A 5 gram bullet is fired horizontally and hits an 8 kg block of wood that is at rest and can move freely. The wood and the bullet move with a velocity of 0.05 m/s after the impact. What is the initial velocity of the bullet?
A 5 gram bullet is fired horizontally and hits an 8 kg block of wood that is at rest and can move freely. The wood and the bullet move with a velocity of 0.05 m/s after the impact. What is the initial velocity of the bullet?
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 impact is equal to the total momentum after the impact.
The formula for momentum is:
Momentum = mass × velocity
Before the impact, only the bullet is moving, so the momentum is given by:
momentum of the bullet = mass of the bullet × velocity of the bullet
After the impact, the bullet and the wood are both moving with a common velocity, so the momentum is given by:
momentum of the bullet + momentum of the wood = (mass of the bullet + mass of the wood) × velocity after the impact
Let's calculate the momentum before and after the impact.
Given:
Mass of the bullet (m1) = 5 grams = 0.005 kg
Mass of the wood (m2) = 8 kg
Velocity after the impact (v) = 0.05 m/s
Before the impact:
Momentum of the bullet = m1 × velocity of the bullet
After the impact:
Momentum of the bullet + momentum of the wood = (m1 + m2) × velocity after the impact
Now, let's substitute the given values into the equations:
Before the impact:
momentum of the bullet = 0.005 kg × velocity of the bullet
After the impact:
momentum of the bullet + momentum of the wood = (0.005 kg + 8 kg) × 0.05 m/s
Since momentum is conserved, we can equate the two equations:
0.005 kg × velocity of the bullet = (0.005 kg + 8 kg) × 0.05 m/s
Now, we can solve for the velocity of the bullet:
0.005 kg × velocity of the bullet = (8.005 kg) × 0.05 m/s
velocity of the bullet = (8.005 kg) × 0.05 m/s ÷ 0.005 kg
Simplifying the equation:
velocity of the bullet = 8.005 m/s
Therefore, the initial velocity of the bullet is approximately 8.005 m/s.