Final answer:
Using the conservation of momentum principle, we calculate that the initial momentum of cart 2 was -12 kg·m/s before the collision.
Step-by-step explanation:
The student's question pertains to the conservation of momentum during a collision on a low-friction track. Specifically, we're looking to find the initial momentum of cart 2 based on the known momenta of the carts before and after the collision. By using the principle of conservation of momentum, which states m1v1 + m2v2 = m1v'1 + m2v'2, where v and v' represent the initial and final velocities respectively, and m represents the mass of each cart, we can solve for the unknown initial momentum of cart 2.
The known quantities are: initial momentum of cart 1 (+10 kg·m/s), final momentum of cart 1 (-5.0 kg·m/s), and final momentum of cart 2 (-7.0 kg·m/s). Applying conservation of momentum:
+10 kg·m/s (initial momentum of cart 1) + m2v2 (initial momentum of cart 2) = (-5.0 kg·m/s) + (-7.0 kg·m/s)
To find the initial momentum of cart 2, we rearrange the equation:
m2v2 = (-5.0 kg·m/s - 10 kg·m/s) - (-7.0 kg·m/s)
This simplifies to:
m2v2 = -12 kg·m/s
Therefore, the initial momentum of cart 2 was -12 kg·m/s.