When a force causes a mass to move in a particular direction that is the positive direction for that mass. It does not matter what the actual direction is (N, S, E, W, up, down, left, right). When the same force causes a different mass to move in a different direction that direction is still the positive direct for that mass. And the momentums of the two masses are added.

Proof: An Atwood’s machine is used to prove F = ma. A little over half of the motion in an Atwood’s is going down and a little less than halve is going up; but the two momentums are added.

So you are not going to make vector mistakes again are you. When one force causes different masses to move in different directions all the directions are positive and the momentums are added together.

A 97.63 kilogram Atwood’s with 25 extra kilograms (122.63 total mass) on one side will accelerate to 2 meter per second velocity after the 25 kilograms has dropped 1 meter. This drop will take one second. With 9.81 newtons per kilogram for 25 kilograms applied for one second; this is 245.25 newton seconds.

After this Atwood’s is in motion it can apply 245.25 newtons for one second.

When 9.81 newtons is applied to this Atwood’s it will take 25 seconds to make the Atwood’s stop.

When 9.81 newtons is applied to a one kilogram mass for 25 seconds it will be moving 245.25 m/sec.

A one kilogram mass moving 245.25 m/sec will rise for 25 second. And it will rise 3065.625 meters.

This is 3065.625 m * 9.81 newtons/ kg * 1 kg = 30,073.78 joules of energy.

Twenty five kilograms dropped one meter is 25 kg * 9.81 N/kg * 1 m = 245.25 joules

So with 245.25 joule you can make 30,073.78 joules.