A 13 g bullet traveling 226 m/s penetrates a 2.0 kg block of wood and emerges cleanly at 162 m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?

9808

45m/s

To find out how fast the block moves after the bullet emerges, we will 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, assuming no external forces are acting on the system.

First, let's find the initial momentum before the bullet hits the wooden block:
The momentum of the bullet can be calculated using the formula: momentum = mass x velocity.
Given: mass of the bullet = 13 g = 0.013 kg, bullet velocity = 226 m/s.
Momentum of the bullet = 0.013 kg × 226 m/s.

The momentum of the wooden block is initially zero because it is at rest.

When the bullet emerges, it carries momentum with it. Let's denote the mass of the wooden block as M.

The final momentum after the bullet emerges is given by:
Final momentum = (mass of bullet × velocity of bullet) + (mass of wooden block × velocity of wooden block)

Given: mass of the wooden block = 2.0 kg, velocity of the bullet = 162 m/s.

Final momentum = (0.013 kg × 162 m/s) + (2.0 kg × velocity of wooden block)

Since the total momentum before and after the event should be equal, we can write:
Initial momentum = Final momentum

Therefore,
Initial momentum = (0.013 kg × 226 m/s)

Now, let's find the velocity of the wooden block after the bullet emerges:
(0.013 kg × 226 m/s) = (0.013 kg × 162 m/s) + (2.0 kg × velocity of wooden block)

Simplifying the equation, we get:
0.013 kg × 226 m/s = 0.026 kg × velocity of wooden block + 2.0 kg × velocity of wooden block

Combining like terms, we have:
0.013 kg × 226 m/s = 0.026 kg + 2.0 kg × velocity of wooden block

Now, let's solve for the velocity of the wooden block:
0.013 kg × 226 m/s - 0.026 kg = 2.0 kg × velocity of wooden block

To find the velocity of the wooden block, divide both sides of the equation by the mass of the wooden block (M):
velocity of wooden block = (0.013 kg × 226 m/s - 0.026 kg) / 2.0 kg

Now, calculate the value to find the velocity of the wooden block after the bullet emerges.