How to Calculate Tension on a Horizontal Clothesline | Calc 2 Physics Problem

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SUMMARY

The discussion focuses on calculating the tension in a horizontal clothesline when a 3-kilogram mass causes a sag of 2 meters. The key formula used is T(y) = 0.5(mg), where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s²). The tension can be determined by first calculating the vertical component of the tension and then applying trigonometric functions to find the total tension in the clothesline. The final tension value is derived using the sag and the geometry of the setup.

PREREQUISITES
  • Understanding of basic physics concepts, specifically forces and tension.
  • Familiarity with free body diagrams and their application in problem-solving.
  • Knowledge of trigonometry, particularly how to calculate angles and use sine and cosine functions.
  • Basic grasp of gravitational force calculations (F = mg).
NEXT STEPS
  • Study the principles of tension in static equilibrium scenarios.
  • Learn how to draw and interpret free body diagrams for complex systems.
  • Explore trigonometric functions and their applications in physics problems.
  • Investigate the effects of varying mass and sag on tension calculations in similar setups.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the mechanics of tension in static systems, particularly in practical applications like clotheslines.

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A horizontal clothesline is tied between 2 poles, 20 meters apart.
When a mass of 3 kilograms is tied to the middle of the clothesline, it sags a distance of 2 meters.

What is the magnitude of the tension on the ends of the clothesline in N?


Ok, I am totally lost on this problem, I've tried drawing the free body diagrams and really hasnt helped.
 
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Hint: If the mass stays sagging at two meters, what must the net force in it be? What individual forces are acting on the mass?
 
I figured it out! T(y)=.5(mg)=.5(29.43)

And then I can use the distance to solve for the angle and then use trig with that angle to find T!
 

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