**Hooke’s law equation** states that the **force **(F) needed to stretch or compress a spring directly depends upon the **displacement **(x) of a spring. Here’s the equation of hooke’s law: **F _{s}**

**= – k x**

Let’s solve some problems based on this equation, so you’ll get a clear idea.

## Hooke’s Law Practice Problems

**Problem 1:** Find the force needed to stretch a spring, if the displacement of a spring is 60 cm. (Take the value of spring constant, k = 85 N/m)

Solution:

Given data:

Force needed to stretch a spring, F = ?

Displacement of a spring, x = 60 cm = 0.6 m

Spring constant, k = 85 N/m

Using the equation of hooke’s law,

F_{s} = – k x

Here, we only require the force needed to stretch a spring. So the (-ve) sign can be neglected.

F = k x

F = (85 × 0.6)

F = 51 N

Therefore, the force needed to stretch a spring is **51 N**.

**Problem 2:** Calculate the force needed to compress a spring, if the displacement of a spring is 20 cm. (Take the value of spring constant, k = 150 N/m)

Solution:

Given data:

Force needed to compress a spring, F = ?

Displacement of a spring, x = 20 cm = 0.2 m

Spring constant, k = 150 N/m

Using the equation of hooke’s law,

F_{s} = – k x

Here, we only require the force needed to compress a spring. So the (-ve) sign can be neglected.

F = k x

F = (150 × 0.2)

F = 30 N

Therefore, the force needed to compress a spring is **30 N**.

**Problem 3:** What force is needed to stretch a spring to a distance of 40 cm? (Take the value of spring constant, k = 120 N/m)

Solution:

Given data:

Force needed to stretch a spring, F = ?

Displacement of a spring, x = 40 cm = 0.4 m

Spring constant, k = 120 N/m

Using the equation of hooke’s law,

F_{s} = – k x

Here, we only require the force needed to stretch a spring. So the (-ve) sign can be neglected.

F = k x

F = (120 × 0.4)

F = 48 N

Therefore, the force needed to stretch a spring is **48 N**.

**Problem 4:** Calculate the force needed to compress a spring, if the displacement of a spring is 25 cm. (Take the value of spring constant, k = 65 N/m)

Solution:

Given data:

Force needed to compress a spring, F = ?

Displacement of a spring, x = 25 cm = 0.25 m

Spring constant, k = 65 N/m

Using the equation of hooke’s law,

F_{s} = – k x

Here, we only require the force needed to compress a spring. So the (-ve) sign can be neglected.

F = k x

F = (65 × 0.25)

F = 16.25 N

Therefore, the force needed to compress a spring is **16.25 N**.

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