A bullet is fired from a rifle,and the rifle | vedclass

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(D) According to the law of conservation of momentum,the momentum of the rifle and the bullet must be equal and opposite,i.e.,$m_b v_b = M_r V_r$,wher

Vedclass · Accepted Answer

Less than the kinetic energy of the bullet

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(D) According to the law of conservation of momentum,the momentum of the rifle and the bullet must be equal and opposite,i.e.,$m_b v_b = M_r V_r$,where $m_b$ and $v_b$ are the mass and velocity of the bullet,and $M_r$ and $V_r$ are the mass and recoil velocity of the rifle.Since the mass of the rifle $M_r$ is much greater than the mass of the bullet $m_b$ $(M_r \gg m_b)$,the recoil velocity of the rifle $V_r$ is much smaller than the velocity of the bullet $v_b$.The kinetic energy $K$ is given by $K = \frac{p^2}{2m}$,where $p$ is the momentum.Since the magnitudes of their momenta are equal $(p_b = p_r = p)$,the kinetic energy is inversely proportional to the mass $(K \propto \frac{1}{m})$.Because $M_r > m_b$,it follows that $K_r Therefore,the kinetic energy of the recoiling rifle is less than the kinetic energy of the bullet.

$A$ bullet is fired from a rifle,and the rifle experiences recoil. What will be the kinetic energy of the recoiling rifle?

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