# Rifle Force: Calculating Force Exerted on Bullet

• knight4life
In summary, the conversation is about solving for the force exerted by a rifle on a bullet while it is in the barrel. The given information includes the mass and muzzle velocity of the bullet, as well as the distance over which the acceleration occurs. The problem can be solved using the equations f=ma and Vx^2=Vox+2ax(x-xo). One approach is to solve for the acceleration first, and then substitute it into Newton's Second Law. However, a more efficient approach is to substitute the equation a=F/m into the other equation and solve for the unknown force. Ultimately, the correct answer is obtained by not taking the square root of the calculated value for acceleration.
knight4life

## Homework Statement

A rifle shoots a 4.20 g bullet out of its barrel. The bullet has a muzzle velocity of 955 m/s just as it leaves the barrel.

Assuming a constant horizontal acceleration over a distance of 43.0 cm starting from rest, with no friction between the bullet and the barrel, what force does the rifle exert on the bullet while it is in the barrel?

## Homework Equations

f=ma Vx^2=Vox+2ax(x-xo)

## The Attempt at a Solution

I did (955)^2/ 2*.43m to get the acceleration of 1029.8m/s^2
when i do F=ma I get 4.3218 which the online homework is saying is incorrect.

You might want to recalculate your acceleration.

Hi, knight4life.

The second relevant equation looks misquoted. Nevertheless, the substituted values in your computation of the acceleration are correct, so you did something wrong when entering them into the calculator.

I noticed how you solved the problem: First, you solved for the acceleration, and then you substituted this value, along with the given mass, into the equation which expresses Newton's Second Law.

A better approach is to substitute the equation, a = F/m, into the other equation and solve for the unknown, which is the force F, and then substitute the values. This will allow you to see how changing one variable, such as the mass, affects the unknown (a generalization of the problem--does a bullet with more mass require more force to obtain the given velocity? this is also a means to check your work), and among other things, it will reduce numerous calculator computations, which could lead to large round-off errors if your not careful. Try it and compare with your approach.

Good luck with your studies. =)

LowlyPion said:
You might want to recalculate your acceleration.

I did (955)^2/ 2*.43m then too square root to get 1029.8 m/s2 should i not have taken the square root of 1060494.186?

knight4life said:
I did (955)^2/ 2*.43m then too square root to get 1029.8 m/s2 should i not have taken the square root of 1060494.186?

What do you think if

a = V2/2x

LowlyPion said:
What do you think if

a = V2/2x

No, I redid my calculations, without taking the square root and I got the correct answer.

All's well that ends well then.

## 1. How is the force exerted on a bullet calculated?

The force exerted on a bullet is calculated using the equation F = m x a, where F is the force, m is the mass of the bullet, and a is the acceleration. This means that the force exerted on a bullet is directly proportional to its mass and the acceleration it experiences while traveling through the rifle barrel.

## 2. What factors affect the force exerted on a bullet?

The force exerted on a bullet is affected by several factors including the mass of the bullet, the velocity of the bullet, the length of the rifle barrel, and the type of firearm being used. Additionally, external forces such as air resistance and gravity can also impact the force exerted on a bullet.

## 3. How does the length of the rifle barrel affect the force exerted on a bullet?

The length of the rifle barrel can affect the force exerted on a bullet by increasing or decreasing the acceleration of the bullet. A longer barrel allows for a longer acceleration time, resulting in a higher force exerted on the bullet. However, the length of the barrel alone does not determine the force exerted, as other factors such as the type of firearm and ammunition also play a role.

## 4. Does the amount of gunpowder used affect the force exerted on a bullet?

Yes, the amount of gunpowder used can affect the force exerted on a bullet. More gunpowder means a higher velocity for the bullet, which in turn leads to a higher acceleration and a greater force exerted on the bullet.

## 5. How does air resistance impact the force exerted on a bullet?

Air resistance can have a significant impact on the force exerted on a bullet. As the bullet travels through the air, it experiences air resistance which can slow it down and decrease its velocity. This results in a lower acceleration and a lower force exerted on the bullet.

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