A bullet is fired into a block of wood that is resting on a frictionless surface. The bullet begins to slow down when it hits the wood, and eventually stops, embedded in the block, while the block slides across the frictionless surface. At what point is the combined momentum of the bullet-block system the greatest?
A) before the bullet hits the block
B) after the bullet hits the block, but before the bullet is stopped by the block
C) after the bullet is stopped by the block and the block and bullet are sliding together across the surface.
D) the momentum is the same at all three of these times.
E) the mass of the block and bullet and the initial speed of the bullet are needed to answer this question.
The correct answer and explanation is:
The correct answer is A) before the bullet hits the block.
Momentum is a conserved quantity in a closed system where no external forces are acting. In this case, the bullet-block system is closed because the surface is frictionless, meaning no external horizontal forces are acting on the system. However, the combined momentum of the bullet-block system changes during the interaction between the bullet and the block due to the nature of the collision.
Initially, when the bullet is fired into the block, the momentum of the system is entirely due to the bullet. The block is at rest, so its momentum is zero. The total momentum of the system before the bullet hits the block is just the momentum of the bullet, which is the product of its mass and velocity (m_bullet * v_bullet).
When the bullet hits the block, the momentum of the bullet begins to be transferred to the block. The block starts to move in the direction of the bullet’s motion, and the bullet begins to lose speed due to the transfer of momentum to the block. The bullet eventually comes to rest within the block, and both the bullet and the block move together as a combined mass.
At this point, the combined momentum of the system is still conserved, but the momentum will be less than it was before the bullet hit the block. This is because the total mass of the system has increased (bullet + block), but the final velocity is lower than the initial velocity of the bullet.
The greatest momentum occurs before the bullet hits the block, when the bullet is moving at its maximum speed and the block is stationary. At that moment, the total momentum of the system is just the momentum of the bullet, which is the highest it will ever be during the interaction.