inclined plane and work...clarification from BR q's

[opensesame0]

Can someone tell me if this logic sounds right?

So I just finished BR Physics lesson 3, passages 1, and I messed up on the first passage on inclined planes.

Basically, there's a 2 m long frictionless ramp that takes you up 1 vertical meter.

#1 stated that F = 500 N, and since I thought work was path independent, and the ramp was frictionless, I reasoned that Work = Force x distance = 500(1) = 500 J.

However, I see now that I should have used the horizontal displacement (for an answer of 1000 J), even though work is path independent, because the 500 N force would have had to be greater if the path was straight up, thus you need to use the horizontal displacement, as using the horizontal displacement takes this into account.

Did I reason that out correctly?

Thanks in advance.

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[inaccensa]

Can someone tell me if this logic sounds right?

So I just finished BR Physics lesson 3, passages 1, and I messed up on the first passage on inclined planes.

Basically, there's a 2 m long frictionless ramp that takes you up 1 vertical meter.

#1 stated that F = 500 N, and since I thought work was path independent, and the ramp was frictionless, I reasoned that Work = Force x distance = 500(1) = 500 J.

However, I see now that I should have used the horizontal displacement (for an answer of 1000 J), even though work is path independent, because the 500 N force would have had to be greater if the path was straight up, thus you need to use the horizontal displacement, as using the horizontal displacement takes this into account.

Did I reason that out correctly?

Thanks in advance.

Work and heat are not state functions. They depend on the path taken. Work down in both cases should be the same. However the force required and the displacement will differ. The force required to lift the object vertically is more, but the displacement is less. On the frictionless surface, the force is reduced, the displacement increases. I hope the question said that the force required to pull the object 2m was 500N