Two springs,P and Q,of force constants k_P an | vedclass

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(C) The energy stored in a spring stretched by a force $F$ is given by $U = \frac{F^2}{2k}$.Given that the forces applied to both springs are equal,le

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$E/2$

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(C) The energy stored in a spring stretched by a force $F$ is given by $U = \frac{F^2}{2k}$.Given that the forces applied to both springs are equal,let $F_P = F_Q = F$.The energy stored in spring $P$ is $U_P = \frac{F^2}{2k_P}$.The energy stored in spring $Q$ is $U_Q = \frac{F^2}{2k_Q} = E$.Since $k_Q = \frac{k_P}{2}$,we have $k_P = 2k_Q$.Substituting this into the expression for $U_P$:$U_P = \frac{F^2}{2(2k_Q)} = \frac{1}{2} \left( \frac{F^2}{2k_Q} \right) = \frac{1}{2} E$.Therefore,the energy stored in spring $P$ is $E/2$.

Two springs,$P$ and $Q$,of force constants $k_P$ and $k_Q$ (where $k_Q = k_P / 2$) are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$,then the energy stored in $P$ is:

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