A 2686-kg elevator moves with a downward acceleration of 4.20 m/s. What is the tension in the cable that supports the elevator? Assume the elevator is supported by a single cable. Forces exerted by the guide rails and air resistance are negligible. 15042 kN
A 2686-kg elevator moves with a downward acceleration of 4.20 m/s. What is the tension in the cable that supports the elevator? Assume the elevator is supported by a single cable. Forces exerted by the guide rails and air resistance are negligible. 15042 kN
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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![**Physics Problem: Calculating Tension in an Elevator Cable**
A 2686-kg elevator moves with a downward acceleration of \(4.20 \, \text{m/s}^2\). What is the tension in the cable that supports the elevator? Assume the elevator is supported by a single cable. Forces exerted by the guide rails and air resistance are negligible.
**Solution:**
Given:
- Mass of the elevator, \( m = 2686 \, \text{kg} \)
- Downward acceleration, \( a = 4.20 \, \text{m/s}^2 \)
- Gravitational acceleration, \( g = 9.81 \, \text{m/s}^2 \)
The net force acting on the elevator can be determined using the formula:
\[ F_{\text{net}} = m \cdot a \]
The gravitational force acting on the elevator is:
\[ F_{\text{gravity}} = m \cdot g \]
The tension (\( T \)) in the cable can be calculated by considering the net force:
\[ T = F_{\text{gravity}} - F_{\text{net}} \]
\[ T = m \cdot g - m \cdot a \]
\[ T = m \cdot (g - a) \]
Substitute the given values:
\[ T = 2686 \cdot (9.81 - 4.20) \]
\[ T = 2686 \cdot 5.61 \]
**Answer:**
The tension in the cable is approximately \( 15042 \, \text{N} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fd20e11-2399-44a5-beb6-e921116d74ba%2F33369b71-a228-47d1-9bad-24ae239883d4%2F81ou2y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Calculating Tension in an Elevator Cable**
A 2686-kg elevator moves with a downward acceleration of \(4.20 \, \text{m/s}^2\). What is the tension in the cable that supports the elevator? Assume the elevator is supported by a single cable. Forces exerted by the guide rails and air resistance are negligible.
**Solution:**
Given:
- Mass of the elevator, \( m = 2686 \, \text{kg} \)
- Downward acceleration, \( a = 4.20 \, \text{m/s}^2 \)
- Gravitational acceleration, \( g = 9.81 \, \text{m/s}^2 \)
The net force acting on the elevator can be determined using the formula:
\[ F_{\text{net}} = m \cdot a \]
The gravitational force acting on the elevator is:
\[ F_{\text{gravity}} = m \cdot g \]
The tension (\( T \)) in the cable can be calculated by considering the net force:
\[ T = F_{\text{gravity}} - F_{\text{net}} \]
\[ T = m \cdot g - m \cdot a \]
\[ T = m \cdot (g - a) \]
Substitute the given values:
\[ T = 2686 \cdot (9.81 - 4.20) \]
\[ T = 2686 \cdot 5.61 \]
**Answer:**
The tension in the cable is approximately \( 15042 \, \text{N} \).
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