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 (σ _{y}) **and

**Modulus of Elasticity (E).**

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

U_{r} = ^{σy²}/_{2E}

Where:

U_{r} = Hooke’s Law Linear Elastic Modulus of Resilience

σ_{y} = 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;

σ_{y} = Stress at y-direction = 18

E = Modulus of Elasticity = 9

U_{r} = ^{σy²}/_{2E}

U_{r} = ^{18²}/_{2(9)}

That is, U_{r} = ^{324}/_{(18)}

U_{r} = 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 are Given**

σ_{y} = √U_{r}(2E)

Where:

σ_{y} = Stress at y-direction

U_{r} = 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;

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U_{r} = Hooke’s Law Linear Elastic Modulus of Resilience = 10

E = Modulus of Elasticity = 8

σ_{y} = √U_{r}(2E)

σ_{y} = √10(2(8))

Then, σ_{y} = √10(16)

σ_{y} = √160

σ_{y} = 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 are Given**

E = ^{σy2} / _{Ur x 2 }

Where:

E = Modulus of Elasticity

U_{r} = Hooke’s Law Linear Elastic Modulus of Resilience

σ_{y} = 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;

U_{r} = Hooke’s Law Linear Elastic Modulus of Resilience = 14

σ_{y} = Stress at y-direction = 20

E = ^{σy2} / _{Ur x 2 }

So, E = ^{202} / _{14 x 2 }

E = ^{40} / _{28}

E = 1.428

Therefore, the **modulus of elasticity **is **1.428**

Read more: How to Calculate and Solve for Linear Elastic Modulus of Resilience | Mechanical Properties

**How to Calculate Hooke’s Law Linear Elastic Modulus of Resilience With Nickzom Calculator**

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:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **to have utter access to all functionalities.

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

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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 (σ _{y}) **and

**Modulus of Elasticity (E).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Stress at y-direction (σ _{y})** 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.