CSEC Physics • Lesson 4 of 4Scalars, Vectors & Resultants · Myers Science Hub Student Centre
CourseCSEC Physics
Practice formatMCQ • Structured • Experimental
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Learning objectives
- Distinguish scalar and vector quantities and give examples.
- Use scale diagrams to add two vectors, including oblique vectors.
- Calculate resultants for parallel, anti-parallel and perpendicular vectors.
- Explain how one vector can be resolved into two perpendicular components.
Core notes
Scalars and vectors
| Scalar | Vector |
|---|---|
| magnitude only | magnitude and direction |
| mass, time, distance, speed, energy, temperature | displacement, velocity, acceleration, force, weight, momentum |
Vector diagrams
Vectors are represented by arrows: arrow length represents magnitude to a stated scale and arrow direction represents direction. For addition, place vectors head-to-tail; the resultant runs from the tail of the first to the head of the last.
Special cases
- Parallel, same direction: add magnitudes.
- Anti-parallel: subtract magnitudes; direction is that of the larger vector.
- Perpendicular: use Pythagoras for magnitude and trigonometry for direction.
A single vector can also be resolved into two mutually perpendicular components.
Video lesson
Paper 01-style MCQ
1. Which quantity is a vector?KC • 1
2. Two horizontal forces of 12 N east and 7 N west act on an object. The resultant isUK • 1
3. Two perpendicular forces of 6 N and 8 N act at a point. The magnitude of their resultant isUK • 1
Paper 02-style structured questions
4. Distinguish between distance and displacement.UK • 4
Distance is the total path length travelled and is a scalar (2). Displacement is the straight-line change in position from initial to final point with direction and is a vector (2).
5. A boat travels 3.0 km east and then 4.0 km north. Determine the magnitude and direction of its resultant displacement.UK • 5
Draw/recognise right triangle (1); magnitude = √(3²+4²) = 5.0 km (2); angle = tan⁻¹(4/3) = about 53° north of east (2).
Experiment-type question
6. Design a practical demonstration to test vector addition using two force meters (or masses over pulleys) and a ring at equilibrium.XS/PD • 8
State aim (1); arrange two known forces at measured directions on a ring (1); add a third force to bring ring to equilibrium (1); measure all magnitudes and directions (1); draw first two vectors head-to-tail to scale (1); determine predicted resultant from diagram (1); compare its magnitude/direction with the equilibrant (opposite direction) (1); identify a source of error such as pulley friction or angle reading (1).