Hooke’s Law Equation | Problems (And Solutions)

Hooke's Law Equation

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: Fs = – 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,
Fs = – 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,
Fs = – 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,
Fs = – 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,
Fs = – 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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