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Mathematical Requirements (Appendix C)

Ratios, proportionality and order of magnitude estimates

  • 3 things to know
  • All three components

Overview

Recall questions on direct and inverse proportionality and how each appears on a graph, testing a proportionality from a table of values, scaling one quantity when another changes, and making an order of magnitude estimate from rough figures.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

State the meanings of the symbols <<, ≈ and Δ as used in physics.

Key term

Interpret the statement F ∝ Δp/Δt in words.

Key term

Why can an efficiency never exceed 100%?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What does the symbol ∝ assert about two physical quantities?

    Model answer

    It asserts that one quantity is directly proportional to the other, so their ratio is constant. Doubling one therefore doubles the other.

  2. 2

    State the meanings of the symbols <<, ≈ and Δ as used in physics.

    Model answer

    The symbol << means much less than, ≈ means approximately equal to, and Δ denotes a change in the quantity that follows it. So Δp is a change of momentum.

  3. 3

    Interpret the statement F ∝ Δp/Δt in words.

    Model answer

    The resultant force acting on a body is proportional to the rate of change of its momentum. In SI units the constant of proportionality is one, so the two are equal.

  4. 4

    The gravitational force between two masses follows an inverse square law. Calculate the factor by which the force changes when their separation is trebled.

    Model answer

    The force falls by a factor of 3² = 9, so it becomes one ninth of its original value. Working back, multiplying by nine restores the original force.

  5. 5

    The kinetic energy of a body is proportional to the square of its speed. Calculate the percentage increase in kinetic energy when the speed rises by 10%.

    Model answer

    The energy rises by a factor of 1.10² = 1.21, an increase of 21%. Working back, √1.21 = 1.10, the speed ratio.

  6. 6

    A machine takes in 250 J and delivers 45 J of useful output. Calculate its efficiency.

    Model answer

    The efficiency is 45/250 = 0.18, or 18%. Working back, 0.18 × 250 = 45 J of useful output.

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