A block of wood (10-kg) at rest is hit by a bullet (50-g) that embeds itself in the block and causes both to now move at 2.7-m/s eastward. What is the initial velocity of the bullet?
conservation of momentum applies
mV+M*0=(M+m)2.7
solve for V
To find the initial velocity of the bullet, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v): p = m * v.
Let's begin by calculating the initial momentum before the collision. We have two objects: the block of wood and the bullet. The bullet is at rest initially, so its initial momentum is zero.
The momentum of the block of wood before the collision is given by:
P_block_initial = (mass of the block) * (velocity of the block before the collision)
Given that the mass of the block is 10 kg and it is at rest initially (0 m/s), the momentum of the block before the collision is zero:
P_block_initial = 10 kg * 0 m/s = 0 kg·m/s
Now, let's calculate the momentum of the bullet after the collision. The bullet is embedded in the block, so the momentum of the bullet and the block together is:
P_after_collision = (mass of the block + mass of the bullet) * (velocity after the collision)
Given that the mass of the bullet is 50 g (or 0.05 kg) and the velocity after the collision is 2.7 m/s to the east, we can substitute these values into the equation:
P_after_collision = (10 kg + 0.05 kg) * 2.7 m/s = (10.05 kg) * (2.7 m/s) = 27.135 kg·m/s
Since momentum is conserved, the initial momentum before the collision should be equal to the momentum after the collision:
P_block_initial = P_after_collision
0 kg·m/s = 27.135 kg·m/s
This implies that the initial momentum of the bullet before the collision is equal in magnitude but opposite in direction to the momentum of the block and bullet after the collision. Therefore, the initial momentum of the bullet can be calculated by dividing the momentum after the collision by the magnitude of the bullet's mass:
Initial momentum of the bullet = P_after_collision / mass of the bullet
Initial momentum of the bullet = 27.135 kg·m/s / 0.05 kg = 542.7 m/s
Hence, the initial velocity of the bullet is 542.7 m/s.