# Will the potential energy of an elastically deformed body increase by a factor of _

Will the potential energy of an elastically deformed body increase by a factor of _ times with an increase in its deformation by a factor of 3?

Given:

k is the stiffness coefficient of the elastically deformed body;

dx1 is the amount of deformation in the first case;

dx2 = 3 * dx1 – the degree of deformation was increased by 3 times.

It is required to determine how many times the potential energy of the body E2 / E1 will increase.

In the first case, the potential energy will be equal to:

E1 = k * dx1 ^ 2/2.

In the second case, the potential energy will be equal to:

E2 = k * dx2 ^ 2/2 = k * (3 * dx1) ^ 2/2 = 9 * k * dx1 ^ 2/2.

Then:

E2 / E1 = (9 * k * dx1 ^ 2/2) / (k * dx1 ^ 2/2) = 9 times.

Answer: with an increase in deformation by 3 times, the potential energy will increase by 9 times.

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