A force $F$ acts on the right end of an inextensible rope of length $l$ located on a perfectly smooth horizontal table in the horizontal direction along the rope. Find the tension of the rope at a distance $x$ from its left end.
Decision:
Due to the inextensibility of the rope, all its points move under the action of an external force $F$ with the same acceleration $a = \frac{F}{M}$, where $M$ is the mass of the rope. The left part of the rope of length $x$ has mass $m(x) = \frac{Mx}{l}$. It moves with acceleration $a$ under the action of the desired tension force $T(x)$. According to Newton's II law $T(x) = m(x)a = \frac{Fx}{l}$.
Decision:
Due to the inextensibility of the rope, all its points move under the action of an external force $F$ with the same acceleration $a = \frac{F}{M}$, where $M$ is the mass of the rope. The left part of the rope of length $x$ has mass $m(x) = \frac{Mx}{l}$. It moves with acceleration $a$ under the action of the desired tension force $T(x)$. According to Newton's II law $T(x) = m(x)a = \frac{Fx}{l}$.