Stuck on Tension on a Hanging Massive Rope

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SUMMARY

The tension at point P in a hanging rope can be calculated using the equation T = λ * g * y, where T is the tension, λ 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. As the height y increases, the tension also increases due to the additional weight of the rope above point P. Conversely, as y decreases, the tension decreases. An alternative equation, T = mg, can also be used, where m represents the mass of the rope, although it does not account for the variable height y.

PREREQUISITES
  • Understanding of basic physics concepts, specifically tension and gravity
  • Familiarity with the variables involved in the equations: λ (mass per unit length), g (acceleration due to gravity), and y (height)
  • Knowledge of how to manipulate algebraic equations
  • Basic understanding of forces acting on objects in equilibrium
NEXT STEPS
  • Study the derivation of tension in different types of ropes and cables
  • Learn about the effects of varying mass distributions on tension in non-uniform ropes
  • Explore applications of tension in real-world scenarios, such as suspension bridges and cranes
  • Investigate the relationship between tension and wave propagation in ropes
USEFUL FOR

Physics students, engineers, and anyone interested in understanding the mechanics of tension in hanging objects.

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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...
 
Last edited:
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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.
 

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