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Cognito Scalars and vectors
Key facts & equations
Scalars and vectors Scalar : magnitude only. Examples: speed, distance, mass, energy, temperature, time.Vector : magnitude AND direction. Examples: velocity, displacement, force, acceleration, momentum.When adding vectors, direction matters. Two 3 N forces can give 0 N (opposite) to 6 N (same direction). Free body diagrams: show all forces acting on an object as arrows from the object. Arrow length represents force magnitude. Arrow direction shows force direction. Resultant forces and equilibrium Resultant force : the single force that has the same effect as all forces acting together.Add forces in the same direction. Subtract opposing forces. If resultant = 0 → object in equilibrium (stationary or constant velocity). Scale drawing: draw forces tip-to-tail → resultant is the closing vector. Pythagoras: for two perpendicular forces. F_resultant = √(F1² + F2²). Resolving forces (Higher) Any force can be split into horizontal and vertical components. Horizontal component: F_h = F cos θ. Vertical component: F_v = F sin θ. Useful for inclined planes: weight component along slope = mg sin θ. Weight component perpendicular to slope = mg cos θ. Contact and non-contact forces Contact forces : friction, normal force, tension, air resistance. Require physical contact.Non-contact forces : gravity, magnetic force, electrostatic force. Act at a distance.Forces always come in interaction pairs (Newton 3rd law). Gravity: always attractive. Electrostatic: attract or repel. Magnetic: attract or repel. Exam questions — 4 questions · 10 marks · AQA 8463 style
⚡ Show all working — the AI marks against the AQA mark scheme. Method marks awarded for correct working even if the final answer is wrong.
1 mark Vector identification AQA 8463 style
Which of the following is a vector quantity?
A Temperature
B Energy
C Force
D Mass
3 marks Resultant force AQA 8463 P1 style 🔢 Calculator
A boat experiences: engine thrust = 1200 N forward, water resistance = 450 N backward, wind force = 300 N forward. Calculate the resultant force and state the direction. (2 marks)
Hint: Add all forces in the same direction first. Then find the difference between forward and backward totals.
Mark my answer +30 XP
1 mark Equilibrium condition AQA 8463 style
An object moves at constant velocity. Which statement must be true?
A No forces act on the object
B Only one force acts on the object
C The resultant force on the object is zero
D The object has no mass
4 marks Perpendicular forces (Higher) AQA 8463 Higher style 🔢 Calculator
A boat is pushed by an engine with force 60 N East and a current with force 80 N North. Calculate the magnitude and direction of the resultant force. (3 marks)
Hint: Perpendicular forces: use Pythagoras. Magnitude = √(60² + 80²). Direction: tan θ = opposite/adjacent.
Mark my answer +40 XP
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