Electromagnetic Attraction: Momentum Calculation

What is the total momentum of the system of the two carts at a certain instant before they collide? What was the velocity of the first cart when the second cart was still at rest? Part a) Total momentum of the system of the two carts is 8.23 kg m/s at the instant before they collide. Part b) The velocity of the first cart was 3.05 m/s when the second cart was still at rest.

Before the carts collide, momentum plays a key role in determining their behavior. The total momentum of the system of the two carts can be calculated by summing the individual momentums of each cart.

Part a: Total Momentum Calculation

The momentum of the first cart (2.7 kg) is calculated by multiplying its mass with its velocity:

Momentum of cart 1: P1 = m1v1 = (2.7)(3.7) = 9.99 kg m/s

The momentum of the second cart (1.1 kg) is calculated in a similar manner:

Momentum of cart 2: P2 = m2v2 = (1.1)(-1.6) = -1.76 kg m/s

Thus, the total momentum of the system is the sum of the individual momentums:

Total Momentum: P = P1 + P2 = 8.23 kg m/s

Part b: Velocity Calculation

As the two carts are drawn towards each other due to electromagnetic attraction and no external forces are present, momentum is conserved. Therefore, the initial momentum of the first cart when the second cart was at rest (Pinitial) is equal to the final total momentum:

Initial Momentum: (2.7 kg) * v = 8.23 kg m/s

Solving for velocity (v), we find that the velocity of the first cart when the second cart was at rest is 3.05 m/s.

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