Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to consider are the mass of the elevator and its load, the final velocity, and the time taken to reach that velocity.

The forces in the free-body diagram are tension and the weight of the elevator. The tension on the cable is calculated as \(5400 N\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of tension force

The tension force is described as the force transferred through a rope, string, or wire when it is pulled by opposing forces.

Step 2: Construct the problem

Let construct the problem with these values and the mass of the elevator. It can be done as follows:

Consider an elevator with load having a mass of \(500 kg\) starts from rest. It moves upwards with an acceleration of \(1 m/{s^2}\) and reached final point after \(12 s\) with the final velocity of \(12 m/s\). Calculate the tension on the elevator cable with the help of a free body diagram.

\(\begin{array}{c}u = 0\\a = 1 m/{s^2}\\t = 12 s\end{array}\)

\(\begin{array}{c}v = 0 + \left( {1 m/{s^2} \times 12 s} \right)\\ = 12 m/s\end{array}\)

Step 3: Draw the free body diagram.

A free-body diagram can be drawn by considering the forces that act on the cable. There is a force, \(W\) acting downwards that is equal to the weight of the elevator. The tension, \(T\) on the cable is acting upwards, opposite to the weight of the elevator, and acceleration is in the upward direction as it moves upwards. Thus, the free body diagram can be drawn as follows:

The forces that act in the y direction are equal to the sum of the tension and weight of the elevator.

\(\begin{array}{l}{F_y} = ma\\T - W = ma\\T - mg = ma\\T = m\left( {a + g} \right)\end{array}\)

Here, \({F_y}\) is the total force acting on the elevator in the y direction and \(g\) is the acceleration due to gravity which is equal to \(9.8 m/{s^2}\). Substitute the known values to calculate tension on the cable.

\(\begin{array}{c}T = 500 kg\left( {1 m/{s^2} + 9.8 m/{s^2}} \right)\\ = 5400 kg.m/{s^2}\\ = 5400 N\end{array}\)

Therefore, tension on the cable is \(5400 N\).

Find Study Materials for

Create Study Materials

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Definition of tension force

Step 2: Construct the problem

Step 3: Draw the free body diagram.

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Definition of tension force

Step 2: Construct the problem

Step 3: Draw the free body diagram.

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics