Words such as force and work have exact meanings in science, often narrower than their everyday ones. Symbols name quantities, and an equation states how quantities are related.
“I worked hard all day” is a normal sentence. In physics it may be false.
Science borrows many everyday words and gives each one a single, fixed meaning. Force, work, energy and reaction are examples. The scientific meaning is usually narrower than the everyday one.
Take work. In physics, work is done on an object only when a force acts on it and the object moves in the direction of that force. For a constant force along the motion, work = force × distance moved. Its unit is the joule (J).
You hold a heavy bag of books completely still for ten minutes. Your arms ache. In the physics sense, how much work have you done on the bag?
Zero. The bag did not move, so the distance moved is 0 m. Force × 0 m = 0 J.
Your arms ache for a separate reason. To hold a load, muscle fibres contract again and again. Each contraction uses chemical energy from your food, and that energy ends up as heat in your body. None of it goes into the bag.
Work, in the scientific sense. Work needs a force and movement in the direction of that force. Aching arms are not part of the definition.
Science is done by people in many countries who speak different languages. A measurement made in Mumbai is checked by a laboratory in Tokyo. The check is only possible if both laboratories mean the same thing by each word.
If “work” meant effort in one place and force × distance in another, the two would report different numbers for the same event. Fixed definitions remove that problem.
A physical quantity is a property that can be measured and expressed as a number with a unit. Mass, time and electric current are physical quantities. Each one has an agreed symbol and an agreed unit.
Three different things. The quantity is what you measure, the symbol is its short name, and the unit is what you measure it in. Notice that current is I but its unit is the ampere — symbol and unit are never the same thing.
A symbol lets a relationship fit on one line. “The distance travelled equals the speed multiplied by the time taken” becomes d = v × t.
The speed of light is written c, not s for speed. The letter comes from the Latin word celeritas, meaning swiftness. Many symbols come from history in this way rather than from the English word.
Since 1983 the speed of light in a vacuum has been fixed by definition at exactly 299,792,458 m/s. The metre is now defined from it: one metre is the distance light travels in 1/299,792,458 of a second.
An equation is not only a tool for getting a number. It states how quantities depend on each other. You can read that dependence before you put in any numbers.
Read it as a sentence. You already knew what this equation says. Writing it in symbols just makes it short enough to calculate with.
Two buses travel for the same time. One moves at 40 km/h, the other at 80 km/h. Without calculating, what can you say about the distances?
The faster bus covers twice the distance.
In d = v × t, the time t is the same for both buses. So d is proportional to v. Doubling v doubles d. You read this from the form of the equation, not from arithmetic.
An equation applied to a situation you have not understood gives a number with no meaning. This order avoids that:
1You push against a wall for five minutes and it does not move. The work you do on the wall is…
2Why does science give everyday words fixed, exact meanings?
3Which symbol stands for electric current?
4The symbol for the speed of light is ____ , from the Latin word celeritas.
5An equation in science is best described as…
6Which of these are physical quantities — measurable, with a defined unit?
More than one answer is correct.
7Two cyclists ride for the same time, one at 10 km/h and one at 30 km/h. Using d = v × t, the second covers…
8What is the best order for using an equation in a problem?
Next: why every country uses the same kilogram.
Noescio