Dimensional Analysis & Metric Calculations Flashcards

Which of the following correctly applies the chain rule of dimensional analysis to convert 60 miles per hour to km/h? (1 mile = 1.609 km)

Answer: 60 × 1.609 = 96.54 km/h

60 mi/h × 1.609 km/mi = 96.54 km/h; multiply by the conversion factor to go from smaller to larger.

A room has dimensions 4 m × 5 m × 3 m. What is its volume in cubic metres?

Answer: 60 m³

Volume = length × width × height = 4 × 5 × 3 = 60 m³.

The density of water is 1,000 kg/m³. What is this in g/cm³?

Answer: 1 g/cm³

1,000 kg/m³ = 1 g/cm³, since 1 kg = 1,000 g and 1 m³ = 1,000,000 cm³, giving 1,000,000/1,000,000 = 1 g/cm³.

Convert 25°C to Kelvin:

Answer: 298 K

K = °C + 273.15, so 25 + 273.15 ≈ 298 K (rounded to 298 K).

Power is defined as energy per unit time. If 600 J of work is done in 0.5 minutes, what is the power in watts?

Answer: 1,200 W

Power = 600 J ÷ (0.5 × 60 s) = 600 ÷ 30 = 20 W.

A 50 kg object is accelerated at 2 m/s². What force is applied in newtons?

Answer: 100 N

F = ma = 50 kg × 2 m/s² = 100 N.