The discussion centers around the definition of the variable \( H \) in the context of a pulley diagram, specifically examining the relationship between the length of the rope \( \ell \), the diagonal stretch of the rope, and the angle \( \theta \). The focus appears to be on the mathematical reasoning behind the expression \( H = \left(\ell - \frac{b}{\sin\theta}\right) \) in a frictionless scenario.
There appears to be a shared understanding among participants regarding the expression for \( H \) and its components, but the discussion does not delve into any disagreements or alternative interpretations of the formula.
The discussion does not address any limitations or assumptions explicitly, nor does it explore the implications of the frictionless condition on the defined variables.
Because $\frac{b}{\sin\theta}$ is the length of the diagonal stretch of the rope.dwsmith said:Why can $H = \left(\ell - \frac{b}{\sin\theta}\right)$ where $\ell$ is the length of the rope.
Evgeny.Makarov said:Because $\frac{b}{\sin\theta}$ is the length of the diagonal stretch of the rope.
Evgeny.Makarov said:Glad to hear that. The picture looks nice!