← Work as energy transfer

Why perpendicular forces do no work

Talia rolls a cart across a level floor. The normal force on the cart acts straight up, and the first lesson said it does no work.

Why does a force at right angles to the motion transfer nothing at all?

Earlier in the course you resolved a force into perpendicular components: a part parallel to one direction, and a part perpendicular to it.

Resolve the normal force against the cart's motion line. The component parallel to the motion comes out as zero: the whole force stands perpendicular to the motion.

level floorcartnormal forcemotionparallel component: 0
The normal force has no component parallel to the motion: it transfers no energy.

Energy transfer needs the force to act through a distance in its own direction.

The normal force acts straight up, and the cart covers no upward distance at all.

Here is the mechanism in one sentence: a force perpendicular to the motion has no component parallel to the direction of movement, so it transfers no energy.

So the normal force does zero work on the rolling cart.

A sailboat glides across a calm bay. Its weight acts straight down, perpendicular to its motion. How much energy does the weight transfer to the sailboat during the glide?

Romy says: 'A force perpendicular to an object's motion transfers no energy to the object, because it has no component parallel to the motion.' Is Romy correct?

The same holds for every perpendicular force, whichever way it points: straight up under a rolling cart, straight down on a gliding sailboat, or sideways on a rising platform.

watersailboatweightmotion
The gliding sailboat's weight is perpendicular to the motion: no energy transferred.

A suitcase rides a moving walkway at a steady height. The suitcase's weight acts straight down. Explain why the weight transfers no energy to the suitcase.

The suitcase moves horizontally, and its weight acts straight down, perpendicular to the motion.

A force perpendicular to the motion has no component parallel to the direction of movement.

A force with no parallel component acts through no distance in its own direction.

So the weight transfers no energy to the suitcase.

A window cleaner's platform rises straight up a building while a steady horizontal wind force acts on it. How much energy does the wind force transfer to the platform?

buildingplatformwind forcemotion
A horizontal force on a rising platform: perpendicular again, so no energy transferred.

The platform moves straight up, and the wind force is horizontal, perpendicular to that motion.

A perpendicular force has no component parallel to the direction of movement.

The wind force transfers no energy to the platform.

Ugo rides a zip line across a ravine, moving horizontally. The cable's supporting force on him acts straight up. Why does that force do no work on him?

Your turn

A parade float moves along a level street. The street's normal force on the float acts straight up. Why does the normal force transfer no energy to the float?

A removal crew slides a couch across a level floor, then lifts the same couch straight up onto a van. In which part does the couch's weight do zero work on it?

Which statement about a force perpendicular to an object's motion is correct?