Does Body A Exert a Negative Impulse on Body B in a Closed System?

[nokia8650]

If body A exerts an impulse of say +2Ns on B, then does body A exert an impulse of -2Ns on B providing no external forces act?

Thanks

 

[RoyalCat]

Consider the definition of impulse, Newton's third law and preservation of momentum.

Spoiler

J₁₂ = F₁₂*dt
J₂₁ = F₂₁*dt
dt is the same for both impulses, since the bodies remain in contact for a set time, which is equal for both of them.

F₁₂ = -F₂₁ (Newton's third law)
Therefore:
J₁₂ = -J₂₁
J_tot = J₁₂+J₂₁ = 0
Which makes perfect sense when you consider:
J = dP
The momentum of a system remains constant if no external forces act on that system.