Ramp Work Distance Scan

Ramp Work Distance Scan

the triangle rule scanned for the first time

Chapter three checked the ramp (triangle-area) work rule at a single displacement; this scan holds force fixed and scans displacement across three rows the way chapter five did for the constant-force rectangle rule. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Four metres under a ramping force gives half the rectangle area

Chapter three checked the ramp force-work rule once, at a single displacement. Here force stays 8 newtons while displacement varies: at 4 metres, the triangular area gives work 16 joules.

12⋅8⋅4=16\tfrac{1}{2}\cdot8\cdot4=16
Mechanical work areaA checked geometric area gives work.forcedistancework

Six metres reproduces chapter three's own checked ramp case

The same force 8 newtons at displacement 6 metres gives work 24 joules, exactly chapter three's ramp-force-work-area example.

12⋅8⋅6=24\tfrac{1}{2}\cdot8\cdot6=24
Mechanical work areaA checked geometric area gives work.forcedistancework

Eight metres doubles the triangular work from the first row

At displacement 8 metres, the same force gives work 32 joules. Three rows show the ramp rule scales linearly with distance, the same as chapter five's rectangle scan, but at half the constant-force value.

12⋅8⋅8=32\tfrac{1}{2}\cdot8\cdot8=32
Mechanical work areaA checked geometric area gives work.forcedistancework