How Do You Calculate Tension in a String When a Ball Is Submerged in a Fluid?

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Discussion Overview

The discussion centers around calculating the tension in a string when a ball is submerged in an unknown fluid. Participants explore the implications of the ball's mass, volume, and the fluid's density on the tension experienced by the string. The context includes both theoretical and practical considerations related to fluid mechanics and buoyancy.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant proposes that the tension T could be expressed as T = pgv, where p is the fluid density, g is the acceleration due to gravity, and v is the volume of the ball.
  • Another participant suggests that both the density of the ball and the density of the liquid need to be included in the equation for tension.
  • There is confusion regarding the representation of the equation, with participants questioning the meaning of including both densities in the calculation.
  • Participants discuss the implications of different materials for the ball, such as steel versus lighter materials, on the tension in the string.

Areas of Agreement / Disagreement

Participants express differing views on how to incorporate the densities of both the ball and the fluid into the tension calculation. The discussion remains unresolved regarding the correct formulation of the equation.

Contextual Notes

There are limitations in the discussion related to missing assumptions about the properties of the ball and fluid, as well as unresolved mathematical steps in deriving the tension equation.

ChanceHint
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Homework Statement


What is the tension in the string when a ball with unknown mass and volume is lowered on the string into a unknown fluid of density. (The ball is sank under the liquid but not touching the bottom due to the string holding up)

Homework Equations


gravity g = 9.8
mass = m
density = p
volume V = m/p
F=pgv

The Attempt at a Solution


Tension T = pgv?
 
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ChanceHint said:

Homework Statement


What is the tension in the string when a ball with unknown mass and volume is lowered on the string into a unknown fluid of density. (The ball is sank under the liquid but not touching the bottom due to the string holding up)

Homework Equations


gravity g = 9.8
mass = m
density = p
volume V = m/p
F=pgv

The Attempt at a Solution


Tension T = pgv?

Wecome to the PF. I think you will need to include both densities in your equation. The density of the ball and the density of the liquid.
 
I still don't understand;; you mean T= PfGV?;; #_@
 
ChanceHint said:
I still don't understand;; you mean T= PfGV?;; #_@

I don't know what you are representing with that equation.

I'm just saying that the equation would need to have both densities in it, the density of the liquid and the density of the ball. Think of the difference where the ball is made from steel, versus one that is made from a lighter material (but still sinks).
 

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