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A spring obeys Hooke's law. If the spring constant is doubled, what happens to t

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Question: A spring obeys Hooke\'s law. If the spring constant is doubled, what happens to the elongation for the same applied force?

Options:

  1. Elongation doubles
  2. Elongation halves
  3. Elongation remains the same
  4. Elongation quadruples

Correct Answer: Elongation halves

Solution: 

According to Hooke\'s law, elongation is inversely proportional to the spring constant; thus, if the spring constant is doubled, the elongation halves.

A spring obeys Hooke's law. If the spring constant is doubled, what happens to t

Practice Questions

Q1
A spring obeys Hooke's law. If the spring constant is doubled, what happens to the elongation for the same applied force?
  1. Elongation doubles
  2. Elongation halves
  3. Elongation remains the same
  4. Elongation quadruples

Questions & Step-by-Step Solutions

A spring obeys Hooke's law. If the spring constant is doubled, what happens to the elongation for the same applied force?
  • Step 1: Understand Hooke's law, which states that the force (F) applied to a spring is equal to the spring constant (k) multiplied by the elongation (x). This can be written as F = k * x.
  • Step 2: Rearrange the formula to find elongation: x = F / k. This shows that elongation (x) depends on the force (F) and the spring constant (k).
  • Step 3: If the spring constant (k) is doubled, we can represent the new spring constant as 2k.
  • Step 4: Substitute the new spring constant into the elongation formula: x' = F / (2k).
  • Step 5: Compare the new elongation (x') with the original elongation (x = F / k). Since x' = F / (2k), we see that x' = (1/2) * (F / k) = (1/2) * x.
  • Step 6: Conclude that if the spring constant is doubled, the elongation is halved.
  • Hooke's Law – Hooke's law states that the force exerted by a spring is directly proportional to its elongation, and the relationship can be expressed as F = kx, where F is the force, k is the spring constant, and x is the elongation.
  • Spring Constant – The spring constant (k) is a measure of a spring's stiffness; a higher spring constant means a stiffer spring that stretches less under the same force.
  • Inversely Proportional Relationship – The elongation (x) is inversely proportional to the spring constant (k), meaning that as k increases, x decreases for a constant force.
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