What Is the Relative Speed of Two Parts of a Spacecraft After Detonation?

[musicmaniac]

Hey everyone,

Homework Statement

A spacecraft is separated into two parts by detonating the explosive bolts that hold them together. The masses of the parts are 1200 kg and 1900 kg. The magnitude of the impulse on each part from the bolts is 400 N·s. With what relative speed do the two parts separate because of the detonation?

Homework Equations

p= mv
no external forces acting, so p initial = p final

The Attempt at a Solution

1st attempt:
400= 3100v

400/3100= .129032 WRONG

2nd attempt:
3100(0)=1200v+1900v
-1200v= 1900v

v= -1200/1900= -.631579?
or v= 1900/.1200= -1.58333?

this attempt seems wrong as well

 

[PhanthomJay]

Instead of using conservation of momentum, what about the impulse-momentum law?

 

[unscientific]

Each part has arbitrary momentum 400 N·s, not both..

 

[musicmaniac]

so does that mean I should do 2(400)N/s= 1200kg+1900kg(v)

so 800N/s= 3100kg(v)

v= .258065m/s?

I am really confused with understanding the way the information is being given to me in this problem. I feel the way I am interpreting the information is where I am getting stuck.

 

[musicmaniac]

does anyone have any ideas of where to go next? I am completely stuck.

 

[naresh]

Make sure you understand the impulse-momentum relation
https://www.physicsforums.com/library.php?do=view_item&itemid=53

Each part is given some impulse (here, 400 Ns), so treat the parts separately.

Impulses are vector quantities, so you cannot add them up to give you 2(400) Ns. Before you attempt the problem even, what directions do you think the impulses on the two parts should have (and why)?

 

[musicmaniac]

the parts should have impulses of opposite directions. One part will increase in momentum and the other will lose momentum, right?

 

[PhanthomJay]

the parts should have impulses of opposite directions.

right

One part will increase in momentum and the other will lose momentum, right?

No. The momentum of each increases, but they increase in opposite directions. What is the velocity of each immediately after the explosion? What is their relative speed with respect to each other?

 

[musicmaniac]

ok so right now here is my thought process:

impulse is 400N*s so p final - p initial = 400

p final = 400 = 1200kg(v)

400/1200kg = .3333 m/s

then, 400 = 1900kg(v)

400/-1900kg = -.210526 m/s

so the two velocities are -.3333 m/s and .210526 m/s

do these velocities seem correct?

relative speed

= .3333 m/s + (-.210526 m/s) = .122807 m/s

did I calculate the relative motion correctly?

 

[LowlyPion]

I don't see how they would subtract. You are looking at 2 speeds each moving away from each other at 180°.

Relative speeds then ...

 

[musicmaniac]

yea you are right, they are moving directly away from each other, so I should add the two speeds together

so .33333 m/s + .210526 m/s = .543859 m/s

I hope I finally finished this problem, lol.

 

[musicmaniac]

is there anyone who knows if my relative speed between the two parts is correct?

 

[LowlyPion]

is there anyone who knows if my relative speed between the two parts is correct?

If your math is correct, that looks better.