Answer to Question #164343 in Classical Mechanics for Mohammed Sani Furqan

Question

particle of mass M1 moving with initial velocity Vo is incident on a stationary particle of mass M2. After collision , M1 was deflected through an angle ∅ and M2 an angle ∅. If the velocities of the particles after collision were V1 and V2 respectively. Show that for an elastic collission; V2=2Vo*M1/M1+M2*cos∅

Answer 1

Answer

Intial case

For M1 particle velocity V₀ and For M2 particle velocity is zero.

After collision

For M1 particle velocity V1and For M2 particle velocity is V2 With same angle $\Phi$ .

So apply momentum conservation

In x-direction

$M_1V_0+0=M_1V_1cos\Phi+M_2V_2cos\Phi----eq1$

In y -direction

$0=M_1V_1sin\Phi-M_2V_2sin\Phi$ ...Eq2

Using

Both equations

Velocity of second particle can be written as

$V_2=2V_0M_1/M_1+M_2cos\Phi$

Hence proved.