# Question 08420

Jun 21, 2017

Newton's second law of motion is mathematically interpreted as

$\Sigma \vec{F} = m \vec{a}$

where

• $\Sigma \vec{F}$ is the net force acting on an object, typically in $\text{N}$

• $m$ is the mass of the object, in $\text{kg}$

• $\vec{a}$ is the acceleration of the object, in "m"/("s"^2)

Some key things to know are:

If a net force acts on an object, there is always an acceleration produced.

If an object is accelerating (changing its velocity in any way), there must always be some net force acting on it to produce that acceleration.

The direction of the net force on an object is always the direction of its acceleration.

If an object is sliding on a surface, there is always some friction force present, and this force always opposes the direction of sliding.

Let's say an object with a mass of $25.0$ $\text{kg}$ is being pushed with a constant horizontal force of $12.5$ $\text{N}$. Let's also say for these purposes there is a constant retarding friction force equal to $5.0$ $\text{N}$.

The net horizontal force experienced by this object is

SigmaF_x = 12.5color(white)(l)"N" + (-5.0color(white)(l)"N") = 7.5# $\text{N}$

The friction force is negative because it always opposes the direction of motion.

You could also calculate the acceleration of this object, with its mass known as $25.0$ $\text{kg}$:

${a}_{x} = \frac{\Sigma {F}_{x}}{m} = \left(7.5 \textcolor{w h i t e}{l} {\text{N")/(25.0color(white)(l)"kg") = 0.300"m"/("s}}^{2}\right)$

Another property about friction you may want to know is that the magnitude of the friction force is never greater than the magnitude of the vector sum of the other forces.

If this were true, an object could completely resist being pushed or pulled in some direction. That is to say, if you're pushing an object at, for example, $5.0$ $\text{N}$, and the friction force acting on the object has a magnitude of $6.0$ $\text{N}$, the net force is $- 1.0$ $\text{N}$. It's accelerating toward you, which of course isn't right!