Newton's Second Law

Acceleration is the net force divided by the mass; the same push gives a lighter object more acceleration and a heavier one less.

mechanics The same 6 N on 2 kg and on 3 kg gives clean 3 and 2 m/s^2, making the mass-acceleration trade-off obvious.

Example

Acceleration is the net force divided by the mass: the same push gives a lighter object more acceleration and a heavier object less. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A net force makes a mass accelerate. The acceleration is the force divided by the mass. Newtons divided by kilograms is metres per second squared.

a = \frac{F}{m}

A 2-kilogram block

Push a 2-kilogram block with 6 newtons: the acceleration is 6 over 2, which is 3 metres per second squared.

a = \frac{6\ \text{N}}{2\ \text{kg}} = \hl{3}\ \text{m}/\text{s}^{2}

The same push on a 3-kilogram block

Now the same 6 newtons on a 3-kilogram block gives 6 over 3, only 2 metres per second squared. Same force, more mass, less acceleration.

a = \frac{6\ \text{N}}{3\ \text{kg}} = \hl{2}\ \text{m}/\text{s}^{2}

Fixed mass makes acceleration track force

Hold the mass at 2 kilograms. A bigger net force gives a bigger acceleration.

\begin{array}{c|c|c}F & m & a \\ \hline 4\ \text{N} & 2\ \text{kg} & 2\ \text{m}/\text{s}^{2} \\ 6\ \text{N} & 2\ \text{kg} & 3\ \text{m}/\text{s}^{2} \\ 8\ \text{N} & 2\ \text{kg} & 4\ \text{m}/\text{s}^{2}\end{array}

Fixed force gives less acceleration to more mass

Hold the force at 6 newtons. More mass means the same push produces less acceleration.

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