_{1}* v = m_{1} *v_{1f} + m_{2}*v_{2f} (1)$

• If the collision is perfectly inelastic, both masses stick together after the collision, which means that both masses will have the same final speed:

        $v_{1f} = v_{2f} (2)$

• We know that both masses are equal each other:

        $m_{1} =m_{2} = m (3)$

• From (1), (2) and (3), we can solve for v₁f = v₂f, as follows:

        $m v = 2*m *v_{1f}$

        ⇒ $v_{1f} = v_{2f} =\frac{v}{2}$

• The velocities of both objects after the collision are the same, and equal to v/2.