Final answer:
When the 1.0-kg balloon is placed on the moving 0.5-kg cart, the conservation of momentum dictates that the combined system must slow down. The final velocity can be calculated using the total initial momentum and the new combined mass, resulting in the cart's velocity decreasing to 0.4 m/s.
Step-by-step explanation:
When a 1.0-kg balloon filled with sand is placed on top of a 0.5-kg cart that is traveling at a speed of 1.2 m/s, the combined system's speed will change according to the principle of conservation of momentum. Assuming no external forces act on the system, the total momentum before and after the balloon is placed on the cart must be the same. Here is how you can calculate the new speed:
Total initial momentum = mass of cart × velocity of cart = 0.5 kg × 1.2 m/s = 0.6 kg · m/s. After adding the balloon, the total mass is 0.5 kg + 1.0 kg = 1.5 kg.
Using conservation of momentum, the final velocity (Vf) can be found with the formula:
0.6 kg · m/s = 1.5 kg × Vf
Solving for Vf gives us a velocity of 0.6 kg · m/s ÷ 1.5 kg = 0.4 m/s. Therefore, the cart slows down after the balloon is placed on it.