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Current situation: a bullet is fired towards a block that is connected to a string which is connect to a ceiling. The bullet is embedded to the block and the object(block+bullet) swings up to a certain height.

Consider this scenario: if there is friction when the bullet is embedding into the block, energy will be converted to internal energy, then the maximum height it reached will be decreased as KE decreases. But if KE decreases, that means the momentum of the block and the bullet after collision is reduced( consider the block and the bullet together as a system, hence frictional force within will not be considered), then I will arrive to a violation of conservation of momentum?

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    $\begingroup$ What kind of "friction when the bullet is embedding into the block" would that be when you simultaneously say that "frictional force within will not be considered"? $\endgroup$
    – Steeven
    Commented Feb 29 at 16:28
  • $\begingroup$ but I consider the block and the bullet as a system, then the friction from contact between the bullet and the block doesn’t have to be considered no?( need not consider as in in the equation of momentum $\endgroup$
    – Mohammed golfa
    Commented Feb 29 at 16:33
  • $\begingroup$ Your question is just yet another one of the thousands of other people asking the same question about firing a bullet into a suspended block. During the collision, linear momentum, really the angular momentum, is conserved. There will be a lot of conversion of energy because it takes a lot of energy to destroy the bullet and dig a hole into the block, and some energy goes into heat and sound energy. You have just completely misunderstood what is conserved and what is not. $\endgroup$
    – naturallyInconsistent
    Commented Feb 29 at 17:43

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Because your block–bullet system is connected to the surroundings with a string, you must consider the surroundings when analyzing the momentum.

The greater the distance of frictional deceleration, the slower the bullet decelerates and therefore the lower the maximum force on the block and the less the block rises.

In the extreme example, the block rises negligibly and heats up the most, and essentially the entire momentum transfer has been shared with the Earth (including the block) rather than the block alone. As expected, momentum conservation is satisfied in all cases.

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