An express elevator in a skyscraper moves only along a vertical shaft
PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
An express elevator in a skyscraper moves only along a vertical shaft. For convenience, engineers analyzing the ride choose a one-dimensional coordinate axis with its origin at street level and the positive direction defined as downward (toward the parking garages).
During one particular trip the elevator:
• starts at a penthouse level located 60m above street level,
• travels upward 30m to pick up passengers,
• descends 90m nonstop to a parking level,
• finally ascends 20m to a mezzanine restaurant where the passengers exit.
(1) For each of the three travel segments listed, determine the signed displacement of the elevator. Present your answers in a clearly labeled table or list.
(2) Using the same coordinate system, calculate the elevator’s net (overall) signed displacement for the entire trip from the penthouse departure to the mezzanine arrival.
(3) Compute the total distance traveled by the elevator during the trip and contrast it with the magnitude of the net displacement. Explain why the two quantities differ even though they describe the same physical journey.
(4) Suppose a safety sensor inside the shaft was programmed with the more conventional choice of upward-positive. Explain qualitatively how the numerical values of the three individual segment displacements and the net displacement would change under that alternative convention, even though the physical motion is identical.