Final answer:
The post-collision speed of the 1.50-kg cart (Cart B) is determined using the conservation of momentum principle. The calculation involves finding the total initial momentum and the final momentum of the 0.500-kg cart (Cart A), then solving for Cart B's velocity to conserve total momentum.
Step-by-step explanation:
To determine the post-collision speed of the 1.50-kg cart (Cart B), we will use the conservation of momentum principle. The momentum before the collision must equal the momentum after the collision because there are no external forces acting on the carts besides the magnetic collision.
Step-by-Step Solution
Firstly, let's calculate the initial momentum of Cart A:
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- Initial momentum of Cart A (pA_initial) = mass of Cart A × velocity of Cart A = 0.500 kg × 129 cm/s = 0.500 kg × 1.29 m/s.
Since Cart B is initially at rest, its initial momentum is 0 kg·m/s. The total initial momentum of the system (ptotal_initial) is just the momentum of Cart A.
Next, we calculate the final momentum of Cart A:
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- Final momentum of Cart A (pA_final) = mass of Cart A × velocity of Cart A after collision = 0.500 kg × (-45 cm/s) = 0.500 kg × (-0.45 m/s).
Since the conservation of momentum applies, the sum of the final momenta should equal the total initial momentum.
ptotal_initial = pA_final + pB_final
0.500 kg × 1.29 m/s = 0.500 kg × (-0.45 m/s) + 1.50 kg × velocity of Cart B
Solving for the velocity of Cart B:
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- velocity of Cart B = (0.500 × 1.29 + 0.500 × 0.45) / 1.50
The final velocity of Cart B is calculated to be velocity of Cart B.