Quick question on explaining the law of conservation of momentum.

[Senjai]

I have done the question already and attained the correct answer. However if it was a written question i do not know how i could prove the following.

A 7.3 x 10^3 kg space vehicle and its empty 6.8 x 10^2 booster unit are moving together through space at 370 m/s. An explosion lasting 2.2s is used to separate the two parts. If the speed of the space vehicle is increased to 430 m/s, what impulse acted on the booster unit?

I used the Impulse formula $$I_{space vehicle} = \Delta{p}$$

And used the change of momentum of the space vehicle to determine the Impulse exerted on it. How would i prove that this impulse is the same in magnitude and opposite in direction as the impulse exerted on the booster unit?

Is their a way to do this question a different way? Did they give the time for no reason?

Regards, Senjai.

 

[ehild]

The space vehicle, the booster unit together with the explosive constitute a closed system in the far space. Only forces of interaction act among them. According to Newton's third law, if a body "1" acts with force F₁₂ on an other body "2" this other one acts with force F₂₁=-F₁₂ force on the first one.
The momentum is $I=F\Delta t$. The sum of the forces of interaction is F₁₂+F₂₁=0, therefore $I=F_{12}\Delta t+F_{21}\Delta t=0 \rightarrow I_1+I_2=0$

The change of momentum is equal to the impulse. When only two bodies are interacting $\Delta p_1+\Delta p_2=0$

The sum of forces in a closed system is 0. So is the overall change of momentum.

The vehicle and booster are separated by an explosion, but we can assume that no momentum is wasted, or this waste (the momentum of escaping particles of the explosive) is negligible -we have only two interacting bodies.

ehild

 

[Senjai]

Thank you so much :P Appreciate it :)