A spring stores potential energy U 0 when it is compressed a distance x 0 from i

ID: 1625896 • Letter: A

Question

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 = ?

a) as the energy stored in the spring is given as

U = 0.50 * k * x^2

now if it is compressure twice as much

Uel/Uo = 2^2 = 4 times

as the energy stored in the spring is given as

U = 0.50 * k * x^2

now if it is compressure half as much

Uel/Uo = 0.5^2 = 1/4 times

for the energy stored to be twice

x/x0 = sqrt(2)

x/x0 = 1.414 times

for the energy stored to be twice

x/x0 = sqrt(1/2)

x/x0 = 0.707 times

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