W = F̅Δs cos θ
displacement caused by
force and displacement are parallel, life is simple.
Apply a force → Displace an object → Do work
force is not quite parallel to displacement, it's like less force is being used
to do the work.
Apply less force → Do less work
also pretty simple. When the angle between force and displacement reaches 90°,
the component of the force parallel to the displacement reduces to zero.
Apply no force → Do no work
that was counterintuitive at first, but now it seems simple too. The farther
the two vectors get from parallel, the less work is done. Expand the angle
beyond 90°. Force and displacement are starting to point in opposite
directions. At 90°, no work was done. Beyond 90°, less than no work must be
done. This is negative work.
Apply less than no force → Do less than no work
is another reason to embrace negative work. The sign of work indicates the
direction of a change. A negative sign indicates a loss of something. In the
case of lowering a book, it means lowering its ability to do work — lowering