How Much Force Accelerates a Bullet in a Rifle?

[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.

 

[Simon Bridge]

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.

 

[Emperor]

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

 

[Simon Bridge]

I do not, as a rule, actually complete the problems here.
That's your job ;)

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

 

[HalfLostAndSearching]

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.