Scalars and vectors
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Define a scalar quantity and provide two examples from physics.
A scalar quantity is one that has magnitude only, not direction. Examples include: mass, temperature, time, distance, speed, energy, and work.
Define a vector quantity and provide two examples from physics.
A vector quantity is one that has both magnitude and direction. Examples include: displacement, velocity, acceleration, force, momentum, and weight.
Describe the process of adding two coplanar vectors graphically.
Coplanar vectors can be added using a vector triangle or parallelogram. Draw the vectors to scale, head-to-tail (triangle) or from a common origin (parallelogram), then measure the resultant vector's magnitude and direction.
Explain how to resolve a vector into two perpendicular components.
A vector can be resolved into horizontal (x) and vertical (y) components using trigonometry. If the vector has magnitude 'A' and makes an angle 'θ' with the horizontal, then Ax = Acosθ and Ay = Asinθ.
Two forces, 3N and 4N, act on an object at right angles to each other. What is the magnitude of the resultant force?
Use Pythagorean theorem: Resultant force = √(3² + 4²) = √25 = 5N.
Describe the difference between distance and displacement.
Distance is a scalar quantity representing the total length of the path traveled. Displacement is a vector quantity representing the change in position from start to finish, with a specific direction.
A car travels 50m North, then 30m East. What is the magnitude of the car's displacement?
The displacement is the hypotenuse of a right-angled triangle. Displacement = √(50² + 30²) = √(2500+900) = √3400 ≈ 58.3m
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