# What Is the Average Force Exerted by a Recoiling Shotgun?

• Emily_20
In summary, a 0.031 kg bullet is fired from a 3.63 kg shotgun at 420 m/s. The collision between the recoiling gun and your shoulder takes 0.013s. Using the momentum, kinematics, and force equations, the average force exerted by the gun on your shoulder is calculated to be 1002 N. Another method can also be used by equating the variation of momentum of the bullet and gun, resulting in the same answer of 1002 N.
Emily_20

## Homework Statement

A 0.031 kg bullet is fired from a shotgun of mass 3.63kg at 420 m/s. If the collision of the recoiling gun with your shoulder takes 0.013s, what is the average force the gun exerts against your shoulder?

p = m • v[/B]
vf=vi + at
F=ma

## The Attempt at a Solution

I calculated the velocity of the gun from the momentum equation : 0+0=mbf*vbf-mgf*gf
which is 3.587 m/s
Then I used the kinematics equation to solve for the acceleration: 3.587 m/s=0 + a (0.013 s) which is 275.9 m/s^2
Then I used the force equation to find the force: (275.9 m/s/s) * (3.63 kg) = 1002 N. Is it right? I am worried about the acceleration because the number is high. Thanks for help.

I believe you are right. The problem can be solved taking another way: the variation of momentum mv is equal to the impulse Ft

The variation of momentum of the bullet is 13,02 m*s, and is the same as the variation of momentum of the gun.

Thus, 13,02 = Ft

As it's stated that the time is 0,013 s, if you solve for F, you get F = 13,02/0,013 = 1002 N

Thanks!

## 1. How does a bullet travel through the air after being fired from a gun?

When a bullet is fired from a gun, it is propelled by the expanding gases from the gunpowder igniting. This creates a force that propels the bullet forward through the air. The bullet's shape and weight also play a role in its trajectory.

## 2. What determines the speed of a bullet as it leaves the gun?

The speed of a bullet as it leaves the gun is determined by several factors, including the type of gun, the type and amount of gunpowder used, the weight and shape of the bullet, and any external forces such as wind or gravity.

## 3. Can a bullet change direction mid-flight?

In most cases, a bullet cannot change direction mid-flight. Once it leaves the barrel of the gun, it will continue on its trajectory until it hits an obstacle or is affected by external forces such as wind or gravity. However, some specialized bullets, such as those used in guided missile systems, have the ability to change direction.

## 4. How far can a bullet travel after being fired from a gun?

The distance a bullet can travel after being fired from a gun depends on several factors, including the type of gun, the type and amount of gunpowder used, the weight and shape of the bullet, and any external forces such as wind or gravity. Generally, a bullet can travel up to a few miles before losing velocity and falling to the ground.

## 5. Is it possible to dodge a bullet?

It is highly unlikely for a person to dodge a bullet after it has been fired from a gun. Bullets travel at incredibly high speeds, making it nearly impossible for a person to move out of its path once it has been fired. However, it is possible for a person to move out of the way before the bullet is fired, if they are able to anticipate the shot.

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