Vectors and Forces

Newton's Second Law

force = mass times acceleration

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

Example

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

highlighted = computed this step

Newton's second law

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=Fma = \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=6 N2 kg=3 m/s2a = \frac{6\ \text{N}}{2\ \text{kg}} = \hl{3}\ \text{m}/\text{s}^{2}
The lighter block speeds up fasterA lighter block pushed to the right with a longer acceleration arrow than the heavier block.2 kgFa

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=6 N3 kg=2 m/s2a = \frac{6\ \text{N}}{3\ \text{kg}} = \hl{2}\ \text{m}/\text{s}^{2}
The heavier block speeds up slowerA heavier block pushed with the same force but a shorter acceleration arrow.3 kgFa
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.