Interesting Physics Problem: Momentum and Velocity Calculation
Given data: Mass of cart 1 (m1): 2.3 kg Mass of cart 2 (m2): 1.5 kg Final velocity of cart 2 (V2): 4.9 m/s Final velocity of cart 1 (V3): -1.9 m/s
To find the total momentum of the system just before the carts collide, we use the formula: total momentum = m1 * v2 + m2 * v2. Plugging in the values, we get:
Total momentum = 2.3 * 4.9 + 1.5 * (-1.9) = 8.42 kgm/s.
Next, to calculate the velocity of the first cart when the second cart was at rest, we apply the conservation of momentum formula: m1 * V + m2 * V1 = m1 * V2 + m2 * V3. Since V1 (initial velocity of the second cart) is 0, the formula becomes:
2.3 * V + 1.5 * 0 = 2.3 * 4.9 + 1.5 * (-1.9)
Solving the equation above, we find that the velocity of the first cart is 3.660 m/s when the second cart was at rest.