A 1.00-kg red cart is moving rightward with a speed of 60cm/s when it collides with a 0.50 -kg blue cart that is initially at rest.After the collision, the blue cart moving rightward with a speed of 80cm/s The red cart is still moving rightward but has slowed down to a speed of 20cm/s Enter the momentum values of each individual cart and of the system of two carts before and after the collision. Also indicate the change in momentum of the carts and of the system

Here's how to analyze the momentum before and after the collision:<br /><br />**Before Collision:**<br /><br />* **Red Cart:**<br /> * Momentum = mass * velocity<br /> * Momentum = (1.00 kg) * (60 cm/s) = 60 kg⋅cm/s<br /><br />* **Blue Cart:**<br /> * Momentum = (0.50 kg) * (0 cm/s) = 0 kg⋅cm/s<br /><br />* **System (Red + Blue):**<br /> * Total momentum = momentum of red cart + momentum of blue cart<br /> * Total momentum = 60 kg⋅cm/s + 0 kg⋅cm/s = 60 kg⋅cm/s<br /><br />**After Collision:**<br /><br />* **Red Cart:**<br /> * Momentum = (1.00 kg) * (20 cm/s) = 20 kg⋅cm/s<br /><br />* **Blue Cart:**<br /> * Momentum = (0.50 kg) * (80 cm/s) = 40 kg⋅cm/s<br /><br />* **System (Red + Blue):**<br /> * Total momentum = 20 kg⋅cm/s + 40 kg⋅cm/s = 60 kg⋅cm/s<br /><br />**Change in Momentum (Δp):**<br /><br />* **Red Cart:**<br /> * Δp = Final momentum - Initial momentum<br /> * Δp = 20 kg⋅cm/s - 60 kg⋅cm/s = -40 kg⋅cm/s (The negative sign indicates a decrease in momentum)<br /><br />* **Blue Cart:**<br /> * Δp = 40 kg⋅cm/s - 0 kg⋅cm/s = 40 kg⋅cm/s<br /><br />* **System (Red + Blue):**<br /> * Δp = 60 kg⋅cm/s - 60 kg⋅cm/s = 0 kg⋅cm/s<br /><br />**Summary Table:**<br /><br />| Cart/System | Momentum Before (kg⋅cm/s) | Momentum After (kg⋅cm/s) | Change in Momentum (kg⋅cm/s) |<br />|---|---|---|---|<br />| Red Cart | 60 | 20 | -40 |<br />| Blue Cart | 0 | 40 | 40 |<br />| System (Red + Blue) | 60 | 60 | 0 |<br /><br /><br />**Key Takeaway:** The total momentum of the system is conserved. The red cart loses momentum, and the blue cart gains an equal amount of momentum. This is consistent with the principle of conservation of momentum, which states that in a closed system (no external forces), the total momentum before a collision is equal to the total momentum after the collision.<br />