A rifle with a mass of 12 g, traveling with a speed of 425 m/s strikes a large wooden block, which it penetrates to a depth of 15 cm. determine the magnitude of the retarding force that acts on the bullet.

workdone is done against bullet by block,Fd which equals its kinetic energy of bullet to stop it F*0.15=1/2*0.012*425^2 F=1083.75/0.15=7225N

To determine the magnitude of the retarding force acting on the bullet, we need to use the concept of impulse.

The impulse experienced by an object is equal to the change in momentum it undergoes. The formula for impulse can be written as:

Impulse = Force × Time

We know that impulse is also equal to the change in momentum. The formula for momentum is:

Momentum = Mass × Velocity

Rearranging the equation for impulse, we can rewrite it as:

Force = Impulse / Time

In this case, the impulse experienced by the bullet is equal to the change in its momentum. Since the bullet penetrates the wooden block, its final velocity after penetration is zero. Therefore, the change in momentum is given by:

Δp = m × Δv

Where:
Δp = Change in momentum
m = Mass of the bullet
Δv = Change in velocity (Initial velocity - Final velocity)

Since the final velocity is zero, the change in velocity is equal to the initial velocity:

Δv = Initial velocity - Final velocity = Initial velocity - 0

Now we can calculate the change in momentum:

Δp = m × (Initial velocity - Final velocity) = m × Initial velocity

Next, we need to determine the time it takes for the bullet to come to rest. This can be done by calculating the displacement of the bullet inside the wooden block and dividing it by its initial velocity.

Given that the bullet penetrates the block to a depth of 15 cm (or 0.15 m), we have:

Time = Displacement / Initial velocity = 0.15 m / Initial velocity

Finally, we can substitute these values back into the formula for force:

Force = (m × Initial velocity) / (0.15 m / Initial velocity)

Simplifying the equation, we get:

Force = m × Initial velocity² / 0.15 m

Now we can substitute the given values into this equation to find the magnitude of the retarding force acting on the bullet.