a bullet with mass 0.281 kg is fired from a rifle. It stick into a block of wood with a mass of 17.8 that was at rest. The block/bullet combo moves at 3 m/s. What was the initial velocity of the bullet?
mv1 = (m+M)vf
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.
Before the collision, the bullet is moving with some initial velocity, and the block is at rest. The momentum of the bullet can be calculated using the formula:
momentum = mass × velocity
Let's denote the initial velocity of the bullet as V, and the final velocity of the block/bullet combo as Vf.
So, the total momentum before the collision is given by:
Total momentum before = momentum of bullet + momentum of block
= mass of bullet × initial velocity + mass of block × 0
= mass of bullet × initial velocity
After the collision, the bullet is embedded in the block, and they move together with a final velocity of 3 m/s. So, the total momentum after the collision is given by:
Total momentum after = (mass of bullet + mass of block) × final velocity
= (mass of bullet + mass of block) × 3
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can set up the equation:
mass of bullet × initial velocity = (mass of bullet + mass of block) × 3
Now, let's plug in the given values:
0.281 kg × initial velocity = (0.281 kg + 17.8 kg) × 3
Simplifying the equation, we have:
0.281 kg × initial velocity = 17.8 kg × 3
Multiplying and dividing, we find:
0.281 kg × initial velocity = 53.4 kg·m/s
Now, to find the initial velocity, we can solve for it by dividing both sides of the equation by the mass of the bullet:
initial velocity = 53.4 kg·m/s / 0.281 kg
Calculating this value, we get:
initial velocity ≈ 190.03 m/s
Therefore, the initial velocity of the bullet is approximately 190.03 m/s.