Push or Pull? The Physics of Opening a Door

When people hold doors for each other it seems easier to push than pull a door. When considering forces however, it should be equally as hard to push and pull.

When pushing a door, we can assume push is directly on the door and pull is pulling on a knob. The Forces include the force of gravity, the force of friction, and the force applied. When pulling a door, the same forces apply, except force is applied to the knob and pulled onto the knob which then applies force to the door.

So why is it harder to pull than push? Although friction between the door and the handle in the opposite direction of force applied takes a bit of force away, this is not significant enough to cause a big discrepancy in difficulty. The major factor when considering door pulling and pushing is momentum. Since when you push you generally are walking and continue at a constant velocity, your momentum helps you push the door in P=mv. When you pull however, you will have to go backwards and not be able to use your forward momentum. Thus due to the loss of momentum, pushing a door seems easier than pulling a door, but if one were to push a door without momentum, it would be almost as easy.