Final answer:
To find the width of the block passed by a bullet in an inelastic collision, one needs to use conservation of momentum and impulse-momentum theorem. The impulse on the bullet is equal and opposite to that on the block, and the average force can be calculated by dividing the change in momentum by the time interval.
Step-by-step explanation:
Finding Width of Block Passed by Bullet in an Inelastic Collision
To determine the width of the block passed by a bullet in an inelastic collision, you first need to understand the conservation of momentum and the principles of impulse. Upon impact, since the collision is inelastic, the bullet is embedded in the block, making the bullet and the block move together as one unit. This means the velocity of the block and bullet combination must be found using conservation of linear momentum.
The magnitude and direction of the impulse on the bullet can be determined using the impulse-momentum theorem, which relates the change in momentum of an object to the impulse applied to it. The impulse by the block on the bullet is equal in magnitude and opposite in direction to the impulse from the bullet on the block, according to Newton's third law.
The average force exerted between the bullet and block can be found using the impulse-momentum theorem, given the time over which the speed changes and the initial and final velocities. Specifically, if the speed of the bullet changes from 400 m/s to a certain final speed after impact in 3 ms, the average force can be calculated by dividing the total change in momentum by the time interval (3 ms).
In the case of the bullet being stopped by a spring, the force exerted by the spring would be similarly considered over the time it takes the block to come to rest, requiring the use of Hooke's law for springs and the impulse equation. Considering the spring's displacement and the spring constant would allow the calculation of the force during the time of impact.