An Analysis of a Man's Weight Reading on a Spring Weighing Machine Inside an Elevator
The spring weighing machine inside an elevator provides a dynamic reading based on the acceleration or deceleration of the elevator. Whether the elevator is going up or down, the weight reading changes due to the varying gravitational forces experienced by the person inside. Understanding this phenomenon is crucial for comprehending the mechanics of weight measurement in dynamic environments.
Understanding Acceleration in Elevators
Let's consider the scenario where a man weighing 60 kg stands on a spring weighing machine inside an elevator that is coming to rest with a retardation of 4.0 m/s2. This retardation, or deceleration, can be used to understand how the weight reading on the machine changes.
Going Down
When the elevator is going down and feels heavier as it comes to rest, it means the effective gravity is increased to 14 m/s2. This is because the elevator decelerates, which adds an additional downward force.
The formula to calculate the new effective gravity is:
geffective 10 m/s2 4 m/s2 14 m/s2
The weight reading on the scale will therefore be:
60 kg * 1.4 84 kg
Going Up
Conversely, when the elevator is going up and feels lighter as it comes to rest, it means the effective gravity is decreased to 6 m/s2. This is due to the elevator accelerating upward.
The formula to calculate the new effective gravity is:
geffective 10 m/s2 - 4 m/s2 6 m/s2
The weight reading on the scale will therefore be:
60 kg * 0.6 36 kg
Behavior When the Elevator is at Rest
If the elevator is at a constant speed, for example, at rest or moving at a constant velocity, the spring weighing machine will show the person's weight as 60 kg. This is because the forces inside the elevator are balanced, and the acceleration is zero.
However, if the elevator is at rest just instantaneously—for an infinite short period of time—while the velocity is changing**, the spring weighing machine will temporarily show a different weight. This occurs due to the non-zero acceleration involved.
The weight reading will be:
Weight Mass * (g (a))
Where a is the acceleration in m/s2.
Conclusion
The reading on the spring weighing machine inside an elevator is dependent on the elevator's acceleration. This principle is particularly useful in understanding the mechanics of weight measurement in dynamic environments such as elevators. Whether the elevator is speeding up, slowing down, or moving at a constant velocity, the weight reading reflects the effective gravity experienced by the person standing on the machine.