2.2 Work, Energy and Power

In everyday life, we say we’re “working” when we study, carry groceries, or hold a heavy box. But in physics, the word work has a very specific meaning:

Work is done only when a force causes an object to move in the direction of the force.

That means three things must happen for work to occur:

1. A force must be applied.
2. The object must move (undergo displacement).
3. The motion must have a component in the direction of the force.

The Formula for Work

Where:

• Force is measured in newtons (N)
• Distance is measured in meters (m)
• θ (theta) is the angle between the force and the direction of motion
• Work is measured in joules (J) → 1 J = 1 N·m

But don’t worry—you don’t need trigonometry here. You may get in much more detail in a physics class, but not here. When force and motion are in the same direction (like pushing a shopping cart forward), cos(0°) = 1, so:

$\text{Work = Force × Distance}$

Real Examples of Work Being Done

• Pushing a stalled car 5 meters down the road → you apply force, and it moves → work is done.
• Lifting a backpack from the floor to your desk → you apply upward force against gravity, and it moves up → work is done.
• Pedaling a bike uphill → you push on the pedals, and the bike moves upward against gravity → work is done.

Common Situations Where NO Work Is Done (in physics terms!)

• Holding a heavy suitcase while standing still: You’re applying force (to counteract gravity), but there’s no displacement → zero work.
• Pushing hard against a wall that doesn’t move: Force? Yes. Motion? No → zero work.
• Carrying a box horizontally across a room: You apply upward force to hold it, but motion is horizontal. Since force (up) and motion (sideways) are perpendicular, no work is done against gravity. (You might get tired—but that’s biology, not physics!)

Units for Work: Joule (J), Calorie (cal), British Thermal Unity (BTU), kilowatt-hour (kWh), foot-pound (foot-lb)

Energy – The “Ability” to Do Work

If work is the act of moving something with force, then energy is what enables you to do that work. As we learned in the last lesson,

Energy is the capacity to do work.

Think of energy as your “work potential.” You can store it, transfer it, or convert it—but you can’t create or destroy it (thanks to the Law of Conservation of Energy).

For example:

• A raised hammer has gravitational potential energy → when dropped, it does work on a nail.
• A charged battery has chemical energy → it can do work to light a bulb or spin a motor.
• A moving soccer ball has kinetic energy → it can do work by knocking over a cup.

Energy Units: Joule (J), Calorie (cal), British Thermal Unity (BTU), kilowatt-hour (kWh), foot-pound (foot-lb)

**Note: Energy and Work have the same units!

Power: The rate at which we work (or energy) is done.

Now, imagine two people lift identical boxes to the same shelf:

• Person A does it in 2 seconds.
• Person B takes 10 seconds.

Both did the same amount of work (same force, same distance).
Both used the same amount of energy.
But Person A delivered more power.

Power is the rate at which work is done or energy is transferred.

 The Formula for Power

$\text{Power = }\frac{Work}{Time}\text{ = }\frac{Energy}{Time}$

• Measured in watts (W) → 1 W = 1 joule per second (J/s) 

  Bicycling Example

• Imagine two bicyclists pedal 10 miles uphill → same work, same energy (218 calories) **assuming the cyclists are approximately the same weight
• If Cyclist Y finishes in 30 minutes; while Cyclist Z the other finishes in 60 minutes
• The amount of energy used in both situation is the same, Cyclist’s Y power output is twice as high—not because he did more, but because he did it faster.
• Cyclist Y completed 10 miles in 30 minutes versus Cyclist Z 10 miles in 60 minutes

Common Units of Power: Watt (W), kilowatt (kW), horsepower (hp), British Thermal unit per hour (BTU/hr), Joule/sec (same as a Watt).

Energy, Work, and Power (3:33)