What was the force exerted on the bullet bringing it to rest?

[esco4706]

Homework Statement

a 3 gram bullet traveling at 350m/s squared hits a tree and slows down uniformly to a stop while penetrating a distance of 12 cm into the tree's trunk. What was the force exerted on the bullet bringing it to rest?

Homework Equations

The Attempt at a Solution

I know the speed is 350m/s , the weight is .003 kg, and the distance it traveled is .12 m. I can't figure out how to get the Newtons so i can get the joules. I am stuck.

 

[cristo]

Welcome to the forums. Please note that for homework questions we need to see your working before we can help you. Do you have any thoughts? Hint: how does the work done by the force stopping the bullet relate to the total energy of the bullet before it hits the tree?

 

[m2003]

To find the force exerted on the bullet bringing it to rest, we can use the equation F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is equal to the change in velocity (350 m/s) divided by the time it takes for the bullet to come to a stop. Since we know the distance it traveled (12 cm or 0.12 m) and the initial velocity (350 m/s), we can use the equation v^2 = u^2 + 2as to find the time it takes for the bullet to come to a stop. This gives us a time of 0.000857 seconds.

Now, we can plug in the values into the equation F=ma, where m is 0.003 kg and a is the acceleration we calculated (408,496 m/s^2). This gives us a force of approximately 1,225 Newtons.

To find the joules, we can use the equation W=Fd, where W is the work done, F is the force, and d is the distance. In this case, the work done would be equal to the force (1,225 N) multiplied by the distance traveled (0.12 m), giving us a value of 147 Joules.

Therefore, the force exerted on the bullet bringing it to rest was approximately 1,225 Newtons, and the work done was approximately 147 Joules.