A 5g bullet is fired horizontally and hits an 8kg block of wood (initially at rest) which can move freely. The wood and the bullet move with a velocity of 0.50 m/s after impact. What is the initial velocity of the bullet?
conserve momentum:
5v = (8000+5)*0.50
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.
Let's break down the problem step by step:
Step 1: Calculate the momentum before the collision.
The momentum is defined as the product of an object's mass and its velocity. The bullet has a mass of 5 grams, which we need to convert to kilograms for consistent units. So, the bullet's mass is 0.005 kg.
Momentum before collision = Mass of the bullet × Initial velocity of the bullet
Step 2: Calculate the momentum after the collision.
The bullet and the wood move together with a velocity of 0.50 m/s after the impact. Since they are moving together as a single system, their momenta are additive.
Momentum after collision = (Mass of the bullet + Mass of the wood) × Final velocity of the system
Step 3: Apply the conservation of momentum principle.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Momentum before collision = Momentum after collision
Therefore:
Mass of the bullet × Initial velocity of the bullet = (Mass of the bullet + Mass of the wood) × Final velocity of the system
Substituting the given values:
0.005 kg × Initial velocity of the bullet = (0.005 kg + 8 kg) × 0.50 m/s
Simplifying:
0.005 kg × Initial velocity of the bullet = 8.005 kg × 0.50 m/s
Step 4: Calculate the initial velocity of the bullet.
Now, isolate the initial velocity of the bullet by dividing both sides of the equation by 0.005 kg:
Initial velocity of the bullet = (8.005 kg × 0.50 m/s) / 0.005 kg
Simplifying:
Initial velocity of the bullet = 400.25 m/s
Therefore, the initial velocity of the bullet is approximately 400.25 m/s.