Define work as a force acting through a distance (W = Fd), define power as the rate of doing work (P = W/t), and apply both to everyday situations (MA STE Introductory Physics, Energy, HS-PS3-1).

What this topic is asking

This topic opens the Energy reporting category (HS-PS3) of the Massachusetts Introductory Physics MCAS. You must define work as a force acting through a distance, $W = Fd$, define power as the rate of doing work, $P = \dfrac{W}{t}$, and use both in everyday situations such as lifting, pushing, and running. Both formulas are on the reference sheet. The crosscutting idea is energy and matter: work is the bridge that transfers energy from one object to another, and power tells you how fast that transfer happens.

Work

Work is the everyday word physicists use for transferring energy by a force. When you push a box and it slides, you do work on the box and give it energy. The reference-sheet formula is

where $W$ is the work (J), $F$ is the force (N), and $d$ is the distance moved in the direction of the force (m). Because a joule is a newton meter, the units take care of themselves: newtons times meters gives joules.

Two points the MCAS expects you to handle:

• The force and the motion must be along the same line for all of the force to do work. When you push a crate horizontally and it slides horizontally, the full force does work. When you carry a tray horizontally, the upward force you apply is perpendicular to the horizontal motion, so that force does no work on the tray.
• No motion means no work, in the physics sense. Holding a heavy bag still feels tiring, but if the bag does not move, $d = 0$ and the work done on it is zero. Your muscles use energy, but no work is done on the bag.

Power

Power answers "how fast?" rather than "how much?" The reference-sheet formula is

where $P$ is the power (W), $W$ is the work done (J), and $t$ is the time taken (s). A 100 W light bulb transfers 100 J of energy every second. A powerful engine does a large amount of work quickly; a weaker motor doing the same job simply takes longer.

Power and work are easy to mix up because both involve energy. Keep them apart with the units: work is in joules, power is in watts (joules per second). A weightlifter and a forklift can raise the same load to the same height, doing the same work, but the forklift does it faster, so it has more power.

Work transfers energy

The Massachusetts framework treats work as the link between forces and energy. The force topics in Modules 1 to 3 explain how forces change motion; the work idea explains how those same forces transfer energy. That is why the next topic, kinetic and potential energy, follows directly: the work you do shows up as one of those energy forms.

Worked example

Reference-sheet note

The reference sheet prints work as $W = Fd$ and power as $P = \dfrac{W}{t}$, with $W$ in joules and $P$ in watts. It does not print a version of work with an angle, so on this test the force and the distance are taken along the same line. What you recall is that work transfers energy, that no motion means no work, and the units (joule for work, watt for power).

Try this

Q1. A force of $25$ N moves an object $8.0$ m in the direction of the force. Calculate the work done. [2]

• Cue. $W = Fd = (25)(8.0) = 200$ J.

Q2. A pump does $1800$ J of work in $6.0$ s. Calculate its power output. [2]

• Cue. $P = \dfrac{W}{t} = \dfrac{1800}{6.0} = 300$ W.