A bullet with a mass of 4.0 g and a speed of 650 m/s is fired at a block of wood with a mass of 9.7×10−2 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 22 m/s.

What is the speed of the bullet when it exits the block?

600

To find the speed of the bullet when it exits the block, we can apply the law of conservation of momentum.

The law of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, assuming there are no external forces acting on the system.

We can use this principle to equate the total momentum before the bullet hits the block to the total momentum after the bullet passes through the block.

The momentum of an object is calculated by multiplying its mass by its velocity.

The initial momentum of the bullet can be calculated as:
Initial momentum of the bullet = mass of the bullet * initial velocity of the bullet

The final momentum of the bullet can be calculated as:
Final momentum of the bullet = mass of the bullet * final velocity of the bullet

The initial momentum of the block can be calculated as:
Initial momentum of the block = mass of the block * initial velocity of the block (which is zero since the block is at rest initially)

The final momentum of the block can be calculated as:
Final momentum of the block = mass of the block * final velocity of the block

Using the conservation of momentum principle, we can set up the following equation:
Initial momentum of the bullet = Final momentum of the bullet + Final momentum of the block

Now we can substitute the given values into the equation.

Mass of the bullet = 4.0 g = 0.004 kg
Initial velocity of the bullet = 650 m/s
Mass of the block = 9.7 × 10^-2 kg
Initial velocity of the block = 0 m/s
Final velocity of the block = 22 m/s

Substituting the values, we get:
0.004 kg * 650 m/s = Final momentum of the bullet + 9.7 × 10^-2 kg * 22 m/s

Now, we can solve for the final momentum of the bullet:
Final momentum of the bullet = (0.004 kg * 650 m/s) - (9.7 × 10^-2 kg * 22 m/s)

Calculating the final momentum of the bullet, we get:
Final momentum of the bullet = 2.6 kg·m/s

Since momentum is calculated by multiplying mass by velocity, we can rearrange the equation to solve for the final velocity of the bullet:
Final velocity of the bullet = Final momentum of the bullet / mass of the bullet

Substituting the values, we get:
Final velocity of the bullet = 2.6 kg·m/s / 0.004 kg

Calculating the final velocity of the bullet, we get:
Final velocity of the bullet ≈ 650 m/s

Therefore, the speed of the bullet when it exits the block is approximately 650 m/s.