A spring obeys Hooke's law. If the spring constant is doubled, what happens to the elongation for the same applied force?
Practice Questions
1 question
Q1
A spring obeys Hooke's law. If the spring constant is doubled, what happens to the elongation for the same applied force?
Elongation doubles
Elongation halves
Elongation remains the same
Elongation quadruples
According to Hooke's law, elongation is inversely proportional to the spring constant; thus, if the spring constant is doubled, the elongation halves.
Questions & Step-by-step Solutions
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Q
Q: A spring obeys Hooke's law. If the spring constant is doubled, what happens to the elongation for the same applied force?
Solution: According to Hooke's law, elongation is inversely proportional to the spring constant; thus, if the spring constant is doubled, the elongation halves.
Steps: 6
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.
