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Mechanics

Resolving vectors and finding resultants

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  • Papers 1 and 3

Overview

Recall questions on resolving a vector into perpendicular components, combining vectors at right angles and at any angle, and the forces on a body on a slope.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

How is a vector resolved into two perpendicular components, and why is that useful?

Key term

What is true of three coplanar forces acting on a body in equilibrium when they are added tip to tail?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How do you resolve a vector of magnitude F acting at an angle θ to the horizontal into two perpendicular components?

    Model answer

    The horizontal component is F cos θ and the vertical component is F sin θ.

  2. 2

    A force of 50 N acts at 30° above the horizontal. What are its horizontal and vertical components?

    Model answer

    The horizontal component is 50 cos 30° = 43 N and the vertical component is 50 sin 30° = 25 N.

  3. 3

    Why is it useful to resolve a vector into two perpendicular components?

    Model answer

    Perpendicular components are independent of one another, so each direction can be treated as a separate one-dimensional problem.

  4. 4

    How do you find the resultant of two vectors that act at right angles to each other?

    Model answer

    The magnitude is found from Pythagoras' theorem and the direction from the inverse tangent of the ratio of the two components.

  5. 5

    A walker travels 3.0 km east and then 4.0 km north. What are the magnitude and direction of the resultant displacement?

    Model answer

    The magnitude is √(3.0² + 4.0²) = 5.0 km, in a direction tan⁻¹(4.0/3.0) = 53° north of east.

  6. 6

    How can the resultant of two coplanar vectors acting at any angle be found using a scale diagram?

    Model answer

    The vectors are set out to scale tip to tail on a scale diagram, and the resultant is the line from the tail of the first to the tip of the second, whose length and angle are then measured.

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