Electric shuttle train A shuttle train moves from one...

Electric shuttle train A shuttle train moves from one station to another. It is powered by equal-magnitude, oppositesign charges on top of each station (see Figure P14.48). If a $7000-\mathrm{N}$ friction force opposes the train's motion, how great must the dipole charge be to induce an initial acceleration of 1.0 $\mathrm{m} / \mathrm{s}^{2} ?$ The train's mass is $2.0 \times 10^{4} \mathrm{kg},$ and it has a positive charge of $+3.0 \times 10^{-2} \mathrm{C}$ on its roof.

Electric shuttle train A shuttle train moves from one station to another. It is powered by equal-magnitude, oppositesign charges on top of each station (see Figure P14.48). If a $7000-\mathrm{N}$ friction force opposes the train's motion, how great must the dipole charge be to induce an initial acceleration of
1.0 $\mathrm{m} / \mathrm{s}^{2} ?$ The train's mass is $2.0 \times 10^{4} \mathrm{kg},$ and it has a positive charge of $+3.0 \times 10^{-2} \mathrm{C}$ on its roof.

Key Concepts

Friction Force

Friction is a resistive force that opposes the relative motion of contacting surfaces. In dynamics problems, friction must be overcome to achieve net acceleration. It acts as an extra load that the applied force, generated by, for example, the interaction of charges, must surpass to ensure movement or acceleration.

Newton's Second Law

Newton's second law relates the net force acting on an object to its mass and acceleration, stated as F = ma. This law is fundamental when determining the required force to achieve a specified acceleration, especially when additional opposing forces like friction are present.

Coulomb's Law

Coulomb's law describes the force between two point charges. It states that the magnitude of the electrostatic force is proportional to the product of the charges and inversely proportional to the square of the distance between them. This concept is crucial for calculating the forces acting on charged objects and is applied when analyzing the interaction between the train's charge and the dipole charge on the stations.

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a distance. The dipole generates an electric field that is characteristic of its configuration, influencing other charges in its vicinity. Understanding the behavior of an electric dipole is essential in problems where a dipole setup induces a force on a charged object, such as the shuttle train.

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