Spring force equation

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Spring force equation
Spring force equation | Image: Learnool

The spring force equation, derived from Hooke’s law, is expressed as Fs = k Δx, where Fs represents the spring force, k is the spring constant, and Δx denotes the displacement from the equilibrium position of the spring. This equation enables the calculation of the force exerted by a spring on an object. The sign of Δx indicates whether the spring is stretched (+ve) or compressed (-ve).

Practice problems

Problem #1

Calculate the force exerted by a spring on a block when the block, attached to a spring with a natural length of 25 cm, moves rightwards and stretches the spring by 50 cm. The spring constant is 75 N/m.

Solution

Given data:

  • Force exerted by spring on a block, Fs = ?
  • Initial length of a spring, x0 = 25 cm = 0.25 m
  • Final length of a spring, x = 50 cm = 0.5 m
  • Spring constant, k = 75 N/m

Applying the formula:

  • Fs = k Δx = k × (x – x0)
  • Fs = 75 × (0.5 – 0.25)
  • Fs = 75 × 0.25
  • Fs = 18.75 N

Therefore, the force exerted by spring on a block is -18.75 N. (left)

Problem #2

Determine the force exerted by a spring on a block when the block, attached to a spring with a natural length of 15 cm, moves leftwards and compresses the spring by 5 cm. The spring constant is 55 N/m.

Solution

Given data:

  • Force exerted by spring on a block, Fs = ?
  • Initial length of a spring, x0 = 15 cm = 0.15 m
  • Final length of a spring, x = 5 cm = 0.05 m
  • Spring constant, k = 55 N/m

Applying the formula:

  • Fs = k Δx = k × (x – x0)
  • Fs = 55 × (0.05 – 0.15)
  • Fs = 55 × (-0.01)
  • Fs = -5.5 N

Therefore, the force exerted by spring on a block is 5.5 N. (right)

Problem #3

A spring is in equilibrium, with its left end fixed to a wall and its right end fixed to a wooden crate. When the wooden crate is moved to the right, the spring stretches from a length of 0.5 m to 0.65 m. Calculate the force exerted by the spring on the wooden crate, given that the spring constant is 150 N/m.

Solution

Given data:

  • Initial length of a spring, x0 = 0.5 m
  • Final length of a spring, x = 0.65 m
  • Force exerted by spring on a wooden crate, Fs = ?
  • Spring constant, k = 150 N/m

Applying the formula:

  • Fs = k Δx = k × (x – x0)
  • Fs = 150 × (0.65 – 0.5)
  • Fs = 150 × (0.15)
  • Fs = 22.5 N

Therefore, the force exerted by spring on a wooden crate is -22.5 N. (left)

Problem #4

A spring is in equilibrium, with its left end fixed to a wall and its right end fixed to a wooden crate. When the wooden crate is moved to the left, the spring compresses from a length of 0.5 m to 0.2 m. Calculate the force exerted by the spring on the wooden crate, given that the spring constant is 170 N/m.

Solution

Given data:

  • Initial length of a spring, x0 = 0.5 m
  • Final length of a spring, x = 0.2 m
  • Force exerted by spring on a wooden crate, Fs = ?
  • Spring constant, k = 170 N/m

Applying the formula:

  • Fs = k Δx = k × (x – x0)
  • Fs = 170 × (0.2 – 0.5)
  • Fs = 170 × (-0.3)
  • Fs = -51 N

Therefore, the force exerted by spring on a wooden crate is 51 N. (right)

Related

External links

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.

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