Conclusion of Systems Analysis
The concept of energy conservation is fundamental to understanding both financial systems and human systems. In financial systems, energy is conserved when systems operate, and in human systems, particularly in the realms of work and energy, the principles of energy transfer and conversion are central. For systems to continue functioning across timescales ranging from milliseconds to millennia, the principles of energy conservation must hold true. This is a foundational concept in physics, where the total energy within a closed system remains constant, and energy redistributes between forms or between a system and its surroundings.
The Work-Energy Principle: Gravitational Potential Energy and Internal Energy
The work-energy principle in physics states that the work done on an object is equal to the change in its kinetic energy. However, in this discussion, we focus on gravitational potential energy and internal energy. Moving up or down stairs does not change your kinetic energy because you remain in the same position. However, moving up 1 meter reduces your gravitational potential energy by 735 joules (as calculated for a 75 kg person), which translates to a decrease in internal energy.
In the context of stair-climbing, moving up 1 meter changes both gravitational and internal potential energy. However, if the person stays in the same place while the stairs move, there is no change in kinetic or potential energy, leading to the sensation of burning no calories. This concept is explored further in the video by Steve Mould.
Stairs vs. Stair Climber: A Physics Perspective
Climbing stairs involves changing your vertical position, but not your horizontal position. In contrast, a stair climber moves in the same direction as the stairs’ movement, effectively increasing both vertical and horizontal speeds. This transformation of motion means that both kinetic and potential energy are involved, but stair climbing appears to require additional energy compared to simply moving upward in stairs.
The video by Steve Mould demonstrates this dynamic using a reference frame. From the stair climber’s perspective, they are stationary, while the stairs move upward at a constant velocity. This perspective aligns with any inertial reference frame, where physical laws remain unchanged. It also highlights that stair climbers experience a change in internal energy due to the constant movement of the stairs, adding complexity to the energy transformation.
The Gravity and Internal Energy Relationship
As explained by physicistBM, the gravitational potential energy (U) between objects is not a constant value because the gravitational field itself is variable. The previously defined formula U = mgy assumes a constant gravitational field, but in reality, the gravitational force decreases with height. This difference in gravitational potential energy is converted into internal energy, primarily due to the movement of the floor and walls as they ascend.
The staircase analogy provides a relatable example of this concept. Moving up a staircase involves both vertical and horizontal motion, leading to a significant change in gravitational potential energy. Simultaneously, theBoundaries, floor, and walls being lifted add to the total energy stored internally within the system, as seen from the stair climber’s frame of reference.
Fixing the Misconception: Why Stair Climbers Are-files Efficiently
The misconception that stair climbers feel more "efficient" is a result of misunderstanding the transformation of energy. Moving up 1 meter on stairs increases both kinetic and potential energy, while a stair climber simultaneously increases these energies due to their motion. This additional energy is often felt during stair climbing, as it requires the body to work against gravity to lift the chair and walls, giving an appearance of higher calorie expenditure.
By reframing this into a reference frame moving with the stairs, the stair climber’s motion becomes stationary, indicating an inertial frame where the work-energy principle remains consistent. This perspective emphasizes that the work done on the stair climber is similar to that required to move up 100 floors, yet the energy expenditure appears less because the stair system itself moves as the individual climbs.
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Final Thought: While stairclimbing and climbing stairs both involve changes in kinetic and gravitational potential energy, the specific dynamics when considering relative motion and reference frames differ. Understanding these principles is crucial for grasping energy transformations, from solar systems to human dynamics.
