13. What is collision ? Prove that collision in one dimensional remains unchanged. [CO4]
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In physics, collisions are categorized as elastic or inelastic based on whether kinetic energy is conserved. Show more…
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As an illustration of the principle of relativity in classical mechanics, consider the following generic collision: In inertial frame $\mathcal{S},$ particle $A\left(\operatorname{mass} m_{A}, \text { velocity } \mathbf{u}_{A}\right)$ hits particle $B$ (mass $m_{B},$ velocity $\mathbf{u}_{B}$ ). In the course of the collision some mass rubs off $A$ and onto $B,$ and we are left with particles $C$ (mass $m_{C},$ velocity $\mathbf{u}_{C}$ ) and $D$ (mass $m_{D}$, velocity $\mathbf{u}_{D}$ ). Assume that momentum $(\mathbf{p} \equiv m \mathbf{u})$ is conserved in $\mathcal{S}$ (a) Prove that momentum is also conserved in inertial frame $\overline{\mathcal{S}}$, which moves with velocity $\mathbf{v}$ relative to $\mathcal{S}$. [Use Galileo's velocity addition rule - this is an entirely classical calculation. What must you assume about mass?] (b) Suppose the collision is elastic in $\mathcal{S} ;$ show that it is also elastic in $\overline{\mathcal{S}}$
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Adi S.
In the two-dimensional collision in Fig. 9-21, the projectile particle has mass $m_{1}=m$, initial speed $v_{1 i}=3 v_{0}$, and final speed $v_{1 f}$ $=\sqrt{5} v_{0}$. The initially stationary target particle has mass $m_{1}=2 m$ and final speed $v_{2 f}=v_{2}$. The projectile is scattered at an angle given by $\tan \theta_{1}=2.0$. (a) Find angle $\theta_{2}$. (b) Find $v_{2}$ in terms of $v_{0}$. (c) Is the collision elastic?
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