A bullet with a mass of 4.0 g and a speed of 736 m/s is fired at a block of wood with a mass of 0.075 kg. The block rests on a frictionless surface, and is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is 27 m/s.
Question??????
To solve this problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system.
Let's break down the problem step by step:
1. Calculate the initial momentum:
The initial momentum is given by the product of mass and velocity of the bullet before it hits the wood block.
Initial momentum of the bullet = mass of the bullet x velocity of the bullet
Given:
Mass of the bullet, m1 = 4.0 g = 0.004 kg
Velocity of the bullet, v1 = 736 m/s
Therefore, initial momentum of the bullet, p1 = m1 * v1
2. Calculate the final momentum:
The final momentum is given by the product of mass and velocity of the block after the bullet passes through it.
Final momentum of the block = mass of the block x velocity of the block
Given:
Mass of the block, m2 = 0.075 kg
Velocity of the block, v2 = 27 m/s
Therefore, final momentum of the block, p2 = m2 * v2
3. Apply conservation of momentum:
According to the conservation of momentum, the total momentum before the event equals the total momentum after the event.
Mathematically, p1 = p2
Substituting the values calculated earlier, we have:
m1 * v1 = m2 * v2
Rearranging the equation to solve for v2:
v2 = (m1 * v1) / m2
Now, let's calculate the final velocity of the block after the bullet passes through it using the given values:
v2 = (0.004 kg * 736 m/s) / 0.075 kg
= 29.83 m/s (rounded to two decimal places)
Therefore, the final velocity of the block after the bullet passes through it is 29.83 m/s.