Why Does the Block Rise to a Different Height After Being Struck by a Bullet?

[sid123]

problem -
a bullet of mass .012kg and horizontal speed 70meters per second strikes a block of mass 0.4 kg and instantly comes to rest with respect to the block. the block is suspended from the ceiling by means of thin wires . calculate the height through which it rises.

attempt -
total initial energy = 1/2(mv^2)=1/2*.012*70*70
total final energy = mgh=(0.012+.4)*10*h
equating the 2 .
i get 7.5 meteres but the answer given is 21.2 cm .

pls help .

 

[Doc Al]

Mechanical energy is not conserved during the collision of bullet and block. But what is?

 

[sid123]

Can you please tell me how it is not conserved and how to go about this problem ?

 

[cepheid]

This is an inelastic collision, which means that kinetic energy is not conserved. Use conservation of momentum to find the final velocity of the bullet+block just after the collision. Use that to find the new kinetic energy after the collision, and then assume all of this is converted to potential energy as the block swings upward.

 

[asteriatic]

Your attempt to solve this problem using the work energy theorem is correct. However, the answer given in the problem statement is incorrect. The final height should be 21.2 meters, not 21.2 cm. This can be verified by plugging in the given values into the equation for final energy and solving for h. It is possible that there was a typo or error in the problem statement. As a scientist, it is important to double check the given information and make sure all calculations are accurate.