Near the hinge, far from it
The four readings from activity 1 all say one thing: the further from the axis you push, the less force you need.
It reads more clearly as a pair. Starting the door turning is one and the same job — but the force you have to pay for it changes with where you apply it.
- Perpendicular distance is large
- Force needed is small
- The door opens easily
- Perpendicular distance is small
- Force needed is large
- The door is hard to open
What "perpendicular distance" means
The distance measured here is not a distance along the door. It is measured from the axis of rotation to the line of action of the force, at right angles to that line. That is why the balance had to be kept perpendicular to the door — when it is, the distance measured along the door is the perpendicular distance.
As one grows, the other shrinks
To turn the same door, doubling the perpendicular distance halves the force needed. Force and distance change in opposite directions, and an increase in one is paid for exactly by a decrease in the other.
That hints that what matters is neither the force on its own nor the distance on its own, but the two of them taken together. On the next page we give that combination its name.
Pushing outwards is not enough
Push exactly at the hinge and the perpendicular distance is zero. However hard you then push, the door will not turn at all. A force whose line passes through the axis can produce no turning whatsoever.