/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1 A steel beam is placed verticall... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 1

A steel beam is placed vertically in the basement of a building to keep the floor above from sagging. The load on the beam is $5.8 \times 10^{4} \mathrm{N},\( the length of the beam is \)2.5 \mathrm{m},$ and the cross- sectional area of the beam is \(7.5 \times 10^{-3} \mathrm{m}^{2}\) Find the vertical compression of the beam.

Short Answer

Expert verified
Answer: The vertical compression of the steel beam is approximately \(0.000096625\) meters.

Step by step solution

01

Write down the given information

We know the following values: Load on the beam (F) = \(5.8 \times 10^{4} \mathrm{N}\) Length of the beam (L) = \(2.5 \mathrm{m}\) Cross-sectional area of the beam (A) = \(7.5 \times 10^{-3} \mathrm{m}^{2}\)
02

Find the stress

Using the formula for stress, we have: Stress (蟽) = \(\frac{F}{A}\) Plug in the values: 蟽 = \(\frac{5.8 \times 10^{4} \mathrm{N}}{7.5 \times 10^{-3} \mathrm{m^2}}\) 蟽 = \(7.73 \times 10^6 \mathrm{Pa}\)
03

Find the strain

Using Hooke's Law, we have: Strain (蔚) = \(\frac{蟽}{E}\) The modulus of elasticity of steel (E) is approximately \(2 \times 10^{11} \mathrm{Pa}\). Plug in the values: 蔚 = \(\frac{7.73 \times 10^6 \mathrm{Pa}}{2 \times 10^{11} \mathrm{Pa}}\) 蔚 = \(3.865 \times 10^{-5}\)
04

Calculate the vertical compression

Using the formula for strain, we have: 蔚 = \(\frac{螖L}{L}\) We need to find 螖L (the vertical compression), so we rearrange the formula: 螖L = 蔚 脳 L Plug in the values: 螖L = \(3.865 \times 10^{-5} \times 2.5 \mathrm{m}\) 螖L = \(9.6625 \times 10^{-5} \mathrm{m}\) Therefore, the vertical compression of the steel beam is approximately \(9.6625 \times 10^{-5}\) meters or \(0.000096625\) meters.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Atmospheric pressure on Venus is about 90 times that on Earth. A steel sphere with a bulk modulus of 160 GPa has a volume of \(1.00 \mathrm{cm}^{3}\) on Earth. If it were put in a pressure chamber and the pressure were increased to that of Venus (9.12 MPa), how would its volume change?
A marble column with a cross-sectional area of \(25 \mathrm{cm}^{2}\) supports a load of \(7.0 \times 10^{4} \mathrm{N} .\) The marble has a Young's modulus of \(6.0 \times 10^{10} \mathrm{Pa}\) and a compressive strength of $2.0 \times 10^{8} \mathrm{Pa} .$ (a) What is the stress in the column? (b) What is the strain in the column? (c) If the column is \(2.0 \mathrm{m}\) high, how much is its length changed by supporting the load? (d) What is the maximum weight the column can support?
(a) Sketch a graph of \(x(t)=A \sin \omega t\) (the position of an object in SHM that is at the equilibrium point at \(t=0\) ). (b) By analyzing the slope of the graph of \(x(t),\) sketch a graph of $v_{x}(t) .\( Is \)v_{x}(t)$ a sine or cosine function? (c) By analyzing the slope of the graph of \(v_{x}(t),\) sketch \(a_{x}(t)\) (d) Verify that \(v_{x}(t)\) is \(\frac{1}{4}\) cycle ahead of \(x(t)\) and that \(a_{x}(t)\) is \(\frac{1}{4}\) cycle ahead of \(v_{x}(t) .\) (W) tutorial: sinusoids)
A \(230.0-\mathrm{g}\) object on a spring oscillates left to right on a frictionless surface with a frequency of \(2.00 \mathrm{Hz}\). Its position as a function of time is given by \(x=(8.00 \mathrm{cm})\) sin \(\omega t\) (a) Sketch a graph of the elastic potential energy as a function of time. (b) The object's velocity is given by \(v_{x}=\omega(8.00 \mathrm{cm}) \cos \omega t .\) Graph the system's kinetic energy as a function of time. (c) Graph the sum of the kinetic energy and the potential energy as a function of time. (d) Describe qualitatively how your answers would change if the surface weren't frictionless.
A \(0.50-\mathrm{kg}\) mass is suspended from a string, forming a pendulum. The period of this pendulum is 1.5 s when the amplitude is \(1.0 \mathrm{cm} .\) The mass of the pendulum is now reduced to \(0.25 \mathrm{kg} .\) What is the period of oscillation now, when the amplitude is \(2.0 \mathrm{cm} ?\) (W tutorial: change in period)
See all solutions

Recommended explanations on Physics Textbooks

Kinematics Physics

Read Explanation

Fluids

Read Explanation

Scientific Method Physics

Read Explanation

Modern Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Oscillations

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.