How Is Tension Calculated for a Submerged Accelerating Object?

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SUMMARY

The tension required in the fishing line for a lead weight submerged in water and accelerating upwards can be calculated using the formula T = F - mg, where F is the net force and mg is the weight of the object. Given the volume of the lead weight as 0.69x10^-5 m^3 and its density of 11.34 g/cm^3, the mass can be determined, and the buoyant force must be considered using Archimedes' principle. The upward acceleration of 1.8 m/s² must also be factored into the calculations to find the exact tension in the line.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Knowledge of Archimedes' principle and buoyancy
  • Ability to convert units (e.g., density from g/cm³ to kg/m³)
  • Familiarity with basic physics equations related to forces
NEXT STEPS
  • Calculate the mass of the lead weight using its volume and density
  • Determine the buoyant force acting on the lead weight
  • Apply the net force equation to find the tension in the fishing line
  • Explore further applications of Archimedes' principle in fluid mechanics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and fluid dynamics, as well as educators looking for practical examples of tension and buoyancy calculations.

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Homework Statement


A lead weight with a volume of 0.69x10^-5 m^3 is lowered on a fishing line into a lake to a depth of 1.0m. What tension is required in the fishing line to give the weight an upward acceleration of 1.8m/s^2?


Homework Equations


T=F-mg F=ma D=mv D of lead= 11.34gcm^3


The Attempt at a Solution


I have tried solving it (first changing density into m, to be compatible with my volume value). Then I found the mass of the lead weight (using the given volume and measured density). But still not sure if I'm going through the proper means to arrive at the tension. Any suggestions?
 
Physics news on Phys.org
Where have you used Archimedes' principal that you cite in your title? It tells you that there is an bouyancy force equal to the weight of water with the same volume as the lead weight.
 

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