Calculating the velocity of of block that was crossed by a bullet

[danielamartins]

1. I have to create an exercise to calculate the velocity of a block of wood (m=1,5 kg). A bullet passed through a block that was on a table also made of wood. What I really want to calculate is the initial velocity of the bullet, but, in order to do that, I need to know the velocity of the block after it was hit by the bullet. I only know that the coefficient of friction between the block and the table is 0,4 (μ) (is it static or kinetic?), and that the block moved 1,2 m (d).

Homework Equations

Eci=Ed+Ecf

The Attempt at a Solution

I used the Work-Energy theorem. Eci=Ed+Efi -> 1/2×m×Vi^2=m×g×µ×d
Which gave me the "initial" velocity of the block - 3,098 m/s

The thing is..can I use the Work-Energy theorem in this case, knowing that the bullet passed through the block? If so, are the calculations right? And which coefficient of friction should I use in the calculations? The static or the kinetic? (Before the bullet hit it, the block was stationary)

 

[cepheid]

Do you actually mean that the bullet passed through the block (i.e. it went in one side and out the other)? Are you sure the question doesn't mean that the bullet became embedded in the block?

Static friction is not that relevant, in the sense that, whatever it is, it was overcome when the bullet struck the block and the block began moving. Kinetic friction is the reason why the block only moves 1.2 m, as opposed to moving forever. You should assume that the coefficient given is the kinetic one. Based on the fact that the block only moved 1.2 m, and the frictional force, you can compute what the initial velocity of the block must have been. Using that, plus conservation of momentum, you can figure out the velocity of the bullet before striking the block.

Your equation, which says that all the initial kinetic energy of the block is lost due to work done by friction, makes sense. [STRIKE]However, 3098 m/s seems like a ridiculously large speed. Maybe double check your arithmetic[/STRIKE]. EDIT: nevermind. I momentarily forgot that you use commas as decimal points, and not as thousands separators. My apologies. Just over 3 m/s seems to be approximately correct.

 

[danielamartins]

Thanks!
It goes in one side and out the other because it's supposed to hit a "person" after.
I'm going to check with my teacher, and I'll post the feedback here tomorrow..

 

[danielamartins]

My teacher just told me that I couldn't use the Eci=Ed+Efi because the block wasn't moving initially. And told me that I needed to use the Wnc = Δ KE (Wnc being the work done by the friction force). But isn't it the same thing? Plus, can't I use the Eci=Ed+Efi if I consider the "initial moment" as the moment right after the bullet hit the block?

 

[Nickie]

I would suggest using the conservation of momentum equation to calculate the initial velocity of the bullet. This equation states that the initial momentum of the bullet (mv) is equal to the final momentum of the bullet and block (m'v' + M'V') after the collision. Here, m' and v' represent the mass and velocity of the bullet after the collision, and M' and V' represent the mass and velocity of the block after the collision.

To solve for the initial velocity of the bullet, you would need to know the final velocity of the block after the collision. This can be calculated using the Work-Energy theorem as you have done, assuming that the block and bullet are the only objects involved in the collision. The coefficient of friction to use in these calculations would be the kinetic friction coefficient, since the block is moving after the collision.

However, it is important to note that the initial velocity of the bullet calculated using this method will not be the true initial velocity, as some of its energy was lost during the collision. To accurately calculate the initial velocity of the bullet, more information about the collision (such as the type of bullet and the material of the block) would be needed. Additionally, I would suggest using a more precise method such as high-speed cameras to measure the velocity of the bullet directly.

In summary, while the Work-Energy theorem can be used to calculate the velocity of the block after the collision, it may not accurately determine the initial velocity of the bullet and more information and precise methods would be needed for a more accurate calculation.