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.

 

[nlightner]

for your question. The answer to this problem depends on the reference frame and the definition of impulse. In the reference frame of body A, if no external forces act on the system, then body A would exert an impulse of -2Ns on body B. This is because the impulse is defined as the change in momentum, and in this case, the direction of momentum of body B would change from positive to negative, resulting in a negative impulse.

However, in a different reference frame, such as the center of mass frame, the impulse would be equal to 0 as there is no change in momentum in that frame.

It is important to note that the impulse is a vector quantity and its direction depends on the direction of the force and the change in momentum. So, the direction of the impulse can change depending on the reference frame.

I hope this helps to clarify the problem. It is always important to carefully consider the reference frame and definitions when solving physics problems.