A Federation starship (2.0 ×10^6 kg) uses its tractor beam...

A Federation starship $\left(2.0 \times 10^{6} \mathrm{kg}\right)$ uses its tractor beam to pull a shuttlecraft $\left(2.0 \times 10^{4} \mathrm{kg}\right)$ aboard from a distance of $10 \mathrm{km}$ away. The tractor beam exerts a constant force of $4.0 \times 10^{4} \mathrm{N}$ on the shuttlecraft. Both spacecraft are initially at rest. How far does the starship move as it pulls the shuttlecraft aboard?

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Key Concepts

Newton's Second Law

Newton's Second Law, expressed as F = ma, relates the net force acting on an object to its mass and the acceleration produced. This fundamental law is used to determine how each object in a system accelerates when subjected to internal forces, providing the basis for calculating displacements over time.

Newton's Third Law

Newton's Third Law states that for every action, there is an equal and opposite reaction. In a two-body interaction, the force that one object exerts on the other is met with an equal and opposite force on itself, ensuring that the forces are balanced and that the motion of each body is interdependent.

Center of Mass

The center of mass is the point that represents the average position of the mass in a system. In an isolated system with no external forces, the center of mass remains fixed even though individual components may move. This principle allows the calculation of relative displacements of objects interacting with each other by ensuring that the overall mass-weighted position does not change.

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