When a spiral spring is compressed by an external force of 200 N, it stores 0.16 J of energy. What amount of energy will it store when compressed by an external force of 700 N?
The elastic potential energy \( E \) is proportional to the square of the force:
\(E \propto F^2\)
(for the same spring).
The relationship between the energies for different forces is given by:
\(\frac{E_2}{E_1} = \left( \frac{F_2}{F_1} \right)^2\)
Now, substituting the known values:
\(E_2 = 0.16 \times \left( \frac{700}{200} \right)^2 = 0.16 \times (3.5)^2 = 0.16 \times 12.25 = 1.96 \, \text{J}\)
There is an explanation video available below.
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