# How much does a bullet penetrate a wall?

• CPShock
In summary, the problem involves a bullet of mass 50g and initial speed 300m/s hitting a wall. The wall applies a time-dependent force on the bullet, with F0 = 70N. The goal is to determine the distance the bullet penetrates the wall, in centimeters. The solution involves understanding the relationship between speed and acceleration, and solving for the case with a constant force before tackling the time-dependent force. This problem may require calculus to solve.
CPShock

## Homework Statement

A bullet weighing m = 50g with a initial speed of v = 300m/s hits a wall. The wall is build in a way that the value of the force it causes on the bullet is given by:
. The time starts after the bullet hits the wall and F0 = 70N. How much does the bullet penetrate the wall, in centimeters?

## Homework Equations

Force made by the wall on the bullet =

## The Attempt at a Solution

My first thought was: to determine the distance I need the time, initial speed, final speed and aceleration, depending on the equation. So, I tried to find the time. Failed. Then I tried to find the aceleration... failed. Note that I'm just beginning and my high-school wasn't that great, so I'm having some troubles with exercises like this.

The problem involves calculus if you're up to that at least.

Can you set up a relationship between speed and acceleration?

This is a tricky problem, so it is very important that you really think about how to approach it instead of just trying different things. Can you describe what is physically happening here?

It would be a useful exercise to solve for the case with a constant force for comparison. Then determine what you need to do differently due to the time-dependent force.

## 1. How does the type of bullet affect its penetration through a wall?

The type of bullet greatly affects its penetration through a wall. A round-nose bullet, for example, is designed to penetrate deep into a target and may not fully penetrate a wall. On the other hand, a hollow-point bullet is designed to expand upon impact and may penetrate further through a wall.

## 2. Does the material of the wall affect the bullet's penetration?

Yes, the material of the wall does affect the bullet's penetration. A thin, drywall wall will not provide as much resistance as a thick concrete wall. Additionally, the density and thickness of the material can also impact the bullet's penetration.

## 3. How does the distance from the wall affect bullet penetration?

The distance from the wall can greatly affect the bullet's penetration. The closer the gun is to the wall, the more energy the bullet will have and the deeper it will penetrate. However, as the distance increases, the bullet's energy decreases, resulting in less penetration through the wall.

## 4. Can a bullet penetrate through multiple walls?

Yes, a bullet can penetrate through multiple walls depending on the type of bullet, the material of the walls, and the distance from the walls. A high-powered rifle round, for example, may have enough energy to penetrate through multiple walls, while a handgun round may not.

## 5. Is there a way to test how much a bullet will penetrate through a wall?

Yes, there are various methods to test how much a bullet will penetrate through a wall. These include using ballistic gel or other materials designed to simulate human tissue, conducting controlled experiments with different types of bullets and walls, and utilizing computer simulations to predict bullet penetration. However, it is important to always follow proper safety precautions when conducting these tests.

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