Question

Show that the ratio of velocities of equal masses in an inelastic collision when one of the masses is
stationary is 1/
2
=
1−/
1+e

Answer 1

Answer:

A. The distance between masses is always proportional to it.

Answer 2

Given:

The mass of the two objects are equal, m₁ = m₂ = m

The collision is an inelastic collision.

To Find:

We have to prove that the ratio of the velocities of equal masses in an elastic collision when one mass is stationary is $\frac{1}{2}$.

Solution:

Let the mass of two objects be m₁ and m₂ and the velocities are v₁ and v₂. Consider the mass m₂ is stationary.

As per the given data, we know that m₁ = m₂ = m and v₂= 0.

An inelastic collision is a collision of objects in which objects stick together after impact, and kinetic energy is not conserved. The kinetic energy is converted to other forms of energy, potential energy, or thermal energy.

Since the two objects stick together after colliding, they move together at the same speed, v'. From the conservation of momentum equation,

            m₁v₁ ₊ m₂v₂ = (m₁ ₊ m₂)×v'

⇒              m(v₁ ₊ 0) = 2m×v'

⇒                        m = 2m×v'

⇒                        v₁ = 2v

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

∴ The ratio of the velocities of equal masses in an elastic collision when one mass is stationary is $\frac{1}{2}$. Hence proved.