In an experiment to measure the Coulomb constant, a tiny...

In an experiment to measure the Coulomb constant, a tiny sphere with charge $+7.0 \mathrm{nC}$ is suspended from a spring. When two other tiny charged spheres, each with a charge of $-4.0 \mu C,$ are placed in the positions shown in the figure, the spring stretches $0.50 \mathrm{mm}$ from its previous equilibrium position. Calculate the spring constant.

Key Concepts

Coulomb's Law

Coulomb's Law provides the foundation for understanding the force between electrically charged objects. It states that the magnitude of the electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is central to calculations involving charged bodies and provides the Coulomb constant, which scales the interaction in the chosen system of units.

Electrostatic Force

Electrostatic force is the interaction force between charged particles. Depending on the nature of the charges, this force can be either attractive or repulsive. In problems involving charged objects, calculating this force using Coulomb's Law is essential for analyzing how charged bodies influence each other and for establishing the conditions under which different forces, such as mechanical forces, are balanced.

Hooke's Law

Hooke's Law explains the behavior of springs and other elastic materials, stating that the force exerted by the spring is directly proportional to the displacement from its equilibrium position. This relationship is expressed as F = kx, where k is the spring constant and x is the displacement. The law is crucial for determining the properties of springs as it relates the mechanical response of the system to the applied forces.

Equilibrium Condition

The equilibrium condition refers to the state where all forces acting on an object are balanced, resulting in no net force and hence no acceleration. In experimental setups, such as determining the spring constant in the presence of an external force, establishing equilibrium allows one to equate the forces from different sources. This balance is key to solving for unknown parameters by setting the net force to zero.

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