/*! 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 17 A marble column with a cross-sec... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 17

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?

Short Answer

Expert verified
Question: Calculate the stress, strain, length change, and maximum weight the marble column can support given the cross-sectional area of 25 cm虏, a load of 7.0 脳 10^4 N, Young's modulus of 6.0 脳 10^10 Pa, and compressive strength of 2.0 脳 10^8 Pa. Answer: a) Stress in the column: 蟽 = 2.8 脳 10^7 Pa b) Strain in the column: 蔚 鈮� 4.67 脳 10^(-4) c) Length change in the column: 鈭哃 鈮� 0.000933 m d) Maximum weight the column can support: F_max = 5.0 脳 10^5 N

Step by step solution

01

Calculate the stress in the column

Using the stress formula (蟽 = F/A), we can determine the stress in the column: 蟽 = (7.0 脳 10^4 N) / (25 cm虏) First, we need to convert the cross-sectional area into square meters: 25 cm虏 = 0.0025 m虏 Now, we can calculate the stress: 蟽 = (7.0 脳 10^4 N) / (0.0025 m虏) = 2.8 脳 10^7 Pa
02

Calculate the strain in the column

Using the strain formula (蔚 = 蟽/Y), we can determine the strain in the column: 蔚 = (2.8 脳 10^7 Pa) / (6.0 脳 10^10 Pa) 鈮� 4.67 脳 10^(-4)
03

Calculate the length change in the column

Using the length change formula (鈭哃 = 蔚 脳 L), we can determine the length change in the column: 鈭哃 = (4.67 脳 10^(-4)) 脳 (2.0 m) 鈮� 9.33 脳 10^(-4) m = 0.000933 m
04

Calculate the maximum weight the column can support

Using the maximum weight formula (F_max = 蟽_max 脳 A), we can determine the maximum weight the column can support: F_max = (2.0 脳 10^8 Pa) 脳 (0.0025 m虏) = 5.0 脳 10^5 N So, the answers are: a) Stress in the column: 蟽 = 2.8 脳 10^7 Pa b) Strain in the column: 蔚 鈮� 4.67 脳 10^(-4) c) Length change in the column: 鈭哃 鈮� 0.000933 m d) Maximum weight the column can support: F_max = 5.0 脳 10^5 N

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

In Problem \(8.41,\) we found that the force of the tibia (shinbone) on the ankle joint for a person (of weight \(750 \mathrm{N})\) standing on the ball of one foot was \(2800 \mathrm{N}\). The ankle joint therefore pushes upward on the bottom of the tibia with a force of \(2800 \mathrm{N},\) while the top end of the tibia must feel a net downward force of approximately \(2800 \mathrm{N}\) (ignoring the weight of the tibia itself). The tibia has a length of $0.40 \mathrm{m},\( an average inner diameter of \)1.3 \mathrm{cm},$ and an average outer diameter of \(2.5 \mathrm{cm} .\) (The central core of the bone contains marrow that has negligible compressive strength.) (a) Find the average crosssectional area of the tibia. (b) Find the compressive stress in the tibia. (c) Find the change in length for the tibia due to the compressive forces.
The prong of a tuning fork moves back and forth when it is set into vibration. The distance the prong moves between its extreme positions is $2.24 \mathrm{mm}\(. If the frequency of the tuning fork is \)440.0 \mathrm{Hz},$ what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.
It takes a flea \(1.0 \times 10^{-3}\) s to reach a peak speed of $0.74 \mathrm{m} / \mathrm{s}$ (a) If the mass of the flea is \(0.45 \times 10^{-6} \mathrm{kg},\) what is the average power required? (b) Insect muscle has a maximum output of 60 W/kg. If \(20 \%\) of the flea's weight is muscle, can the muscle provide the power needed? (c) The flea has a resilin pad at the base of the hind leg that compresses when the flea bends its leg to jump. If we assume the pad is a cube with a side of \(6.0 \times 10^{-5} \mathrm{m},\) and the pad compresses fully, what is the energy stored in the compression of the pads of the two hind legs? The Young's modulus for resilin is $1.7 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} .$ (d) Does this provide enough power for the jump?
Show that the equation \(a=-\omega^{2} x\) is consistent for units, and that \(\sqrt{k / m}\) has the same units as \(\omega\).
An object of mass \(m\) is hung from the base of an ideal spring that is suspended from the ceiling. The spring has a spring constant \(k .\) The object is pulled down a distance \(D\) from equilibrium and released. Later, the same system is set oscillating by pulling the object down a distance \(2 D\) from equilibrium and then releasing it. (a) How do the period and frequency of oscillation change when the initial displacement is increased from \(D\) to $2 D ?$ (b) How does the total energy of oscillation change when the initial displacement is increased from \(D\) to \(2 D ?\) Give the answer as a numerical ratio. (c) The mass-spring system is set into oscillation a third time. This time the object is pulled down a distance of \(2 D\) and then given a push downward some more, so that it has an initial speed \(v_{i}\) downward. How do the period and frequency of oscillation compare to those you found in part (a)? (d) How does the total energy compare to when the object was released from rest at a displacement \(2 D ?\)
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Medical Physics

Read Explanation

Electricity and Magnetism

Read Explanation

Thermodynamics

Read Explanation

Translational Dynamics

Read Explanation

Physical Quantities And Units

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.