Two springs having spring constants 4 N/m and 6 N/m are attached in series. What is the energy stored in the system when it is compressed by .5 m

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The two springs have a spring constant of 4 N/m and 6 N/m respectively. They are attached in series. To calculate the potential energy of the system when the springs are compressed, first we need to determine the equivalent spring constant.

The equivalent spring constant Keq for two springs with spring constants k1 and k2  is given by 1/Keq = 1/k1 + 1/k2.

Here, (1/Keq) = 1/4 + 1/6

=> 1/Keq = 10/24

=> Keq = 2.4 N/m

When the length of a spring with a spring constant k is changed by x, the potential energy in the system is given by (1/2)*k*x^2

Keq has been determined to be 2.4 N/m and the length is decreased by 0.5 m.

The potential energy in the system is (1/2)*(2.4)*(0.5)^2 = 0.3 J.

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