Conservation of Momentum: Speed of Trolley Calculation

What is the speed of the trolley after the entire sand bag is empty?

Can you calculate the final speed of the trolley?

Answer:

The speed of the trolley after the entire sand bag is empty is approximately 29.3 km/h.

When dealing with the conservation of momentum, it's important to consider the initial and final states of the system. In this scenario, we have a trolley with a mass of 300 kg moving uniformly with a speed of 27 km/h while carrying a sandbag of 25 kg. As the sand leaks out of the trolley, the total mass of the system decreases, affecting the final speed of the trolley.

According to the law of conservation of momentum, the total momentum of a system remains constant if no external forces are acting on it. This means that the initial momentum of the system must equal the final momentum after the sandbag is empty.

Initially, the total mass of the system (trolley + sandbag) is 325 kg moving at 7.5 m/s. This gives us an initial momentum of 2437.5 kg m/s. After the sandbag is empty, the mass of the trolley reduces to 300 kg. Using the conservation of momentum equation, we can calculate the final velocity of the trolley after the sandbag is empty.

By solving the equation, we find that the final velocity of the trolley is approximately 8.125 m/s, which when converted back to km/h gives us the final speed of the trolley as approximately 29.3 km/h.

Understanding concepts like the conservation of momentum can help us solve complex physics problems and explain the behavior of objects in motion. It's essential to apply these principles to various scenarios to deepen our understanding of physics.