Why less force is required to shut the door from edge of the door
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because with increase in moment arm less force is required to shut the door
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One other way of looking at it is that the total amount of work needed for opening the door is constant. The work done by a force is the force multiplied by the path length: W=F⋅sW=F⋅s. If the force changes along the path (or is not parallel to it), this expression generalises to an integral:
W=∫s2s1F⃗ ⋅ds→W=∫s1s2F→⋅ds→
From this, you can see that if you apply the force over a longer path, you need less force to perform the same amount of work. This is exactly what you're doing when you're pushing the door at a point further away from the hinge. The arc your hand makes becomes larger (see image), so you don't need to apply as much force to open the door.
W=∫s2s1F⃗ ⋅ds→W=∫s1s2F→⋅ds→
From this, you can see that if you apply the force over a longer path, you need less force to perform the same amount of work. This is exactly what you're doing when you're pushing the door at a point further away from the hinge. The arc your hand makes becomes larger (see image), so you don't need to apply as much force to open the door.
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