Magnitude of Net Force in Plane Motion – Rankers Physics
Topic: Laws of Motion
Subtopic: Definition of Force Inertia and First Law

Magnitude of Net Force in Plane Motion

A \(3.0\text{ kg}\) mass is moving in a plane, with its x and y coordinates given by \(x = 24t^2 - 1\) and \(y = 3t^3 + 2\), where x and y are in meters and t is in second. Find the magnitude of the net force acting on this mass at \(t = 2\text{ sec}\).
\(120\text{ N}\)
\(150\text{ N}\)
\(180\text{ N}\)
\(210\text{ N}\)

Solution:

Differentiating position equations twice yields accelerations: \(a_x = 48\text{ m/s}^2\) and \(a_y = 18t\text{ m/s}^2\). At \(t = 2\text{ s}\), \(a_y = 36\text{ m/s}^2\). Total acceleration \(a = \sqrt{a_x^2 + a_y^2} = 60\text{ m/s}^2\). The net force is \(F = ma = 3.0 \times 60 = 180\text{ N}\).

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