Suppose a scientist repeats the Millikan oil-drop experiment but reports the charges on the drops using an unusual (and imaginary) unit called the warmomb (wa). The scientist obtains the following data for four of the drops: Droplet Calculated Charge (wa) A 3.84⨉10⁻⁸ B 4.80⨉10⁻⁸ C 2.88⨉10⁻⁸ D 8.64⨉10⁻⁸ (a) If all the droplets were the same size, which would fall most slowly through the apparatus?

Key Concepts

Stokes' Law

Stokes' Law describes the motion of a sphere through a viscous fluid, stating that the drag force experienced by the sphere is proportional to its radius, the fluid's viscosity, and the velocity of the sphere. In the context of the Millikan oil-drop experiment, larger droplets experience greater drag, which affects their falling speed. Thus, understanding Stokes' Law is essential for predicting which droplet will fall most slowly.

Charge-to-Mass Ratio

The charge-to-mass ratio of a droplet influences its motion in an electric field. In the Millikan experiment, droplets with higher charge experience greater electrostatic forces, which can counteract gravitational forces. This concept is crucial for determining how the charge of each droplet affects its terminal velocity and overall falling speed in the apparatus.

Terminal Velocity

Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium prevents further acceleration. In the case of the oil droplets, terminal velocity is achieved when the gravitational force is balanced by the drag force. Understanding terminal velocity helps in analyzing which droplet, based on its charge and size, will fall more slowly through the oil.