High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 8.8 m/s You board an elevator on a skyscraper's ground floor and are transported 190 m above the ground level in three steps acceleration of magnitude 1.2 m/s from rest to 8.8 m/s. followed by constant upward velocity of 8.8 m/s. then deceleration of magnitude 1.2 m/s² from 8.8 m/s to rest
High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 8.8 m/s You board an elevator on a skyscraper's ground floor and are transported 190 m above the ground level in three steps acceleration of magnitude 1.2 m/s from rest to 8.8 m/s. followed by constant upward velocity of 8.8 m/s. then deceleration of magnitude 1.2 m/s² from 8.8 m/s to rest
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Elevator Dynamics and Human Comfort
High-speed elevators function under two limitations:
1. The maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about \( 1.2 \, \text{m/s}^2 \).
2. The typical maximum speed attainable is about \( 8.8 \, \text{m/s} \).
When you board an elevator on a skyscraper's ground floor, the elevator moves 190 m above the ground level in three steps:
- Acceleration of magnitude \( 1.2 \, \text{m/s}^2 \) from rest to \( 8.8 \, \text{m/s} \).
- A constant upward velocity of \( 8.8 \, \text{m/s} \).
- Deceleration of magnitude \( 1.2 \, \text{m/s}^2 \) from \( 8.8 \, \text{m/s} \) to rest.
#### Part A
**Task:** Determine the elapsed time for each of these 3 stages.
*Express your answers using two significant figures separated by commas.*
- Input for acceleration time, constant speed time, and deceleration time (in seconds):
\[
t_{\text{acc}}, \ t_{\text{constant}}, \ t_{\text{dec}}
\]
#### Part B
**Task:** Determine the change in the magnitude of the normal force, expressed as a percentage of your normal weight during each stage.
*Express your answers using two significant figures separated by commas.*
- Input for percentage change of normal force during acceleration, constant speed, and deceleration:
\[
\frac{\Delta F_{N,\text{acc}}}{F_N}, \ \frac{\Delta F_{N,\text{constant}}}{F_N}, \ \frac{\Delta F_{N,\text{dec}}}{F_N}
\]
### Part C
*Complete previous part(s) to proceed.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F939f19e0-6626-477a-ba7a-4282434e880a%2Fd54a133d-331a-4c85-b763-22a82497ca8a%2Fz2yqkjv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Elevator Dynamics and Human Comfort
High-speed elevators function under two limitations:
1. The maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about \( 1.2 \, \text{m/s}^2 \).
2. The typical maximum speed attainable is about \( 8.8 \, \text{m/s} \).
When you board an elevator on a skyscraper's ground floor, the elevator moves 190 m above the ground level in three steps:
- Acceleration of magnitude \( 1.2 \, \text{m/s}^2 \) from rest to \( 8.8 \, \text{m/s} \).
- A constant upward velocity of \( 8.8 \, \text{m/s} \).
- Deceleration of magnitude \( 1.2 \, \text{m/s}^2 \) from \( 8.8 \, \text{m/s} \) to rest.
#### Part A
**Task:** Determine the elapsed time for each of these 3 stages.
*Express your answers using two significant figures separated by commas.*
- Input for acceleration time, constant speed time, and deceleration time (in seconds):
\[
t_{\text{acc}}, \ t_{\text{constant}}, \ t_{\text{dec}}
\]
#### Part B
**Task:** Determine the change in the magnitude of the normal force, expressed as a percentage of your normal weight during each stage.
*Express your answers using two significant figures separated by commas.*
- Input for percentage change of normal force during acceleration, constant speed, and deceleration:
\[
\frac{\Delta F_{N,\text{acc}}}{F_N}, \ \frac{\Delta F_{N,\text{constant}}}{F_N}, \ \frac{\Delta F_{N,\text{dec}}}{F_N}
\]
### Part C
*Complete previous part(s) to proceed.*
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