Mass-Force Acceleration Three-Row Scan

Three Newton's-second-law rows hold acceleration fixed while mass changes, exposing force as the scaled output.

mechanics At 3 m/s squared, masses 1 kg, 2 kg, and 3 kg require net forces 3 N, 6 N, and 9 N.

Example

With acceleration fixed, Newton's second law makes force scale with mass. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Hold acceleration fixed and scan mass

Newton's second law is a scaling rule: more mass needs more force for the same acceleration.

F = m a

Light cart

Mass 1 kg at the fixed acceleration needs 3 N.

F = m a = 1\ \text{kg}\,\cdot\,3\ \text{m}/\text{s}^{2} = 3\ \text{N}

Middle cart

Mass 2 kg at the same acceleration needs 6 N.

F = m a = 2\ \text{kg}\,\cdot\,3\ \text{m}/\text{s}^{2} = 6\ \text{N}

Heavy cart

Mass 3 kg at the same acceleration needs 9 N.

F = m a = 3\ \text{kg}\,\cdot\,3\ \text{m}/\text{s}^{2} = 9\ \text{N}

The force column follows mass

Acceleration is held fixed, so doubling mass doubles the required net force; tripling mass triples it.

\begin{array}{c|c|c}m & a & F \\ \hline 1\ \text{kg} & 3\ \text{m}/\text{s}^{2} & 3\ \text{N} \\ 2\ \text{kg} & 3\ \text{m}/\text{s}^{2} & 6\ \text{N} \\ 3\ \text{kg} & 3\ \text{m}/\text{s}^{2} & 9\ \text{N}\end{array}