Question

two similar spheres of equal masses with initial velocities u1 and u2 respectively undergo an elastic collision. if u1=2u2=20 m s^-2 , determine their velocities after collision​

Answer 1

Answer:

$v_{1} = 10 \ m/s$

$v_{2} = 20 \ m/s$

Explanation:

Given :

$u_{1} = 20 \ m/s$

As $2u_{1} = 20 \ m/s$,

∴ $u_{2} = 10 \ m/s$

m₁ = m₂

Procedure :

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

⇒ mu₁ + mu₂ = mv₁ + mv₂

⇒ u₁ + u₂ = v₁ + v₂

∴ v₁ + v₂ = 30 m/s -------------------- 1

In elastic collision, e = 1

[ $e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}}$ ]

⇒ $\frac{v_{2} - v_{1}}{20-10} = 1$

∴ v₂ - v₁ = 10 m/s ----------------------2

From Equation 1 and 2 :

v₁ = 20 m/s

v₂ = 10 m/s

Tip :

Generally, Velocities interchange in an elastic collision if the masses are equal.

Thanks !