# A question in Linear Momentum

1. Oct 2, 2008

### omeromer

1. The problem statement, all variables and given/known data
A piece of wood mass of 10 kilograms Placed on a smooth surface.
15 bullets were fired towards the piece and stabilized in .
The mass of one bullet is 40 grams and its velocity is 1000 meters in second.
Find the velocity of the piece of wood after the 15 bullets were stabilized in .

2. Relevant equations

3. The attempt at a solution

2. Oct 2, 2008

### maniacp08

Although I am new, even I know this will not be answered because no one is going to do the homework for you.

3. Oct 2, 2008

### omeromer

Thank you mania,

Actually this is not a homework question, and I am not studying a physics course. I am mathematician not physician. so why did I post the question ? The answer is that i was asked to convent my sisters daughter in the solution of her teacher.

Her teacher answered the problem as follows

Linear Momentum(before) = Linear Momentum(after)
10 X zero = (10 + 0.6 X 1000) X V where V is the wanted velocity

My sisters daughter wants the solution to be as follows

Linear Momentum(before) = Linear Momentum(after)
10 X zero + 0.6 X 1000 = (10 + 0.6 X 1000) X V, (V still the wanted velocity)

She is claiming that the Linear Momentum(before) depinds on the motion of the bullets as it depends on the motion of the wood piece

What I am suugesting is

Linear Momentum(initial) = Linear Momentum(after the 1st bullet stabilized in the wood piece ) = Linear Momentum(after the 2nd bullet stabilized in the wood piece ) = ...............................= Linear Momentum(after the 15th bullet stabilized in the wood piece )

This yeils to the following

10 X zero + 0.040 X 1000 = (10 + 0.040 ) X V_1 = (10+ 0.040 + 0.040) X V_2 = ...............................= (10 + 15 X 0.040) X V_15

(V_n is the velocity after the nth bullet stabilized in the wood piece , n= 1,2,.....,15 )

Note that v_15 is the wanted velocity

So V = 40 / 10.6 meters /second

Is this true ? or which is?
Thank you all

Last edited: Oct 2, 2008
4. Oct 2, 2008

### LowlyPion

Welcome to PF.

Actually the problem doesn't state as it is worded whether they are fired serially or simultaneously.

But happily it doesn't really matter. 15*bullet mass * speed = (mass of block+ 15 bullets)*final speed.

After the first bullet, if you were doing it serially, you have the momentum of the first in the block and it would be moving forward subsequently with the momentum imparted by the first and it would then add to the momentum of the second to become the new momentum of block and 2 bullets. And so on. And so on to the 15th that would be insinuating itself into a block that already had the momentum of the first 14.
Should be
mb*vb = (B+m)*V
.6 *1000 = 10.6 *V
V= 600/10.6