Physics

Problem

Two perpendicular forces,

F_{1}=6\,\text{N}

due east and

F_{2}=8\,\text{N}

due north, act simultaneously on a particle of unknown mass. The resulting acceleration of the particle is

5\,\text{m\,s}^{-2}

towards the north-east. Determine the inertial mass of the particle. a)

2.8\,\text{kg}

1.0\,\text{kg}

2.0\,\text{kg}

1.6\,\text{kg}

Intuitive explanation

The key is recognizing that perpendicular forces combine as vectors, and their resultant must point in the direction of acceleration. Find the magnitude of the net force using the Pythagorean theorem (since $F_1$ and $F_2$ are perpendicular), then apply Newton's second law $F_{\text{net}} = ma$ to solve for mass. The direction check confirms your vector addition is correct.

Intuitive explanation

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