# How does work change if distance increases?

Jun 23, 2015

This is a very intersting question!
I would say that Work (considered as energy transferred from a system to another) should increase.

#### Explanation:

Considering the definition of Work $W$:
$W = \vec{F} \cdot \vec{d} = | \vec{F} | \cdot | \vec{d} | \cdot \cos \left(\theta\right)$
Where
$\vec{F}$ is the force;
$\vec{d}$ is the displacement;
$\theta$ is the angle between the two.
$| \vec{d} |$ will be the distance covered; so increasing it, work increases. The $\cos \left(\theta\right)$ term can be positive or negative but this tells us whether work is done BY the system or ON the system.

Consider you pushing a box on the floor; work represents the energy you have to put in it (ON the system, the box gains kinetic energy)!!! If you maintain the same force but you have to push further...you need to supply more energy!!!

Now consider your box sliding on the floor and you now want to stop it, again using the same amount of force; you are moved across the floor by the box...the box is transferring energy to you doing a work on you (BY the system, you gain kinetic energy) and slowing down. If it pushes you for a longer distance it transfer more energy.