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

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

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.