Question

particle of rest m0 and speed v collides with a stationary particle of mass M and sticks to it. what is the final speed of the composite particle??
please answer​

Answer 1

Final Speed of Composite Particle : $\frac{m_o v}{m+M}$

Explanation:

1) Let the final speed of composite particle be 'u' .

Since, Net External Force on system of both the particles along the horizontal direction is 0.

That is,

$F_x=0$

2) Then , Momentum is conserved along horizontal direction.

That is,

Initial Momentum, $P_i$ = $m_ov$

Final Momentum ,$P_f=(m+M)u$

Now, Conserve :

$P_i=P_f\\ \\=>m_ov=(m+M)u\\ \\=>u=\frac{m_ov}{M+m}$

Above expression is of  final speed of composite particle

Answer 2

SOLUTION.

Initial speed of mass m = v

Initial speed of mass M = 0

Final speed of mass m = u

Final velocity of mass M = u

The final velocity of both the particle are same because after collision both the particle sticks and act as a single particle of mass (m + M)

As we see there is no external force so we can apply conservation of momentum.

Initial momentum of the system = mv + M×0

Final MOMENTUM of the system = (M+m)×u

Final MOMENTUM = Initial momentum

(M+m)u = mv

u = mv/M+m

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