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A bullet of mass 10$\,$g travels horizontally with speed of 100$\,$m/s and is absorbed by a wooden block of mass 990$\,$g suspended by a string. Find the vertical height through which the block rises, take $g=10\,$m/s$^2$

(Answer: 5$\,$cm)

In this question, why can't we equate the initial velocity of the bullet to the final potential energy of the system (since final velocity should be zero), i.e., $\frac12\times0.01\times100^2 = (0.01+0.990)\times10\times h\qquad\implies\qquad h=500\,$cm?

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why can't we equate the intitial velocity of the bullet to the final potential energy of the system

In this problem mechanical energy is not conserved. The collision of the bullet with the block is highly inelastic. A lot of mechanical energy is converted into heat and internal deformation of the block.

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    $\begingroup$ Oh ok thank you so much!! I couldn't find an explanation anywhere and my teacher hadn't explained it. $\endgroup$
    – ivy
    Commented Oct 13, 2023 at 12:52
  • $\begingroup$ @Archisha, there is an important concept in this problem. Kinetic energy is conserved only in perfectly elastic collisions, while momentum is conserved in all collisions. $\endgroup$
    – David White
    Commented Oct 13, 2023 at 15:07

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