2 11 Inelastic Collision In Two Dimensions – Class 11TH Physics

2.11 Inelastic Collision in Two Dimensions

The macroscopic collisions are generally inelastic and do not conserve Kinetic energy.

The perfect inelastic collision is one in which the colliding objects stick together to make a single mass after collision. Its analysis can be carried out as follows:

Let us take two balls having masses $m_{1}$ and $m_{2}$ moving with velocities, $v_{1}$ and $v_{2}$ , respectively, in a two-dimensional $xy$ -plane. Assume that the first body is moving along the $x$ -axis while the second body moves in a direction, making an angle $\theta$ with $x$ -axis. Both the bodies collide at the origin as shown in the figure 2.17.

After collision, bodies stick together, having combined mass $M = m_{1} + m_{2}$ , which moves with velocity $v$ , making an angle $\phi$ with $x$ -axis.

Momentum in the $x$ -direction:

m_{1}v_{1} + m_{2}v_{2}\cos\theta = Mv\cos\phi \quad \ldots (2.38)

Momentum in the $y$ -direction:

0 + m_{2}v_{2}\sin\theta = Mv\sin\phi \quad \ldots (2.39)

Equation 2.38 and 2.39 can be used to find the final velocity.

2.11 Inelastic Collision in Two Dimensions

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