Why is distance measured in the vertical instead of diagonal when calculating the work used to climb stairs?

Question

amistre64 · Answer

becasue the distance is vertical ...

amistre64 · Answer

it takes the same amount of work to climb a 10 foot ladder as it does to climb 10 feet of stairs

anonymous · Answer

so even if the stairs were really really long but only rise 10 feet its the same amount of work?

amistre64 · Answer

i believe the intent of the question relates to taking one step at a time

amistre64 · Answer

if there is movement across teh horizontal that is in addition to stepping up; your going to have more work involved since there are more steps to take

anonymous · Answer

but walking up stairs still involves a horizontal component does it not? why is that disregarded?

amistre64 · Answer

i think it resides in the idea that stairs provide no mechanical advantage in and of themselves

amistre64 · Answer

the amount of work to life a mass 7 inches is the same whether you lift it straight up or straight up .....

amistre64 · Answer

the work isnt spread out across a distance like on a ramp

anonymous · Answer

ohhhh, thats great. thanks a lot bro! really helps

amistre64 · Answer

youre welcome, im sure if im wrong someone will correct me :)

anonymous · Answer

The answer is because gravitational force which occurs in your problem is conservative force. Conservative force, on the one hand, always does the same amount of work between two points whatever path you move. 
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work for path 1 = work for path 2
On the other hand there is such a notion as equipotential which comes with conservative forces. It means the line(2d) or some surface(3d) on which the potential energy of the object is the same. 
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When you calculate work done by a conservative force you just can take the difference of the potential energies of the body at the two points.
$$W=U _{2}-U _{1}$$ 
But as long as these points lie on some equipotential it means that all the other points on the latter will give you the same result for work. Thus the work done between any two points lying on the two equipotentials is the same.
W btwn 3 & 1 = W btwn 2 & 4 = W 1 & 4 = W 2 & 3.