Elevator Free Fall and Scale Readings: The Physics Behind Weightlessness
Imagine a 50 kg person, Amanda, standing on a scale in an elevator that was initially stationary. Suppose the cables are cut, and the elevator begins to free fall. What would be the reading on the scale in Newtons (N) in this scenario?
Understanding Free Fall and Weightlessness
When the elevator is in free fall, it accelerates downward at approximately 9.81 m/s2. In this scenario, Amanda would experience zero apparent weight. This is because the scale measures the normal force exerted on it. In free fall, both Amanda and the scale are accelerating downward at the same rate of 9.81 m/s2, meaning the scale does not exert any upward force on Amanda.
Key Facts and Concepts
The key fact to understand is that everything, including Amanda, the elevator, and the scale, accelerates at the same rate due to gravity. Inside the elevator, there is a sensation of weightlessness, assuming no air resistance.
This is similar to the experience of astronauts aboard the International Space Station (ISS), where they are in a state of microgravity due to the continuous free fall of the station around Earth.
Free Body Diagram and Pseudoforce Analysis
To analyze Amanda's situation, we can create a free body diagram. Amanda is subject to two forces: the gravitational force Fg pulled by the Earth, equal to her mass times gravity (mg), and an inertial pseudoforce Fp acting in the opposite direction due to the elevator's acceleration in free fall, which is also equal to mg.
Given these forces, the net force on Amanda is:
Fnet Fg - Fp mg - (-mg) 0
Therefore, Amanda is effectively weightless in the frame of reference of the elevator, resulting in a scale reading of zero.
Additional Considerations
It's important to note that in a modern elevator, the scale would initially show Amanda's weight dropping to zero during the free fall period. However, as the safety brakes engage, the scale reading would spike back up briefly before settling to her normal weight. This is because the elevator's stopping mechanism counteracts Amanda's downward motion.
Under normal circumstances, the elevator's brakes are designed to engage quickly and safely, preventing the cabin from falling more than 1 or 2 meters.
Conclusion
When an elevator in free fall accelerates downward at 9.81 m/s2, the person standing on the scale will experience zero apparent weight. This phenomenon, known as weightlessness, is reversible and allows us to understand the physics behind the situation more clearly. Astronauts on the ISS experience a similar sensation due to the continuous free fall of the space station around Earth.