{"id":8537,"date":"2023-01-05T22:19:23","date_gmt":"2023-01-05T21:19:23","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=8537"},"modified":"2024-06-08T18:35:14","modified_gmt":"2024-06-08T17:35:14","slug":"how-to-calculate-and-solve-for-hookes-law-linear-elastic-modulus-of-resilience-mechanical-properties","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2023\/01\/05\/how-to-calculate-and-solve-for-hookes-law-linear-elastic-modulus-of-resilience-mechanical-properties\/","title":{"rendered":"How to Calculate and Solve for Hooke’s Law Linear Elastic Modulus of Resilience | Mechanical Properties"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents Hooke’s law linear elastic modulus of resilience. To calculate hooke’s law linear elastic modulus of resilience, two essential parameters are needed and these parameters are Stress at y-direction (\u03c3y<\/sub>)\u00a0<\/strong>and\u00a0Modulus of Elasticity (E).<\/strong><\/p>\n

The formula for hooke’s law linear elastic modulus of resilience:<\/strong><\/h3>\n

Ur<\/sub>\u00a0=\u00a0\u03c3y<\/sub>\u00b2<\/sup>\/2E<\/sub><\/p>\n

Where:<\/p>\n

Ur<\/sub>\u00a0= Hooke’s Law Linear Elastic Modulus of Resilience
\n\u03c3y<\/sub>\u00a0= Stress at y-direction
\nE = Modulus of Elasticity<\/a><\/p>\n

Given an example;
\nFind the hooke’s law linear elastic modulus of resilience when the stress at y-direction is 18 and the modulus of elasticity is 9.<\/p>\n

This implies that;<\/p>\n

\u03c3y<\/sub> = Stress at y-direction = 18
\nE = Modulus of Elasticity = 9<\/p>\n

Ur<\/sub>\u00a0=\u00a0\u03c3y<\/sub>\u00b2<\/sup>\/2E<\/sub>
\nUr<\/sub>\u00a0=\u00a018\u00b2<\/sup>\/2(9)<\/sub>
\nThat is, Ur<\/sub>\u00a0=\u00a0324<\/sup>\/(18)<\/sub>
\nUr<\/sub> = 18<\/p>\n

Therefore, the\u00a0hooke’s law linear elastic modulus of resilience\u00a0<\/strong>is\u00a018 Pa.<\/strong><\/p>\n

Calculating the Stress at y-direction when the Hooke’s Law Linear Elastic Modulus of Resilience and the Modulus of Elasticity are Given<\/strong><\/h3>\n

\u03c3y<\/sub> = \u221aUr<\/sub>(2E)<\/p>\n

Where:<\/p>\n

\u03c3y<\/sub>\u00a0= Stress at y-direction
\nUr<\/sub>\u00a0= Hooke’s Law Linear Elastic Modulus of Resilience
\nE = Modulus of Elasticity<\/p>\n

Let’s solve an example;
\nFind the stress at y-direction when the hooke’s law linear elastic modulus of resilience is 10 and the modulus of elasticity is 8.<\/p>\n

This implies that;<\/p>\n

Ur<\/sub> = Hooke’s Law Linear Elastic Modulus of Resilience = 10
\nE = Modulus of Elasticity =\u00a0 8<\/p>\n

\u03c3y<\/sub> = \u221aUr<\/sub>(2E)
\n\u03c3y<\/sub> = \u221a10(2(8))
\nThen, \u03c3y<\/sub> = \u221a10(16)
\n\u03c3y<\/sub> = \u221a160
\n\u03c3y<\/sub> = 12.64<\/p>\n

Therefore, the\u00a0stress at y-direction\u00a0<\/strong>is 12.64<\/strong><\/p>\n

Calculating the Modulus of Resilience when the Hooke’s Law Linear Elastic Modulus of Resilience and the Stress at y-direction are Given<\/strong><\/h3>\n

E = \u03c3y<\/sub>2<\/sup><\/sup> \/ Ur<\/sub> x 2 <\/sub><\/p>\n

Where:<\/p>\n

E = Modulus of Elasticity
\nUr<\/sub>\u00a0= Hooke’s Law Linear Elastic Modulus of Resilience
\n\u03c3y<\/sub> = Stress at y-direction<\/p>\n

Let’s solve an example;
\nFind the modulus of elasticity when the hooke’s law linear elastic modulus of resilience is 14 and the stress at y-direction is 20.<\/p>\n

This implies that;<\/p>\n

Ur<\/sub> = Hooke’s Law Linear Elastic Modulus of Resilience = 14
\n\u03c3y<\/sub> = Stress at y-direction = 20<\/p>\n

E = \u03c3y<\/sub>2<\/sup><\/sup> \/ Ur<\/sub> x 2 <\/sub>
\nSo, E = 202<\/sup><\/sup> \/ 14 x 2 <\/sub>
\nE = 40<\/sup> \/ 28<\/sub>
\nE = 1.428<\/p>\n

Therefore, the\u00a0modulus of elasticity\u00a0<\/strong>is\u00a01.428<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Linear Elastic Modulus of Resilience | Mechanical Properties<\/a><\/p>\n

How to Calculate Hooke’s Law Linear Elastic Modulus of Resilience With Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the hooke’s law linear elastic modulus of resilience.<\/p>\n

\n

To get the answer and workings of the hooke’s law linear elastic modulus of resilience using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><\/p>\n

Apple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Materials and Metallurgical\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n<\/div>\n

<\/p>\n

Now, Click on\u00a0Mechanical Properties<\/strong>\u00a0<\/b>under\u00a0Materials and Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on Hooke’s Law Linear Elastic Modulus of Resilience<\/strong>\u00a0<\/strong>under\u00a0Mechanical Properties<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the hooke’s law linear elastic modulus of resilience according to the respective parameter which is the Stress at y-direction (\u03c3y<\/sub>)\u00a0<\/strong>and\u00a0Modulus of Elasticity (E).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Stress at y-direction (\u03c3y<\/sub>)<\/strong> is 18 <\/strong>and Modulus of Elasticity (E)<\/strong> is 9<\/strong>.<\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/p>\n

\"How<\/p>\n

As you can see from\u00a0the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the hooke’s law linear elastic modulus of resilience and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents Hooke’s law linear elastic modulus of resilience. To calculate hooke’s law linear elastic modulus…","protected":false},"author":5,"featured_media":16642,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Calculate Hooke's Law Linear Elastic Modulus of Resilience","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Master the steps, formula, and parameters on How to Calculate Hooke's Law Linear Elastic Modulus of Resilience in Mechanical 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