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# How to Calculate and Solve for Hooke’s Law Linear Elastic Modulus of Resilience | Mechanical Properties

Last Updated on January 9, 2023

The image above represents Hooke’s law linear elastic modulus of resilience.

To compute for hooke’s law linear elastic modulus of resilience, two essential parameters are needed and these parameters are Stress at y-direction (σyand Modulus of Elasticity (E).

The formula for hooke’s law linear elastic modulus of resilience:

Ur = σy²/2E

Where:

Ur = Hooke’s Law Linear Elastic Modulus of Resilience
σy = Stress at y-direction
E = Modulus of Elasticity

Given an example;
Find the hooke’s law linear elastic modulus of resilience when the stress at y-direction is 18 and the modulus of elasticity is 9.

This implies that;

σy = Stress at y-direction = 18
E = Modulus of Elasticity = 9

Ur = σy²/2E
Ur = 18²/2(9)
Ur = 324/(18)
Ur = 18

Therefore, the hooke’s law linear elastic modulus of resilience is 18 Pa.

Calculating the Stress at y-direction when the Hooke’s Law Linear Elastic Modulus of Resilience and the Modulus of Elasticity is Given.

σy = √Ur(2E)

Where:

σy = Stress at y-direction
Ur = Hooke’s Law Linear Elastic Modulus of Resilience
E = Modulus of Elasticity

Let’s solve an example;
Find the stress at y-direction when the hooke’s law linear elastic modulus of resilience is 10 and the modulus of elasticity is 8.

This implies that;

Ur = Hooke’s Law Linear Elastic Modulus of Resilience = 10
E = Modulus of Elasticity =  8

σy = √Ur(2E)
σy = √10(2(8))
σy = √10(16)
σy = √160
σy = 12.64

Therefore, the stress at y-direction is 12.64

Calculating the Modulus of Resilience when the Hooke’s Law Linear Elastic Modulus of Resilience and the Stress at y-direction is Given.

E = σy2 / Ur x 2

Where:

E = Modulus of Elasticity
Ur = Hooke’s Law Linear Elastic Modulus of Resilience
σy = Stress at y-direction

Let’s solve an example;
Find the modulus of elasticity when the hooke’s law linear elastic modulus of resilience is 14 and the stress at y-direction is 20.

This implies that;

Ur = Hooke’s Law Linear Elastic Modulus of Resilience = 14
σy = Stress at y-direction = 20

E = σy2 / Ur x 2
E = 202 / 14 x 2
E = 40 / 28
E = 1.428

Therefore, the modulus of elasticity is 1.428

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the hooke’s law linear elastic modulus of resilience.

To get the answer and workings of the hooke’s law linear elastic modulus of resilience using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

You can also try the demo version via https://www.nickzom.org/calculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Mechanical Properties under Materials and Metallurgical

Now, Click on Hooke’s Law Linear Elastic Modulus of Resilience under Mechanical Properties

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 (σyand Modulus of Elasticity (E).

Now, enter the values appropriately and accordingly for the parameters as required by the Stress at y-direction (σy) is 18 and Modulus of Elasticity (E) is 9.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the hooke’s law linear elastic modulus of resilience and presents the formula, workings and steps too.