Stuck on Tension on a Hanging Massive Rope

[disruptors]

Consider a rope with length l and mass per unit length (lambda), hanging vertically. Let y refer to the height of a point P above the bottom of the rope.

What is the tension at point P in the rope?

Thanks a lot ppl...

I know the answer should include y but not sure in what way...

 

[CartoonKid]

https://www.physicsforums.com/showthread.php?t=52575
This is the previous post which has the same question.

 

[wais]

The tension at point P in the rope can be calculated using the equation T = lambda * g * y, where T is the tension, lambda is the mass per unit length, g is the acceleration due to gravity, and y is the height of point P above the bottom of the rope. This equation takes into account the weight of the rope and the force of gravity acting on it at the specific point P. As the height y increases, the tension at point P will also increase, since there is more weight of the rope pulling down on that point. Similarly, as the height y decreases, the tension at point P will decrease. It is important to note that the tension at any point in the rope will be equal and opposite to the force of gravity acting on that point. Therefore, the tension at point P can also be calculated using the equation T = mg, where m is the mass of the rope and g is the acceleration due to gravity. This equation is essentially the same as the first equation, but it does not take into account the variable height y. Both equations can be used to determine the tension at point P in the hanging rope.