Question

A rope of length $L$ is pulled by a constant force $F$. What is the tension in the rope at a distance $x$ from the end where the force applied:

• A. $\frac{F}{x}$
• B. $\frac{F(L-x)}{L}$
• C. $\frac{FL}{(L-x)}$
• D. $\frac{Fx}{(L-x)}$

Answer 1

Answer: (B)

$\frac{F(L-x)}{L}$

Tension at A$=F$.

Tension at B$=O$.

Assuming a linear decrease in tension.

Let tension at distance $x$ be

$T_x=F-kx$ for $x=L,O=F-kL\Rightarrow k=\frac{F}{L}$

$\therefore T_x=F-\frac{Fx}{L}=F\left(\frac{L-x}{L}\right)$.