Elastic Potential Energy Flashcards

All 7 cards in this deck

What is the equation for the energy transferred (work done) in stretching a spring?

$E = \frac{1}{2} \times k \times x^2$
energy (J) = $\frac{1}{2} \times$ spring constant (N/m) $\times$ (extension (m))$^2$

What energy store does the work done in stretching a spring elastically go into?

The elastic potential (elastic strain) energy store of the spring.

What are the steps to calculate the energy transferred in stretching a spring?
e.g. $k = 24$ N/m, extension $= 12$ cm

1. Convert extension to metres: $12$ cm $= 0.12$ m
2. Substitute into $E = \frac{1}{2} \times k \times x^2$: $\frac{1}{2} \times 24 \times 0.12^2$
3. $E = 0.17$ J

What are the steps to find the extension of a spring from the work done on it?
e.g. $E = 45$ J, $k = 140$ N/m

1. Substitute into $E = \frac{1}{2} \times k \times x^2$: $45 = \frac{1}{2} \times 140 \times x^2$
2. Rearrange: $x = \sqrt{\dfrac{2E}{k}} = \sqrt{\dfrac{2 \times 45}{140}}$
3. $x = 0.80$ m

What does the area between the line of a force–extension graph and the extension axis represent?

The work done on the spring / the energy transferred to its elastic potential energy store.

True or false? Doubling the extension of a spring doubles the energy stored in it.

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

True or false? Extension must be converted to metres before using $E = \frac{1}{2} \times k \times x^2$.

True. Using centimetres gives an answer that is wrong by a power of ten (a POT error).