A bullet is fired horizontally and penetrates into a block of wood. The block and bullet then move together after impact. Explain the total linear momentum and total kinetic energy of the system before and after the collision
momentum
mass bullet * u + mass wood * 0
= (mass bullet + mass wood) * v
energy
(1/2)mass bullet * u^2 + 0
= (1/2)(mass bullet+mass wood) * v^2
The Ke after will be less :) Energy was converted to heat while slowing the bullet.
To explain the total linear momentum and total kinetic energy of the system before and after the collision, let's break down the process step by step:
1. Before the collision:
- The bullet is fired horizontally, which means it has an initial velocity only in the horizontal direction.
- Since there is no force acting vertically on the bullet, there is no initial velocity in the vertical direction.
- The block of wood is initially at rest, meaning it has zero velocity.
- Thus, the total linear momentum of the system before the collision is the momentum of the bullet, which is given by its mass multiplied by its initial velocity in the horizontal direction.
2. During the collision:
- When the bullet penetrates into the block of wood, it experiences a force due to the resistance offered by the wood.
- This force decreases the bullet's momentum, gradually slowing it down.
- As the bullet loses momentum, it transfers it to the block of wood.
- This transfer of momentum causes the block of wood to acquire momentum in the direction of the bullet's initial velocity.
3. After the collision:
- Since there is no external force acting on the system in the horizontal direction, the total linear momentum of the system is conserved.
- As a result, the total linear momentum of the system after the collision is equal to the total linear momentum before the collision.
- Since the bullet and the block move together after the impact, their velocities become the same after the collision.
- Therefore, the final velocity of the block of wood and the bullet is the same, and they both move in the same direction.
4. Regarding the total kinetic energy:
- Kinetic energy is given by the formula KE = 1/2 * mass * velocity^2.
- Before the collision, the block of wood has zero velocity, so it has zero kinetic energy.
- The bullet, on the other hand, has an initial velocity, and therefore it possesses kinetic energy.
- After the collision, when the bullet and block move together with the same final velocity, the total kinetic energy of the system is the sum of the kinetic energies of the block and the bullet.
- This is because the kinetic energies of the block and the bullet add up since they are both moving.
In summary, the total linear momentum of the system is conserved before and after the collision, while the total kinetic energy of the system increases after the collision due to the fact that the block acquires kinetic energy from the bullet.