Question

substitute expressions for the kinetic and potential energies. note that both the potential energy at the bottom and the kinetic energy at the top are zero.
solve for the final velocity of the block - bullet system, ( v_{sys} ).
(b) calculate the initial speed of the bullet.
write the conservation of momentum equation and substitute expressions.
solve for the initial velocity of the bullet, and substitute values.
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remarks because the impact is inelastic, it would be incorrect to equate the initial kinetic energy of the incoming bullet to the final gravitational potential energy associated with the bullet - block combination. the energy isnt conserved!
question the ways that mechanical energy is lost from the system in this experiment include: (select all that apply.)
energy loss from the change in height of the block
thermal energy loss due to air drag
emission of sound waves
friction in the mechanisms
friction to bring the bullet to a stop relative to the ground

Explanation:

• Energy loss from the change in height of the block: This is a gain in gravitational potential energy, not a loss of mechanical energy.
• Thermal energy loss due to air drag: Air drag does work against the motion of the block - bullet system, converting mechanical energy into thermal energy (heat), so this is a loss of mechanical energy.
• Emission of sound waves: Sound is a form of energy. When the bullet embeds in the block and the system moves, some mechanical energy is converted into sound energy (vibrations in the air), so this is a loss of mechanical energy.
• Friction in the mechanisms: Friction does non - conservative work. It converts mechanical energy (kinetic energy of the system) into thermal energy (due to the rubbing of parts), so this is a loss of mechanical energy.
• Friction to bring the bullet to a stop relative to the ground: This is not relevant. The problem is about the mechanical energy of the block - bullet system. Once the bullet is embedded in the block, we are considering the system's energy changes during its rise (related to \(h\)). Friction that would bring the bullet to a stop relative to the ground (if it were not embedded) is not part of the energy analysis of the block - bullet system's motion after the inelastic collision.

Answer:

B. thermal energy loss due to air drag, C. emission of sound waves, D. friction in the mechanisms