Calculating Charge of Two Spheres in Equilibrium

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Homework Help Overview

The problem involves two plastic spheres of equal mass suspended from strings, which are charged and repel each other, achieving equilibrium at a specific distance apart. The subject area includes electrostatics and mechanics, specifically focusing on the forces acting on charged objects in equilibrium.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the assumptions regarding the setup, including the attachment of the strings and the geometry of the system. There are attempts to analyze the forces acting on the spheres, including gravitational and electric forces, and questions arise about the calculations leading to different results compared to the book answer.

Discussion Status

The discussion is ongoing, with participants providing insights into the problem setup and calculations. Some guidance has been offered regarding the geometric considerations and the need for a diagram to visualize the forces and displacements involved. There is no explicit consensus yet, as differing interpretations of the problem and calculations are being explored.

Contextual Notes

Participants are working under the constraints of the problem statement and the provided equations, while also grappling with discrepancies between their calculations and the book's answer. The exact values and methods used in calculations are not fully detailed, leading to further inquiry.

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Homework Statement


Two plastic spheres each of mass 100.0 mg are suspended from very fine insulating strings of length 85 cm. When equal charges are placed on the spheres, the spheres repel and are in equilibrium when 10 cm apart.
(a) What is the charge on each sphere?


Homework Equations


F=kq2/r2


The Attempt at a Solution


I assumed that the strings were attached to the same place at the top. This eventually gave tan theta = kq2/mgr2.
I did sin-15/85 to get theta
I then plugged in all the values and got around 2.5x10-7
The book answer is 8x10-9.

Thanks for your time
 
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Show your substitution and calculation.
 
I am hesitant to mention this, because when I follow this method, I arrive at a different answer than the given book answer. That said, I would analyze it like so:

Each sphere is repelled by an electric force that is sufficient to balance the gravitational force when the sphere is deflected 5 cm.

Draw a diagram - the spheres are connected to the ceiling by 85 cm strings and are displaced a total of 10cm (5cm each from vertical). What is the height difference from their displaced position and their straight down position? How much energy does that require?
 
Take the projection of L on the vertical line.
Difference in height h = L - Lcosθ.
 

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