Physics · Both
Hooke’s Law & Springs
Extension of springs, Hooke’s law, spring constant and elastic potential energy.
For many springs, extension is proportional to force – until the limit of proportionality. Beyond that the spring may not return to its original length.
Hooke’s law
F = k x
• F – force (N)
• k – spring constant (N/m)
• x – extension (m) = new length − original length
Linear force–extension graph through the origin up to the limit of proportionality.
Worked example
A spring extends 0.05 m under 10 N. Spring constant?
Solution
k = F / x = 10 / 0.05 = **200 N/m**
Elastic potential energy
Energy stored in a stretched spring (provided elastic limit not exceeded):
E = ½ k x²
Also equal to the area under the force–extension graph.
Practice questions
Try these without looking at the answers first.
Q1.Hooke’s law formula?
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F = k x
Q2.k = 50 N/m, x = 0.1 m. Force?
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5 N
Q3.Energy stored: k = 100, x = 0.2?
Hint: ½ × 100 × 0.04
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2 J