A body of mass m moving with velocity v colli | vedclass

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(B) Initial kinetic energy of the system is $K_i = 1/2 mv^2 + 1/2 (2m)(0)^2 = 1/2 mv^2$.Since the collision is perfectly inelastic,the two bodies stic

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$1/3 mv^2$

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(B) Initial kinetic energy of the system is $K_i = 1/2 mv^2 + 1/2 (2m)(0)^2 = 1/2 mv^2$.Since the collision is perfectly inelastic,the two bodies stick together after the collision and move with a common velocity $V$.By the law of conservation of linear momentum: $mv + (2m)(0) = (m + 2m)V$.$mv = 3mV$,which gives $V = v/3$.The final kinetic energy of the system is $K_f = 1/2 (m + 2m)V^2 = 1/2 (3m)(v/3)^2 = 1/2 (3m)(v^2/9) = 1/6 mv^2$.The loss in kinetic energy is $\Delta K = K_i - K_f = 1/2 mv^2 - 1/6 mv^2 = (3/6 - 1/6) mv^2 = 2/6 mv^2 = 1/3 mv^2$.

$A$ body of mass $m$ moving with velocity $v$ collides head-on with another body of mass $2m$ which is initially at rest. If the collision is perfectly inelastic,what is the loss in kinetic energy of the system?

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