Bullet shot through stationary wooden block

[yokialana]

Homework Statement

So I have a block that has had a bullet shot through it at an initial speed of 280m/s. It is 0.03kg and after it leaves the block it is traveling at 190m/s. The block is a length of 0.012m and weighs 1.50kg. What is the average force exerted on the block?

Homework Equations

ek=0.5mv2
f=ma

The Attempt at a Solution

I have no idea what I'm doing. I found the first part of the question, which was the change in kinetic energy.

 

[CFede]

As you said, you already did the first part of this problem, which is to find the change in kinetic energy (This isn't just a random question, you're going to need this for the second part).

The bullet leaves the block with less kinetic energy because of the work the block does. Since the bullet doesn't interact with anything else, then the change on it's kinetic energy has to be equal to the work done by the block.

Now, with this, you should be abble to easily determine the work excerted by the block and you know the width of the block. Getting the average force should be pretty straight forward from there.

 

[yokialana]

Oh so you just use w/d= f? I think I got it.

 

[CFede]

Precisely :D

 

[Nickie]

But I don't know how to find the average force exerted on the block.

I can provide a response to this content by explaining the physical principles and equations that can be used to solve this problem.

Firstly, we can use the conservation of momentum principle to solve this problem. This principle states that the total momentum before an event is equal to the total momentum after the event, assuming there are no external forces acting on the system. In this case, the initial momentum of the bullet is equal to its final momentum after it exits the block, and the initial momentum of the block is zero since it is stationary.

We can express this mathematically as:
m_bullet * v_initial_bullet = m_bullet * v_final_bullet + m_block * v_final_block

where m_bullet is the mass of the bullet, v_initial_bullet is the initial velocity of the bullet, v_final_bullet is the final velocity of the bullet, m_block is the mass of the block, and v_final_block is the final velocity of the block.

Rearranging this equation, we can solve for the final velocity of the block:
v_final_block = (m_bullet * v_initial_bullet)/m_block

Plugging in the given values, we get:
v_final_block = (0.03kg * 280m/s)/1.50kg = 5.6m/s

Next, we can use the equation f=ma to find the average force exerted on the block. This equation states that force is equal to mass multiplied by acceleration. In this case, the acceleration of the block can be calculated by dividing the change in velocity by the time it takes for the bullet to pass through the block.

We can express this mathematically as:
f = m_block * (v_final_block - v_initial_block)/t

where t is the time it takes for the bullet to pass through the block.

Since the block is 0.012m long and the bullet is traveling at 190m/s when it exits the block, we can calculate the time as:
t = 0.012m/190m/s = 0.000063s

Plugging in the values, we get:
f = 1.50kg * (5.6m/s - 0m/s)/0.000063s = 133.33N

Therefore, the average force exerted on the block