# Hooke’s law equation

The Hooke’s law equation, Fs = – k x, describes the relationship between the force (Fs) required to stretch or compress a spring and the displacement (x) of the spring. In this equation, Fs represents the force exerted by the spring on an object, k is the spring constant, and x denotes the displacement of the spring from its equilibrium position. The negative sign in the equation signifies that the force exerted by the spring is opposite to the direction of the displacement. By utilizing this equation, one can determine the force exerted by a spring based on the amount of displacement it undergoes.

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## Practice problems

### Problem #1

Find the force required to stretch a spring with a displacement of 60 cm. Use a spring constant value of 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

Applying the formula:

• Fs = – k x

The negative sign in the equation indicates that the spring force acts in the opposite direction to the displacement. In this problem, the focus is on determining the magnitude of the force rather than its direction, so the negative sign can be ignored.

• 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 with a displacement of 20 cm. Use a spring constant value of 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

Applying the formula:

• Fs = – k x

The negative sign in the equation indicates that the spring force acts in the opposite direction to the displacement. In this problem, the focus is on determining the magnitude of the force rather than its direction, so the negative sign can be ignored.

• 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 necessary to stretch a spring to a distance of 40 cm? Take the spring constant value as 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

Applying the formula:

• Fs = – k x

The negative sign in the equation indicates that the spring force acts in the opposite direction to the displacement. In this problem, the focus is on determining the magnitude of the force rather than its direction, so the negative sign can be ignored.

• F = k x
• F = (120 × 0.4)
• F = 48 N

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

### Problem #4

Determine the force needed to compress a spring with a displacement of 25 cm. Take the spring constant value as 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

Applying the formula:

• Fs = – k x

The negative sign in the equation indicates that the spring force acts in the opposite direction to the displacement. In this problem, the focus is on determining the magnitude of the force rather than its direction, so the negative sign can be ignored.

• F = k x
• F = (65 × 0.25)
• F = 16.25 N

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