Define work as $W = Fd$ for a force along the displacement, relate work to the energy transferred, and define power as the rate of doing work, $P = W/t = Fv$.

What this topic is asking

Work and power connect forces to energy. The Physical Setting/Physics course asks you to recognize when a force does work (it must act along the displacement), to calculate work with $W = Fd$, to see work as the energy transferred to or from an object, and to define power as the rate of doing work. The Regents tests these as direct calculations and as the link between a force and the energy it changes.

Work

Two conditions are needed for work to be done: a force must act, and the object must move along (a component of) that force. So holding a heavy bag still does no physical work, however tiring, because there is no displacement. Carrying it horizontally at constant height also does no work against gravity, because the lifting force is vertical while the motion is horizontal, perpendicular to it.

Work as energy transferred

This is why work and energy share the same unit, the joule. Pushing a cart faster does work that becomes its kinetic energy; lifting a box does work that becomes its gravitational potential energy; friction does negative work that becomes heat. Tracking which energy the work changes is the bridge to energy and its conservation.

When no work is done

A force does no work when it is perpendicular to the motion, because it has no component along the displacement. Two Regents examples recur:

• The normal force on an object sliding along a level floor does no work (it is vertical, the motion is horizontal).
• The centripetal force in uniform circular motion does no work (it points to the center, perpendicular to the velocity), which is why the speed stays constant.

Recognizing these "zero-work" forces avoids a common error of multiplying a perpendicular force by a distance.

Power

Power measures how quickly work is done, not how much. Two motors that each do $1000$ J of work differ in power if one takes $2$ s and the other $10$ s. The form $P = Fv$ is handy when a constant force moves an object at a known speed, for instance a car engine pushing at constant velocity against drag.

Reference Tables note

The Reference Tables print $W = Fd$, $W = \Delta E_T$, $P = \dfrac{W}{t}$ and $P = Fv$ in the Mechanics section, and $P = VI$ in the Electricity section (the same idea, rate of energy transfer, applied to circuits). You supply the recognition of when a force is along or perpendicular to the motion, and the link between work and the specific energy it changes.

Try this

Q1. A $50.$ N force moves an object $3.0$ m in the direction of the force. Calculate the work done. [2 points]

• Cue. $W = Fd = (50.)(3.0) = 150$ J.

Q2. State why the centripetal force in circular motion does no work. [1 point]

• Cue. It is perpendicular to the velocity (it points to the center), so it has no component along the motion.