Object A has mass 90.0 g and hangs from an insulated thread....

Object $A$ has mass $90.0 \mathrm{g}$ and hangs from an insulated thread. When object $B$, which has a charge of $+130 \mathrm{nC}$. is held nearby, $A$ is attracted to it. In equilibrium, $A$ hangs at an angle $\theta=7.20^{\circ}$ with respect to the vertical and is $5.00 \mathrm{cm}$ to the left of B. (a) What is the charge on $A ?$ (b) What is the tension in the thread?

Key Concepts

Coulomb's Law

Coulomb's Law quantifies the electrostatic force between two point charges. 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 fundamental law is the basis for calculating the electric force exerted by one charged object on another in a system.

Static Equilibrium

Static equilibrium occurs when an object is at rest and all the forces acting on it balance out, resulting in no net force. In these problems, it is assumed that the sum of all horizontal and vertical forces are zero. This condition is essential for setting up equations that relate gravitational force, tension, and electrostatic force.

Force Decomposition

Force decomposition involves breaking a force into its horizontal and vertical components using trigonometric functions such as sine and cosine. In scenarios where an object is suspended at an angle, decomposing the tension into its components is key to properly balancing gravitational and other forces (like the electrostatic force) in their respective directions.

Tension in a String

The tension in a string or thread is the force exerted along it when it is used to support an object. In equilibrium problems, the tension must be calculated by resolving the net forces acting on the suspended object, typically involving both gravitational and other applied forces such as those from electric fields.

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