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 is applied?

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 is applied? (A) (F L/x) (B) (F(L-x)/L) (C) (F L/L-x) (D) (F x/L-x)

Tardigrade Admin · Accepted Answer

Let mass per unit length of rope =λ. F=m a=(λ L) a

F-T=(λ x) a ; T =F-λ x a=F-λ x((F/λ L)) T=F(1-(x/L))=F((L-x/L))

Q. 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 is applied?

$\frac{F L}{x}$

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

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

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

Let mass per unit length of rope $= λ$ . $F = ma = (λ L) a$

$F - T = (λ x) a; T$
$= F - λ x a = F - λ x (\frac{F}{λ L})$
$T = F (1 - \frac{x}{L}) = F (\frac{L - x}{L})$

Q. 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 is applied?

xFL​

LF(L−x)​

L−xFL​

L−xFx​