Ugo slides a packing box across a warehouse floor and lets go. The box keeps sliding forward, slowing as it goes.
Friction is doing work on the box the whole time. The same was true of the rope that towed it earlier. Should the two works be counted the same way?
While the rope towed the box forward, the rope's force on the box pointed forward, the same direction the box moved: the force pointed with the motion.
Friction is different. The box slides forward, and friction from the floor acts on it pointing backward: against the motion.
The sign tells the two apart.
So the rope's work on the box is positive, and friction on the sliding box does negative work.
The sign records direction only: with the motion, positive; against the motion, negative.
A perpendicular force gets no sign at all: it does zero work, so the with-or-against question is never asked of it.
What a negative sign means for the box's energy is the next lesson's question. This lesson only attaches the right sign.
A cyclist coasts forward along a flat road. Air resistance on her acts backward. Is the work done by air resistance on the cyclist positive or negative?
The cyclist moves forward, and air resistance points backward: against the motion.
The work done by air resistance on the cyclist is negative.
A stone falls down a well. The stone's weight acts straight down. Is the work done by the weight on the stone positive or negative?
The stone moves downward, and its weight points downward too: with the motion.
The work done by the weight on the stone is positive.
A parachutist falls straight down. Air resistance on her acts straight up. Is the work done by air resistance on the parachutist positive or negative?
A tractor tows a hay wagon forward along a lane. The towbar's force on the wagon points forward. Is the work done by the towbar's force on the wagon positive or negative?
An apple falls from a branch. The apple's weight acts downward. Is the work done by the weight on the apple positive or negative?
A rescue rope hauls a climber upward, and the climber moves upward. Is the work done by the rope's force on the climber positive or negative?
A curling stone slides along the ice. Friction from the ice on the stone acts backward. Is the work done by friction on the stone positive or negative?
A train slows as it enters a station. The braking force on the train points backward, against the motion. Is the work done by the braking force on the train positive or negative?
A gardener drags a sack of soil forward across a lawn with a horizontal rope. Which force does negative work on the sack?
What decides whether a force's work on a moving object is positive or negative?
Soren tosses his keys straight up, and the keys rise. Which statement is correct?