In the usual analysis, work needed to lift an object of mass (m) a certain distance (h) is the same whether it is through lifting the object straight up (W=mgh) or pushing it up a ramp with length d and angle A (W = mgsinA x h/sinA = mgh).
However, this does not account for the work needed to move the said object the ground distance (h/tan A), no?
For example, in a 30/60/90 degree triangle scenario with height of 1 meter ramp 2 meter, and ground distance square root of 3 meter, the work needed to move an object of 2 kg horizontally first would be 2gxsquare root of 3 and the work to move the object up 1 m would be 2g. The combined work would be 2g (square root of 3 + 1), no?
The usual analysis of moving that object up the 2m ramp is 2gx(1/2) divided by 1/(1/2) = g x 2 = 2g. These two methods don't add up. What am I missing?
Is the usual ramp analysis wrong, in that mgxsin A or 2gx(1/2) or g can't the force needed to move the object up the 2 meter ramp? Should that force be (1+square root of 3)g instead?
What am I missing? Thank you so very much for helping out!