https://www.youtube.com/watch?v=8Q7L2BOYkjEThe reason this works is because you can apply the same quantity of force for different periods of time. You can apply the force for a short period of time on the side going up; and on the side going down you can apply the same force for a long period of time. This process will produce massive quantities of energy.

By throwing a mass up fast; you can pass units of distance that result in only minimal loss of momentum. By changing the arrangement of the applied force (from the same mass); these passed units of distance can give you larger units of momentum on the way back down. Momentum is a function of time.

An example for a one kilogram mass: The first meter of an upward throw of 100 meters only costs you .222 units of momentum. The same meter of drop on the way back down can give you 4.429 units of momentum. The speed of the upward throw of 100 meters; changes from only (square root of (100 m*2*9.81m/sec/sec) 44.294 m/sec to 44.0724 m/sec in the first meter up. But you get 4.429 units of momentum on each individual meter on the way back down. You gain (4.429 -.222) 4.207 units of momentum.

It takes .4515 sec to drop one meter: that means you have applied the force for .4515 second.

If you are moving up at 100 meter per second you can cross 19 meters in .4515 second.

On the way back down ‘each’ of these 19 units of distance can be crossed in .4515 seconds; this is 18 more units of time from the same distance of 19 meters. Gravity does not make you pay for these 18 extra units of ‘time’ over which the force is applied.

In the kilowatt hour you are paying for each unit of time ‘of the applied force’; you won’t get 18 free units. Gravity will apply the force for free.