State the two components that together make up any physical quantity.
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a numerical magnitude / value; a unit
Physical Quantities
Explain why writing a measurement as just “12” is not a valid expression of a physical quantity.
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a physical quantity requires both a magnitude and a unit; without a unit, the value has no defined physical meaning / size cannot be compared to a standard
Estimate, to the nearest order of magnitude, the mass of an adult human in kilograms.
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approximately 70 kg (accept 50–100 kg)
Estimate the volume of water, in cubic metres, contained in a full bathtub. State any assumptions you make.
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assume bathtub dimensions of approximately 1.5 m × 0.6 m × 0.4 m; volume ≈ 0.36 m³; accept any value between 0.1 m³ and 0.5 m³ with a stated assumption
A student claims that the mass of a small apple is about 1 kg. Explain whether this estimate is reasonable.
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the estimate is not reasonable; a typical apple has a mass of approximately 0.1 kg, so the student’s value is roughly ten times too large
Estimate the mass of water in a swimming pool of length 25 m, width 10 m, and average depth 1.5 m. Take the density of water as 1000 kg m⁻³.
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Finding the volume $$V=25\times 10\times 1.5$$ $$V=375{\text{ m}}^{3}$$ Finding the mass $$m=\rho V=1000\times 375$$ $$m=3.75\times {10}^{5}\text{ kg}$$ The mass of water in the pool is approximately 3.75 × 10⁵ kg (2 s.f.).
Discuss why estimation skills are important in physics, and outline the strategy you would use to estimate the number of breaths an average person takes in one day.
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estimation allows physicists to check whether a calculated answer is physically reasonable; it identifies large arithmetic or unit errors quickly; it is essential when exact data are unavailable; strategy — assume a typical breathing rate of approximately 15 breaths per minute; convert one day to 24 × 60 = 1440 minutes; multiply rate by time to give 15 × 1440 ≈ 2.2 × 10⁴ breaths per day; state assumption that breathing rate is constant over the day