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?

검증된 단계별 안내

Identify the relationship between the charge of the droplets and their rate of fall. In the Millikan oil-drop experiment, the rate at which a droplet falls is influenced by the balance between gravitational force pulling it downward and the electric force lifting it upward.

Understand that the gravitational force is constant for droplets of the same size, but the electric force is proportional to the charge on the droplet. A higher charge results in a stronger upward electric force.

Recognize that a droplet with a higher charge experiences a greater upward force, which opposes the gravitational pull more effectively. This means the droplet will fall more slowly through the apparatus.

Compare the charges of the droplets given in the problem: Droplet A has a charge of 3.84×10⁻⁸ wa, Droplet B has 4.80×10⁻⁸ wa, Droplet C has 2.88×10⁻⁸ wa, and Droplet D has 8.64×10⁻⁸ wa.

Conclude that Droplet D, having the highest charge, will experience the strongest upward electric force and thus will fall most slowly through the apparatus.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.