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  4. 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?

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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?

Laws of Motion

Solution:

Let mass per unit length of rope $=\lambda$. $F=m a=(\lambda L) a$
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$F-T=(\lambda x) a ; T$
$=F-\lambda x a=F-\lambda x\left(\frac{F}{\lambda L}\right)$
$T=F\left(1-\frac{x}{L}\right)=F\left(\frac{L-x}{L}\right)$
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