Why it gets easier to push open a door, the further you are from the hinge?
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Leverage. If the hinge is the fulcrum and your hand applies the force, the torque you apply is proportional to the distance from the fulcrum.
Imagine a FBD of a beam on a pivot. Torque is defined as Force x Distance. The closer you are to the hinge the more force is required to push that door oepen, vice versa. That is why it is easier to push open a door the further you are from the hinge.
It takes a set amount of energy to move something, like a door. That energy can be from high effort over a short distance or low effort over a long distance. When you’re further from the hinge, you have to push a few feet compared to a few inches near the hinge.
Energy = force (effort) x distance
Edit: this is true for a set door speed.
The longer the lever arm, the more pressure is applied per the same amount of force. Think of it like lifting a big stone, if you try to lift it yourself you cannot budge it. But I you use a lever arm and a pivot point you can move the stone with only a portion of your force available.
Torque. τ = F×r where F is the force you apply and r is the distance from the axis of rotation (the hinge). The further you are the the hinge, the less force you need to reach the necessary torque to rotate the door open.
Is it easier?
As others have mentioned, it’s the product of force x distance, so if you apply a large force you only need a short distance. If you only have a small force then you need to push for longer.
Big x little or little x big, you’re still using the same amount of energy.
Other answers are sort of correct, but they’re missing an important component: time. When you push on the door from farther away from the hinge, you’re often pushing the door over a longer period of time than if you’re pushing right at the hinge. It’s easier because you’re exerting that energy over a large period of time, which means that your rate of producing the energy (the power, in physics terms) is smaller. So you effectively don’t have to push as hard to get the same result because you’re pushing for longer.
It’s the same amount of “work”–pushing hard for a short distance or pushing less hard for a longer distance–, but that doesn’t answer your question.
“Why is it easier?”
Imagine moving a large bucket of pennies. You could struggle to lift the whole bucket or you could scoop them out a handful at a time or you could pick each penny out one by one. You would probably pick the middle option, because that’s “easier”. It’s a task sized for you. If you were much stronger, you’d just lift the whole bucket. If you were much weaker, you would move one penny at a time. In all cases, you pick the “easy” option.
Back to doors. Why is it “easy” to push where the knob is? Because we deliberately put knobs where it would be easiest for a human to use. When we have very heavy doors, like on ships or in banks, we use wheels and cranks to make it less like lifting a heavy bucket and more like scooping handfuls of pennies. It becomes “easy” because we made it easy.
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Because the farther out you are from the pivot point, the more leverage you have. The distance multiplies the torque you can generate. It’s basically a lever. Middle school physics.
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