A spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length.

a] In terms of U0, how much energy does it store when it is compressed twice as much? Uel/U0 =?

b] In terms of U0, how much energy does it store when it is compressed half as much? Uel/U0 = ?

c] In terms of x0, how much must it be compressed from its uncompressed length to store twice as much energy? x/x0 = ?

d] In terms of x0, how much must it be compressed from its uncompressed length to store half as much energy? x/x0 = ?

Explanation:

Using Hooke's law

Elastic potential energy = 1/2 K x²

K is elastic constant of the spring

x is the extension of the spring

a) The elastic potential energy when the spring is compressed twice as much  Uel = 1/2 k (2x₀) ² =  4 (1/2 kx₀²)= 4 U₀

b) when is compressed half as much Uel = 1/2 k = ( U₀)

c) make x₀ subject of the formula in the equation for elastic potential

      x₀ =

x, the amount it will compressed to tore twice as much energy =

x = √2 x₀

d) x₁, the new length it must be compressed to store half as much energy =

x₁ = x₀

gravititional force is a force that is acting around you, it is non-contactable and it is a force that pulls you to the core of the earth.

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