Average force applied by bullet

[joel amos]

Homework Statement

What is the average force applied by a 75 g bullet that leaves a gun at 1350 m/s and hits a target 75m from the barrel of the gun?

Homework Equations

F = ma

The Attempt at a Solution

First I had the equation F = ma, and began filling in all the variables I could. In this case, I only started with the mass. As for acceleration, I don't know how to find it. Could I rearrange Vf^2 = Vi^2 + 2ax to solve for a? If so, what's the final and initial velocity?

 

[haruspex]

The question makes little sense to me. Average force over what time? The time from reaching the target to coming to rest? How long is that?? You could determine the average over the time from leaving the barrel to being embedded in the target, but that seems a strange thing to ask for.
Please confirm you have represented the question accurately.

 

[joel amos]

The question is as posted. It did seem quite strange to me too. But since the bullet is no longer accelerating after its fired, how can it have a force?

 

[PhanthomJay]

Something is missing in the problem statement. In flight, neglecting air resistance, the bullet exerts a small gravitational force on the Earth and nothing more, until such time as it embeds into the target with a substantial force, but you don't give any more data which is necessary to determine what this force might be.

 

[Nickie]

I understand the importance of using accurate and precise measurements in calculations. In this case, we have a bullet with a mass of 75 g and a velocity of 1350 m/s. To calculate the average force applied by the bullet, we need to know the acceleration experienced by the bullet as it travels from the barrel of the gun to the target.

To find the acceleration, we can use the equation Vf^2 = Vi^2 + 2ax, where Vf is the final velocity (in this case, 1350 m/s), Vi is the initial velocity (which we can assume to be 0 m/s), and a is the acceleration we are trying to find. Solving for a, we get a = (Vf^2 - Vi^2) / 2x.

Plugging in the values, we get a = (1350 m/s)^2 / 2(75 m) = 121500 m^2/s^2 / 150 m = 810 m/s^2.

Now that we have the acceleration, we can use the equation F = ma to calculate the average force applied by the bullet. Plugging in the mass of the bullet (75 g = 0.075 kg) and the acceleration we just found (810 m/s^2), we get F = 0.075 kg * 810 m/s^2 = 60.75 N.

Therefore, the average force applied by the bullet is 60.75 Newtons. It is important to note that this is an average force, as the force applied by the bullet will vary throughout its trajectory. This calculation only gives us an estimate of the overall force applied by the bullet.