Vectors, Scalars and Free-Body Diagrams
Sorting quantities into scalars, which carry only a size, and vectors, which carry a direction too. Every force on one object is then drawn as an arrow whose length is its size, and the resultant is read off the diagram.
What a learner can do afterwards
- Sorts distance, speed and mass from displacement, velocity, force and weight, saying which need a direction
- Draws a free-body diagram for a hanging lamp, a towed sledge and a falling ball, with arrows to scale
- Finds the resultant of two forces along one line, and of two forces at right angles by scale drawing
1 · Read
Scalars have a size but no direction. Distance, speed and mass are scalars. Vectors have size and direction: displacement, velocity, force and weight. Distance counts the whole path. Displacement describes the change from start to finish, including direction. Velocity gives speed and direction.
A force is a push or pull with size and direction. Friction and tension act through contact; weight is the force of gravity. Only the combined force, called the resultant, determines the change in motion. Equal opposite forces cancel, leaving motion unchanged.
For a point-model free-body diagram, draw one dot for the chosen object. Draw each external force from it at one scale and label its source. Keep the resultant separate. A still lamp has tension up and weight down. A horizontally towed sledge has weight down, ground support up, tow force forward and friction backward when present. A falling ball has weight down and air resistance up when relevant.
Along one line, choose a positive direction. Add same-direction forces and subtract opposing forces. A pull of 11 N forward opposed by 6 N leaves 5 N forward. The number line shows these signed force additions, not distances travelled. Equal opposite forces give zero.
For perpendicular forces, draw them head to tail using a ruler, at a right angle and one scale. At 1 cm for 2 N, draw 6 N east as 3 cm, then 8 N north as 4 cm from its tip. The resultant joins the first tail to the last tip: 5 cm represents 10 N. The arrows and resultant form a right triangle. Squaring means multiplying a number by itself; a square root undoes this. For perpendicular forces only, R = square root of (6² + 8²) = square root of 100 = 10 N.
Sort scalars from vectors, draw every force as a scaled arrow, then read the resultant.
Lesson, questions and flashcards written for this dataset.
Replacement readings written for this dataset. Linked videos are credited to Khan Academy; video terms have not been verified.
2 · Watch
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Where this leads
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