The physics of big sack over beautiful wall

[struggle4progress]

17. You need to know the total energy, which at any time during the trajectory

is the sum of the kinetic and potential parts.

The total energy initially added is a product (Force x Distance), involving the length over which the source is actively doing work on the sack and the actual force generating the acceleration: a larger force is required if one wants to impart a certain kinetic energy over a shorter distance than if one wants to impart the same kinetic energy over a longer distance. And in the same way, decelerating an object from a given speed to a complete stop over a shorter distance involves more force acting on the object than decelerating that object from the same speed to a complete stop over a longer distance: think of the difference between dropping an egg from a short height onto a solid wood floor, as opposed to dropping the egg from the same height onto a deep but loose pile of shredded paper