a 16.0-g bullet is shot into a wooden block at rest with mass 4550g on a frictionless surface. the block moves 1.20m/s after the bullet strikes and becomes lodged in the block. find the speed of the bullet before striking the block.
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To find the speed of the bullet before striking the block, 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 of an object is defined as the product of its mass and velocity. In this case, we need to calculate the momentum of the bullet and the momentum of the block before the collision, and then set it equal to the total momentum of the block (with the bullet lodged) after the collision.
Let's start by calculating the momentum of the bullet before the collision. The velocity of the bullet after the collision is given as 1.20 m/s. The mass of the bullet is 16.0 g, which is equal to 0.016 kg (since 1 g = 0.001 kg).
So, the momentum of the bullet after the collision is:
Momentum = mass × velocity
Momentum = (0.016 kg) × (1.20 m/s)
Momentum = 0.0192 Ns
Now, let's calculate the momentum of the block before the collision. The block is at rest before the collision, meaning its initial velocity is zero. The mass of the block is 4550 g, which is equal to 4.55 kg.
Therefore, the momentum of the block before the collision is:
Momentum = mass × velocity
Momentum = (4.55 kg) × (0 m/s)
Momentum = 0 Ns
Since the total momentum before the collision is equal to the total momentum after the collision, we can set up the following equation:
Momentum of bullet before collision + Momentum of block before collision = Momentum of block after collision
0.0192 Ns + 0 Ns = (4.55 kg + 0.016 kg) × (1.20 m/s)
Now, let's solve for the velocity of the bullet before the collision:
0.0192 Ns = (4.566 kg) × (1.20 m/s)
Rearranging the equation, we have:
Velocity of bullet before collision = 0.0192 Ns / (4.566 kg)
Calculating the value, we find:
Velocity of bullet before collision = 0.0042 m/s
Therefore, the speed of the bullet before striking the block is approximately 0.0042 m/s.