Work Done on a Spring Flashcards

All 5 cards in this deck

Which equation gives the elastic potential energy stored in a stretched spring?

$E_e = \tfrac{1}{2} k e^2$, with $E_e$ in J, $k$ in N/m and $e$ in m.

How does the work done on a spring compare with the elastic potential energy stored in it?

They are equal, provided the spring is not inelastically deformed.

What are the steps to calculate the elastic potential energy stored in a stretched spring?

e.g. $k = 13$ N/m and extension $= 20$ cm

1. Convert extension to metres: $e = 0.20$ m
2. Substitute into $E_e = \tfrac{1}{2} k e^2$: $E_e = 0.5 \times 13 \times 0.20^2$
3. $E_e = 0.26$ J

On a force–extension graph, what does the area under the line represent?

The work done on the spring, which equals the elastic potential energy stored.

True or false? Doubling the extension of a spring doubles the elastic potential energy stored.

False. Energy depends on $e^2$, so doubling the extension stores four times the energy.