F = ma: resultant force and acceleration

By the end of this lesson

By the end you can use $F = ma$ with the resultant force, and explain why the acceleration always points the same way as that resultant force, even when the object is moving the other way.

One equation, three ideas

Shove an empty shopping trolley and it zooms off; shove harder and it zooms off faster. Load it with 40 bottles of water and the same shove gives a lazy roll. That supermarket experiment is Newton's second law:

$F = ma$

Symbol	Quantity	Unit
$F$	resultant force	N
$m$	mass	kg
$a$	acceleration	$\text{m s}^{-2}$

Double the resultant force and the acceleration doubles. Double the mass and it halves. (This is the second law for an object of constant mass; its full form uses momentum, later in this topic.)

Definition

The newton

One newton is the force that gives a mass of $1\ \text{kg}$ an acceleration of $1\ \text{m s}^{-2}$ in the direction of the force. So $1\ \text{N} = 1\ \text{kg m s}^{-2}$ .

Resultant first, always

$F$ in $F = ma$ is the resultant force: add up every force on the object as vectors. Along a straight line, choose a positive direction and give each force a sign.

Push $50\ \text{N}$ to the right, friction $20\ \text{N}$ to the left: resultant $= 50 - 20 = 30\ \text{N}$ to the right.
On a $10\ \text{kg}$ crate that gives $a = 30 / 10 = 3.0\ \text{m s}^{-2}$ , to the right.

Plugging the $50\ \text{N}$ push straight into $F = ma$ is the single most common way to lose this mark.

Quick check

CalculateQuestion 1 · Recall

Multiple choiceQuestion 2 · Recall

Answer the 2 questions above to continue.