Two spheres, each of mass M=2.33 g, are attached by pieces of string of length L=45.0 cm to a

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Two spheres, each of mass M=2.33 g, are attached by pieces...

Two spheres, each of mass $M=2.33 \mathrm{~g}$, are attached by pieces of string of length $L=45.0 \mathrm{~cm}$ to a common point. The strings initially hang straight down, with the spheres just touching one another. An equal amount of charge, $q$, is placed on each sphere. The resulting forces on the spheres cause each string to hang at an angle of $\theta=10.0^{\circ}$ from the vertical. Determine $q,$ the amount of charge on each sphere.

Key Concepts

Coulomb's Law

Coulomb's Law describes the magnitude of the electrostatic force between two point charges. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is a fundamental principle in electrostatics and is key to understanding how charged objects interact.

Force Equilibrium

Force equilibrium involves setting up the condition where the net force acting on an object is zero. In equilibrium, all forces balance out, meaning that the sum of the forces in any direction is zero. This concept is critical when analyzing problems involving multiple forces, such as gravitational forces, tension, and electrostatic forces, to determine the system's steady state.

Decomposition of Forces

Decomposition of forces refers to the process of breaking a force into its component vectors, typically along mutually perpendicular axes such as horizontal and vertical. This approach is essential in analyzing physical systems, as it allows for the independent resolution of forces acting in different directions, helping to simplify complex equilibrium problems.

Trigonometric Relationships in Equilibrium

Trigonometric relationships are used in equilibrium problems to relate the angles of force application to their components. Functions like sine and cosine are typically applied to express the components of a force acting at an angle. These relationships are essential for calculating unknown quantities such as angles, distances, or forces in systems where forces are not aligned with the coordinate axes.

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