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Physics · Forces

Scalars, vectors and forces

Distinguish scalar and vector quantities, describe contact and non-contact forces, and represent forces as vectors.

  • 6 key terms
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is a force?

    Show answerHide answer

    A push or a pull

  2. 2

    What is the unit of force?

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    The newton (N)

  3. 3

    Give an example of a quantity with direction.

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    Velocity

  4. 4

    What is friction?

    Show answerHide answer

    A force that opposes motion between surfaces

  5. 5

    What does a longer arrow mean on a force diagram?

    Show answerHide answer

    A bigger force

Learning Objectives

  1. 1Distinguish scalar quantities from vector quantities.
  2. 2Represent a vector using an arrow.
  3. 3Describe contact and non-contact forces with examples.
  4. 4Describe the interaction between pairs of objects that produce a force on each object.

SCALARS AND VECTORS

Scalar quantities have magnitude only. Vector quantities have magnitude and direction.

A vector is drawn as an arrow: the length shows the magnitude and the arrowhead shows the direction. Force is a vector quantity.

Scalar or Vector?

Learn which is which.

  • Distance

    Vector (size and direction): Displacement

  • Speed

    Vector (size and direction): Velocity

  • Mass

    Vector (size and direction): Force and weight

  • Energy, time, temperature

    Vector (size and direction): Acceleration and momentum

Contact or Non-contact?

Contact forces (objects touching)

Non-contact forces (objects separated)

  • Gravitational force.
  • Electrostatic force.
  • Magnetic force.

Drawing a Force Vector

Draw an arrow to represent a force of 6 N to the right. Use a scale of 1 cm = 2 N.

Show the solutionHide the solution
  1. 1 Length \(6 \div 2 = 3\) cm
  2. 2 Direction An arrowhead pointing right

AnswerA 3 cm arrow pointing to the right.

Interaction Pairs

Two magnets are brought close together with their north poles facing. Describe the forces.

Show the solutionHide the solution
  1. 1 Force on each magnet Each magnet exerts a force on the other
  2. 2 Direction Like poles repel, so each force points away from the other magnet
  3. 3 Type Non-contact, because the magnets are not touching

AnswerEach magnet pushes the other away: equal and opposite non-contact forces.

Key Points

Use the right words.

  • Force is a vector

    It has a size in newtons and a direction.

  • Pairs of forces

    When two objects interact, each exerts a force on the other.

  • Scale

    Choose a scale so the arrows fit on the page.

  • Examples

    Name the force and its direction: 'friction to the left'.

Sort Them

Sort into scalar and vector: mass, velocity, distance, acceleration, time, force. Then say whether each of these forces is contact or non-contact: friction, gravity, magnetic force, tension.

1. Does it have direction?

2. Are the objects touching?

A good answer shows: Scalars: mass, distance, time. Vectors: velocity, acceleration, force. Contact: friction, tension. Non-contact: gravity, magnetic force.

Can I...?

  1. 1Define scalar and vector.
  2. 2Give examples of each.
  3. 3Draw a vector arrow to scale.
  4. 4List contact forces.
  5. 5List non-contact forces.
  6. 6Describe an interaction pair.
  7. 7Use the word magnitude.
  8. 8Write force directions.

Summary & Exam Focus

  • Scalar: magnitude only. Vector: magnitude and direction.
  • Force is a vector.
  • Contact: friction, tension, air resistance, normal contact force.
  • Non-contact: gravity, electrostatic, magnetic.

Exam focus

State whether velocity is a scalar or a vector quantity. (1 mark) (1 marks)

Vector: it has direction.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Scalar
A quantity with magnitude only.
Vector
A quantity with magnitude and direction.
Contact force
A force between objects that are touching.
Non-contact force
A force between objects that are separated.
Magnitude
The size of a quantity.
Newton
The unit of force.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 State 2 marks

    Give one example of a scalar quantity and one example of a vector quantity.

    Show answerHide answer

    Model answer

    Scalar: any of distance, speed, mass, time, energy. Vector: any of force, velocity, displacement, acceleration.

    Mark scheme

    • A scalar quantity — 1 mark
    • A vector quantity — 1 mark
  2. Question 2 Complete 3 marks

    Some forces are contact forces and some are non-contact forces. Give one example of each.

    Show answerHide answer

    Model answer

    Contact: friction, air resistance, tension or normal contact force. Non-contact: gravitational, electrostatic or magnetic force.

    Mark scheme

    • Contact example — 1 mark
    • Non-contact example — 1 mark
    • Correct link to touching or separated — 1 mark
  3. Question 3 Draw 2 marks

    A force of 6 N acts to the right on an object. Draw an arrow to represent this force. Use a scale of 1 cm = 2 N.

    Show answerHide answer

    Model answer

    An arrow 3 cm long pointing to the right.

    Mark scheme

    • Length 3 cm — 1 mark
    • Arrowhead pointing right — 1 mark
  4. Question 4 Explain 2 marks

    Explain the difference between speed and velocity.

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    Model answer

    Speed is a scalar: it has magnitude only. Velocity is a vector: it has both magnitude and direction.

    Mark scheme

    • Speed has no direction — 1 mark
    • Velocity has direction — 1 mark
  5. Question 5 Describe 3 marks

    A book rests on a table. Describe the forces acting on the book. State the type of each force.

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    Model answer

    The weight of the book acts downwards (a non-contact gravitational force). The normal contact force from the table acts upwards (a contact force). The two forces are equal in size.

    Mark scheme

    • Weight downwards, non-contact gravitational — 1 mark
    • Normal contact force upwards, contact — 1 mark
    • Equal in size or balanced — 1 mark

Quick check

  1. Which of these is a vector?

    1. AMass
    2. BForce
    3. CTime
    4. DEnergy
    Show answerHide answer

    B: Force

    It has direction.

  2. Which is a contact force?

    1. AGravity
    2. BMagnetic force
    3. CFriction
    4. DElectrostatic force
    Show answerHide answer

    C: Friction

    The objects are touching.

  3. Which is a scalar quantity?

    1. ADisplacement
    2. BVelocity
    3. CForce
    4. DDistance
    Show answerHide answer

    D: Distance

    It has no direction.

  4. The length of a force arrow shows the...

    1. Asize of the force
    2. Bdirection of the force
    3. Cmass
    4. Dtime
    Show answerHide answer

    A: size of the force

    Longer means bigger.

  5. Gravitational force is a...

    1. Acontact force
    2. Bnon-contact force
    3. Cscalar
    4. Dfriction
    Show answerHide answer

    B: non-contact force

    Objects do not need to touch.

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