Forces as Vectors: Resolving and Resultants
Draw every force acting on a body as an arrow, add them as vectors to get the resultant, and split any force into components along two perpendicular directions of your choosing.
What a learner can do afterwards
- Resolve a 20 N force at 30° to the horizontal into two components
- Find the magnitude and direction of the resultant of two perpendicular forces
- Draw a diagram showing every force on a body and nothing that is not a force
1 · Read
A tilted force is two forces in disguise: one across and one up, at right angles to each other. With the angle measured from the horizontal, the across part is F times cos and the up part is F times sin. A 20 N force at 30 degrees gives 20 times 0.5, which is 10 N upward, and about 17.3 N across.
Perpendicular forces add through Pythagoras, and the direction comes from tan. A 3 N pull east with a 4 N pull north gives root 25, which is 5 N, pointing about 53 degrees north of east. A 6 N pull east with an 8 N pull north gives root 100, which is 10 N.
A free body diagram shows every force on the body and nothing else. For a book resting on a table, draw gravity down and the normal force up, with each arrow starting on the book. The push of the book on the table acts on the table, so it stays out of the book diagram.
Split tilted forces into parts before you balance anything. Each direction then balances on its own, which turns one tilted problem into two straight line ones.
Split each force into across and up parts, add perpendicular forces with Pythagoras, and draw only forces on the body.
2 · Watch
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.