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Force arrows

Forces and motion · level 3, lesson 1 of 6

A question to start

A book lies on a table. Nothing is moving. Are there any forces on the book at all? How could you draw them?

The idea

A force has two things that matter: how big it is, and which way it points. An arrow shows both at once:

  • The arrow points the way the force pushes or pulls.
  • The arrow's length shows how big the force is. Twice the force, twice as long.
  • The arrow starts on the thing the force acts on.
  • A label says what the force is: weight, push, friction, and so on.

The book on the table has two forces on it. Its weight, the Earth's pull, points down. The table pushes up on it, just as hard. That upward push from a surface is called the normal force or the reaction.

table pushes upweight

Drawing arrows for every force on one thing is the first step in solving almost any problem about forces. Engineers draw them for bridges, and mission teams draw them for landers on Mars.

Worked examples

1. Pulling a sledge. Arrows: your pull along the rope, forwards; friction from the snow, backwards; weight, down; the snow pushing up.

2. A balloon on a string. Arrows: the air lifting it, up; its weight, down; the string pulling it, down.

3. A rover parked on Mars. Weight, down (shorter than on Earth for the same rover); the ground pushing up through its wheels, just as long.

Try it

  1. What two things does a force arrow show?
  2. Draw the forces on an apple hanging from a tree.
  3. A force arrow is 4 cm long and stands for 20 units of force. How long would an arrow for 10 units be?
  4. What is the name of the upward push of a surface?
Answers
  1. Which way the force points, and how big it is.
  2. Weight, down; the stalk pulling it, up. Same length.
  3. 2 cm.
  4. The normal force (or reaction).

Common mistake

"Something that is not moving has no forces on it." It has forces on it; they just balance. The book on the table has its weight and the table's push, equal and opposite.

Where it leads