Physics (not) by the numbers: work and energy

I tutor several physics students right now, and I find myself starting a lot of conversations with the phrase ‘let’s look at this conceptually for a second’. Don’t get me wrong, I love math, but sometimes we have to step away from the numbers and formulae and use our words.

Work and energy are good topics to tackle conceptually. Like many words, they have very specific meanings in physics that differ from the colloquial usage.

Work is a force applied to an object that causes it to move in the same direction as that force. If you pull a sled north and the sled moves north, you are doing work on the sled. The classic example of a force applied to a moving object that isn’t doing work is a waiter carrying a tray of food: the waiter is applying an upward force on the tray, but the tray is moving horizontally, so the applied force isn’t doing work on the object. Doing work on an object increases its energy.

Energy is the ability to do the aforementioned work; less circularly, it is also the ability to ‘make change’. Examples of these changes include, but are not limited to, temperature increases, phase changes (solid to liquid, liquid to gas, etc.), and making/breaking chemical bonds. There are many different types of energy, but the two that beginning students are primarily concerned with are potential and kinetic. Potential energy is stored in an object and comes from its position relative to a fixed point: consider a spring compressed from its natural length or an object at a given height above the ground. If released, both have the ability to do work on another object. Kinetic energy is the energy that a moving object has; if viral videos have taught us anything, it’s that a sledder flying down a hill absolutely has the ability to do work on an innocent bystander. In many instances, potential energy is transformed into kinetic energy and vice versa.

Let’s take a closer look at the work-energy transformations in the sledding example. A sledder must do work on herself/the sled to get to the top of the hill; doing work on the person/sled system increases its energy. At the top of the hill, all of this energy is stored as (gravitational) potential energy. As she sleds down the hill and speeds up, that potential energy is converted into kinetic energy. Suppose another person is standing in the sledder’s path. Upon colliding, the sledder’s energy allows her to push on the person and move her a certain distance, indicating that the sledder has done work on this person.

It’s winter! Grab a sled, find a hill, and do your own qualitative work-energy investigations.


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