Conservation of Momentum involving a space ship blowing up into three pieces

[SherBear]

Homework Statement

A spaceship of mass 2.30×10^6kg is cruising at a speed of 5.40×10^6m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.20×10^5kg, is blown straight backward with a speed of 2.20×10^6m/s. A second piece, with mass 7.80×10^5kg, continues forward at 1.20×10^6m/s.

What is the speed of the third piece? in m/s

Homework Equations

M3=m3=M-m1+m2

Conservation of Momentum says:

m1v1+m2v2+m3v3=MV

The Attempt at a Solution

To get the weight of the third piece i used
M3=m3=M-m1+m2=
2.30*10^6kg - 5.20*10^5 kg + 7.80*10^5kg= 2.56*10^6 kg

Then
m1v1+m2v2+m3v3=MV

(5.20*10^5kg)(2.20*10^6)+(7.80*10^5kg)(1.20*10^6 m/s)+(2.56*10^6 kg) V3 = (2.30*10^6kg)(5.40*10^6ms)=

This may sound dumb but I don't know how to do this equation

I have 1.44*10^12 + 9.36*10^11 + 2.50*10^6

2.0800025*10^12 = 1.242*10^13

Then do I divide those 2, if so I get 1.67*10^-1 and it's wrong

What am I doing wrong?

Thank you

 

[Doc Al]

To get the weight of the third piece i used
M3=m3=M-m1+m2=
2.30*10^6kg - 5.20*10^5 kg + 7.80*10^5kg= 2.56*10^6 kg

Shouldn't that be: m3 = M - m1 - m2 ?

 

[SherBear]

Shouldn't that be: m3 = M - m1 - m2 ?

I don't know, that piece is going to the right which is to the east and I'm calling that way positive?

 

[SherBear]

I don't know, that piece is going to the right which is to the east and I'm calling that way positive?

It is positive just a mistake, I added it in the equation.

 

[Doc Al]

I don't know, that piece is going to the right which is to the east and I'm calling that way positive?

The direction of motion doesn't affect the mass. (It affects momentum, of course.)

 

[SherBear]

The direction of motion doesn't affect the mass. (It affects momentum, of course.)

I tried subtracting that and I have
1*10^6kg for mass 3

When i plugged it into the conservation I still get 1.67*10^-1 ?

 

[Doc Al]

I tried subtracting that and I have
1*10^6kg for mass 3

Good.

When i plugged it into the conservation I still get 1.67*10^-1 ?

How can you get the same answer with different numbers?

Then
m1v1+m2v2+m3v3=MV

(5.20*10^5kg)(2.20*10^6)+(7.80*10^5kg)(1.20*10^6 m/s)+(2.56*10^6 kg) V3 = (2.30*10^6kg)(5.40*10^6ms)=

Two problems:
(1) As already pointed out, you have the wrong value for the mass of the third piece.
(2) You didn't incorporate the direction of motion. Things that go forward should have + velocity; things that go backward should have -.

 

[SherBear]

Good.


How can you get the same answer with different numbers?


Two problems:
(1) As already pointed out, you have the wrong value for the mass of the third piece.
(2) You didn't incorporate the direction of motion. Things that go forward should have + velocity; things that go backward should have -.

Ok m1 is positive and v1 is negative because it's going backwards?
m2 positive because it's weight, and m2 is positive because it's going forwards?
m3 doesn't matter because it's weight...then solve to get v3?

 

[Doc Al]

Ok m1 is positive and v1 is negative because it's going backwards?
m2 positive because it's weight, and m2 is positive because it's going forwards?
m3 doesn't matter because it's weight...then solve to get v3?

Almost: Masses are always positive, regardless of direction.

v1 is negative, v2 is positive. v3 you will solve for.

 

[SherBear]

Almost: Masses are always positive, regardless of direction.

v1 is negative, v2 is positive. v3 you will solve for.

Ok good, the only value i had to change was v1 to negative because it is going to the left or to the west.

it made V1 value negative

(5.20*10^5)(-1.144*10^12)+(9.36*10^11)+(1*10^6)=(2.30*10^6kg)(5.40*10^6m/s)

i get -1.69*10^-2, is this correct?

 

[SherBear]

Ok good, the only value i had to change was v1 to negative because it is going to the left or to the west.

it made V1 value negative

(5.20*10^5)(-1.144*10^12)+(9.36*10^11)+(1*10^6)=(2.30*10^6kg)(5.40*10^6m/s)

i get -1.69*10^-2, is this correct?

oopse disregard the (5.20*10^5), my mistake

 

[SherBear]

Ok good, the only value i had to change was v1 to negative because it is going to the left or to the west.

it made V1 value negative

(5.20*10^5)(-1.144*10^12)+(9.36*10^11)+(1*10^6)=(2.30*10^6kg)(5.40*10^6m/s)

i get -1.69*10^-2, is this correct?

I was able to use a more simple way and now it's correct, thanks!