On a low-friction track, a 0.56-kg cart initially going at 1.85 m/s to the right collides with a cart of unknown inertia initially going at 2.17 m/s to the left. After the collision, the 0.56-kg cart is going at 1.32 m/s to the left, and the cart of unknown inertia is going at 3.22 m/s to the right. The collision takes 0.010 s

To solve this problem, we can apply the principles of conservation of momentum and solve for the unknown inertia of the second cart.

1. Start by writing down the given information:
- Mass of the first cart (m1): 0.56 kg
- Initial velocity of the first cart (v1 initial): 1.85 m/s to the right
- Mass of the second cart (m2): unknown
- Initial velocity of the second cart (v2 initial): 2.17 m/s to the left
- Final velocity of the first cart (v1 final): 1.32 m/s to the left
- Final velocity of the second cart (v2 final): 3.22 m/s to the right
- Collision time (Δt): 0.010 s

2. Apply the conservation of momentum principle:
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, it can be expressed as:
m1 * v1 initial + m2 * v2 initial = m1 * v1 final + m2 * v2 final

3. Substitute the given values into the equation:
(0.56 kg * 1.85 m/s) + (m2 * (-2.17 m/s)) = (0.56 kg * (-1.32 m/s)) + (m2 * 3.22 m/s)

4. Simplify the equation:
1.028 kg·m/s - 2.34 m2/s + 0.7392 kg·m/s - 1.03 m2/s = - 0.7392 kg·m/s + 3.82 m2/s

5. Combine like terms:
-1.311 m2/s - 1.34 m2/s = 3.08 m2/s

6. Combine the t