/*! 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 16 Given two springs of identical s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 16

Given two springs of identical size and shape, one made of steel and the other made of aluminum, which has the higher spring constant? Why? Does the difference depend more on the shear modulus or the bulk modulus of the material?

Short Answer

Expert verified
Answer: The shear modulus has a more significant impact on the spring constant because it determines the material's resistance to shearing deformation (twisting), which is a primary concern in spring systems.

Step by step solution

01

Understanding the spring constant

The spring constant (k) measures a spring's stiffness, determining how much force is needed to cause a certain displacement. It can be found using Hooke's Law: F = kx, where F is the force applied to the spring, and x is the displacement from the spring's resting position.
02

The relationship between spring constant and material properties

The spring constant depends on the material's properties and the spring geometry. Generally, the spring constant can be written as k = (d^4 * G) / (8 * D^3 * N), where d is the wire diameter, G is the shear modulus, D is the mean coil diameter, and N is the number of active coils. In our case, since the springs are of identical size and shape, the factors related to geometry (d, D, and N) are equal. Therefore, we can conclude that k is directly proportional to G (shear modulus).
03

Comparing the shear modulus of steel and aluminum

The shear modulus of steel is around 80 GPa, while the shear modulus of aluminum is around 26 GPa. Since the spring constant is directly proportional to the shear modulus, the spring made of steel has a higher spring constant than the one made of aluminum.
04

Explaining the importance of shear modulus and bulk modulus

In this context, the shear modulus (G) is the dominant factor determining the spring constant because it describes how resistant a material is to shearing deformation (twisting). Bulk modulus (B) measures a material's resistance to uniform compression, which is not a primary concern in spring systems. Therefore, the difference in spring constants depends more on the shear modulus of the material than the bulk modulus.

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

A fountain sends water to a height of \(100 . \mathrm{m}\). What is the difference between the pressure of the water just before it is released upward and the atmospheric pressure?

A beaker is filled with water to the rim. Gently placing a plastic toy duck in the beaker causes some of the water to spill out. The weight of the beaker with the duck floating in it is a) greater than the weight before adding the duck. b) less than the weight before adding the duck. c) the same as the weight before adding the duck. d) greater or less than the weight before the duck was added, depending on the weight of the duck.

Salt water has a greater density than freshwater. A boat floats in both freshwater and salt water. The buoyant force on the boat in salt water is that in freshwater. a) equal to b) smaller than c) larger than

If you turn on the faucet in the bathroom sink, you will observe that the stream seems to narrow from the point at which it leaves the spigot to the point at which it hits the bottom of the sink. Why does this occur?

A sealed vertical cylinder of radius \(R\) and height \(h=0.60 \mathrm{~m}\) is initially filled halfway with water, and the upper half is filled with air. The air is initially at standard atmospheric pressure, \(p_{0}=1.01 \cdot 10^{5} \mathrm{~Pa}\). A small valve at the bottom of the cylinder is opened, and water flows out of the cylinder until the reduced pressure of the air in the upper part of the cylinder prevents any further water from escaping. By what distance is the depth of the water lowered? (Assume that the temperature of water and air do not change and that no air leaks into the cylinder.)
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Magnetism

Read Explanation

Rotational Dynamics

Read Explanation

Dynamics

Read Explanation

Medical Physics

Read Explanation

Translational Dynamics

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.