A 75-kg man stands on a spring scale in an elevator. During the first 3 seconds of motion from rest, the tension T in the hoisting cable is 8300 N. Find the reading R of the scale in newtons during this interval and the upward velocity v of the elevator at the end of the 3 seconds. The total mass of the elevator, man, and scale is 750 kg.
A 75-kg man stands on a spring scale in an elevator. During the first 3 seconds of motion from rest, the tension T in the hoisting cable is 8300 N. Find the reading R of the scale in newtons during this interval and the upward velocity v of the elevator at the end of the 3 seconds. The total mass of the elevator, man, and scale is 750 kg.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
A 75-kg man stands on a spring scale in an elevator. During the first 3 seconds of motion from rest, the tension T in the hoisting cable is 8300 N. Find the reading R of the scale in newtons during this interval and the upward velocity v of the elevator at the end of the 3 seconds. The total mass of the elevator, man, and scale is 750 kg.
Transcribed Image Text:### Elevator and Passenger Forces Diagram
This diagram illustrates the forces acting on an elevator and a passenger standing inside it.
#### Components:
1. **Elevator System:**
- The elevator is depicted as a rectangular box containing a standing passenger.
- **Forces Acting on the Elevator:**
- **Tension (T):** An upward force of 8300 N is acting on the elevator.
- **Weight of the Elevator:** The weight acting downward is calculated as \(750 \times 9.81 = 7360 \, \text{N}\).
- **Acceleration (\(a_y\)):** Indicates the direction of net acceleration acting upwards.
2. **Passenger:**
- Illustrated as a figure standing on a platform, representative of the elevator floor.
- **Forces Acting on the Passenger:**
- **Normal Reaction (R):** An upward reaction force supporting the passenger.
- **Weight of the Passenger:** The weight is calculated as \(75 \times 9.81 = 736 \, \text{N}\).
- **Acceleration (\(a_y\)):** Points upward, indicating the acceleration affecting the passenger.
#### Explanation:
- **Tension vs. Weight (Elevator):** The tension in the cable (\(T = 8300 \, \text{N}\)) is greater than the weight of the elevator (\(7360 \, \text{N}\)), suggesting an upward acceleration.
- **Net Force on Passenger:** The normal reaction \(R\) ensures the passenger remains stationary relative to the elevator when considering the net effect of gravity and motion.
- **Acceleration of System:** The upward-directed arrows labeled \(a_y\) indicate that both the elevator and passenger experience a net acceleration upward, which affects the normal forces and the sensation of weight.
This diagram is useful for understanding the interplay of forces in a system subject to gravitational and mechanical forces, such as an elevator in motion.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY