If a 5 kg hammer and a 0.001 kg feather are dropped in a frictionless environment from 2 m high on Earth, which will reach the ground first? Would the time it takes for the fall be greater or smaller if this was done on the Moon?

In a **frictionless environment**—essentially a vacuum where there's no air resistance—the behavior of falling objects is governed solely by gravity. Here's a detailed breakdown of your questions: ### 1. **Dropping a 5 kg Hammer and a 0.001 kg Feather on Earth:** - **Experience of Gravity:** On Earth, both the hammer and the feather are subject to the same gravitational acceleration, approximately **9.81 m/s²**. - **Effect of Mass:** In the absence of air resistance, **mass does not affect the rate of fall**. This principle was famously demonstrated by Apollo 15 astronaut David Scott when he simultaneously dropped a hammer and a feather on the Moon; both hit the ground at the same time. - **Conclusion:** **Both the hammer and the feather will reach the ground simultaneously** when dropped from the same height of 2 meters on Earth in a frictionless environment. ### 2. **Dropping Them on the Moon:** - **Gravitational Acceleration on the Moon:** The Moon's gravitational acceleration is about **1/6th of Earth's**, approximately **1.625 m/s²**. - **Time to Fall:** The time it takes for an object to fall from a certain height is given by the equation: \[ t = \sqrt{\frac{2h}{g}} \] Where: - \( t \) = time to fall - \( h \) = height (2 meters in this case) - \( g \) = gravitational acceleration - **Calculations:** - **On Earth:** \[ t = \sqrt{\frac{2 \times 2\, \text{m}}{9.81\, \text{m/s}²}} \approx 0.64\, \text{seconds} \] - **On the Moon:** \[ t = \sqrt{\frac{2 \times 2\, \text{m}}{1.625\, \text{m/s}²}} \approx 1.57\, \text{seconds} \] - **Conclusion:** **Both objects will still land simultaneously on the Moon**, just taking **longer** to do so compared to Earth because of the Moon's weaker gravitational pull. ### **Summary:** - **On Earth:** In a frictionless environment, the 5 kg hammer and the 0.001 kg feather will **reach the ground at the same time** when dropped from 2 meters. - **On the Moon:** They will **still land simultaneously**, but the **fall will take longer** due to the Moon's weaker gravity. This outcome highlights the fundamental principle that in the absence of air resistance, **all objects accelerate at the same rate regardless of their mass**.