I have a question related to centripetal force. Say there is a pendulum, then \begin{align} mg[h_{max} - h_{current}] = \frac{1}{2}mv^2 = \frac{1}{2}\ell F_{cp} \, . \end{align} Solving for centripetal force would lead to a factor of 2 on the left hand side. Is there a physical meaning for this factor?
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The factor 2 comes from the kinetic energy, so the physical meaning of that factor is the same as if you solve for $v^2$. The centripetal force does no work since the $F_{cp}$ vector is perpendicular to the direction of motion, so while $\ell F_{cp}$ has the dimension of energy, it has no meaning in terms of $F \cdot \Delta x$ work.
The $\frac{1}{2}$ in kinetic energy has its own story, see for example the answers to this question. Ultimately, it's due to how energy is defined in special relativity, but there are also non-relativistic explanations.
