# How Much Force Accelerates a Bullet in a Rifle?

• Emperor
In summary: Keep practicing and you'll get there!In summary, a rifle bullet with a mass of 20g is fired from a gun at 800 m/s, with a barrel length of 80cm. Using the equations F=ma and F=mg, a force of 8000 N is needed to accelerate the bullet at a constant rate from rest to 800 m/s along the length of the barrel. It is important to complete algebra before substituting in numbers.
Emperor

## Homework Statement

A rifle bullet leaves the muzzle of a gun at 800. m/sec. The rifle barrel is 80. cm long and the mass of the bullet is 20.g. What force was needed to accelerate the bullet?

## Homework Equations

Formulas:

F(Total)= ma

F= mg

F = micrometers (m)(g)

## The Attempt at a Solution

t= 80 $\div$ 800 = .1s

a= 800 - 0 $\div$ .1 = 8000 m/s^2

The answer is provided on my sheet as 8000 N, but I don't have a clue as to how to do that. Its the closest I've gotten to the answer.

Welcome to PF;
The equation you used was for time assumed a constant speed along the barrel - but if the bullet travels at a constant speed, then the force must be zero.

if you imagine the bullet has constant acceleration from rest to 800m/s along the length of the barrel, then you use a kinematic equation to find the acceleration.

note: it is best practice to complete the algebra before using the numbers.

Thanks for the help. Did you get the answer "8000 N" just like I did this time around?

I do not, as a rule, actually complete the problems here.

You'll find that the answer is not as important as your understanding of the physics behind it.

To find the force needed to accelerate the bullet, we can use the formula F = ma, where F is the force, m is the mass of the bullet, and a is the acceleration.

First, we need to convert the mass of the bullet from grams to kilograms, since the unit for force is Newtons (N) and the unit for mass is kilograms (kg). 20 grams is equal to 0.02 kilograms.

Next, we need to find the acceleration of the bullet. We can use the formula a = v/t, where a is the acceleration, v is the velocity, and t is the time. We are given the initial velocity (v) of the bullet, which is 800 m/s, and we can calculate the time (t) it takes for the bullet to travel through the barrel using the length of the barrel (80 cm) and the initial velocity (800 m/s).

t = 0.8 m / 800 m/s = 0.001 s

Now we can plug in our values into the formula F = ma:

F = (0.02 kg)(800 m/s^2) = 16 N

Therefore, the force needed to accelerate the bullet is approximately 16 Newtons. This is the force exerted on the bullet by the gun as it accelerates it through the barrel.

## What is force and motion?

Force and motion is the relationship between the movement of an object and the forces acting upon it. Force is a push or pull on an object, and motion is the change in position of an object over time.

## What is Newton's First Law of Motion?

Newton's First Law of Motion states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force.

## What is the difference between speed and velocity?

Speed is the rate at which an object moves, while velocity is the rate at which an object moves in a specific direction. In other words, velocity includes both the speed and direction of an object's motion.

## What factors affect an object's acceleration?

An object's acceleration is affected by the magnitude and direction of the force applied to it, as well as its mass. The greater the force or the smaller the mass of an object, the greater its acceleration will be.

## How can the motion of an object be described using graphs?

The motion of an object can be described using position-time and velocity-time graphs. A position-time graph shows the change in an object's position over time, while a velocity-time graph shows the change in an object's velocity over time. By analyzing these graphs, we can determine an object's speed, direction of motion, and acceleration.

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