Physicists often need a quick estimate of a quantity: an approximate value found using sensible, rounded values, usually to one significant figure. Estimates check whether calculated answers are reasonable and give answers when exact data are missing. The result is often given as an order of magnitude, the nearest power of ten.Useful values to remember:
• mass of an adult: about 70 kg; height: about 1.7 m
• mass of a car: about 1000 kg; walking speed: about 1.5 m s−1
• density of water: about 1000 kg m−3; density of air: about 1.2 kg m−3
• atmospheric pressure: about 1 × 105 Pa
• diameter of an atom: about 10−10 m; wavelength of visible light: about 5 × 10−7 mWorked example 1: Estimate the mass of air in a room 5 m × 4 m × 3 m.
Volume = 5 × 4 × 3 = 60 m3
Mass = density × volume = 1.2 × 60 = 72 kg ≈ 70 kg, so the order of magnitude is 102 kg.Worked example 2: Estimate the power of a 70 kg person climbing 3 m of stairs in 4 s.P = mgh ÷ t = 70 × 9.81 × 3 ÷ 4 ≈ 500 W Always state the values you assumed, round sensibly and check that the final answer is realistic.
• mass of an adult: about 70 kg; height: about 1.7 m
• mass of a car: about 1000 kg; walking speed: about 1.5 m s−1
• density of water: about 1000 kg m−3; density of air: about 1.2 kg m−3
• atmospheric pressure: about 1 × 105 Pa
• diameter of an atom: about 10−10 m; wavelength of visible light: about 5 × 10−7 mWorked example 1: Estimate the mass of air in a room 5 m × 4 m × 3 m.
Volume = 5 × 4 × 3 = 60 m3
Mass = density × volume = 1.2 × 60 = 72 kg ≈ 70 kg, so the order of magnitude is 102 kg.Worked example 2: Estimate the power of a 70 kg person climbing 3 m of stairs in 4 s.