物理量的估算：練習題

What is the order of magnitude for the diameter of a typical atom?

A school physics laboratory has approximate dimensions of \(10 \, \text{m} \times 8 \, \text{m} \times 3 \, \text{m}\). Which of the following is the most reasonable estimate for the mass of air inside the laboratory?

A high-speed train travels at a constant velocity of \( 300 \text{ km h}^{-1} \). The engine provides a constant driving force to overcome resistive forces, which are estimated to be approximately \( 40 \text{ kN} \).

Estimate the order of magnitude of the total energy, in joules, expended by the train's engine during a continuous \( 4 \)-hour journey.

Which of the following is the most reasonable estimate for the mass of a typical adult human, expressed to the nearest order of magnitude?

Estimate the number of heartbeats of a healthy resting adult in a single day to the nearest order of magnitude.

Estimate the order of magnitude for the total volume of air in a standard secondary school classroom, expressed in \( \text{m}^3 \).

Estimate the total kinetic energy, in joules, of a \( 1200 \text{ kg} \) car travelling at a typical urban speed limit of \( 50 \text{ km h}^{-1} \).

Estimate the average power developed by a \( 75 \text{ kg} \) person who climbs a vertical flight of stairs of height \( 4.0 \text{ m} \) in a time of \( 5.0 \text{ s} \).

(a) Estimate the mass of air in a classroom with dimensions \( 10 \text{ m} \times 8 \text{ m} \times 3 \text{ m} \). Assume the density of air is approximately \( 1.2 \text{ kg m}^{-3} \).
(b) Estimate the weight of this air, taking the acceleration due to gravity \( g = 9.8 \text{ m s}^{-2} \).
(c) A typical small passenger car has a mass of \( 1200 \text{ kg} \). Calculate the ratio of the weight of the air in the room to the weight of the car. State whether the air in the room is heavier than the car.

A large hydroelectric power station reservoir has an approximate surface area of \( 5.0 \text{ km}^2 \) and an average depth of \( 40 \text{ m} \).

(a) Estimate the order of magnitude of the total mass of water contained in the reservoir. (Density of water \( \approx 1000 \text{ kg m}^{-3} \))
(b) The water falls through a vertical height of \( 120 \text{ m} \) to reach the turbines. Estimate the total gravitational potential energy stored in the reservoir relative to the turbine level. Give your answer in terajoules (\( \text{TJ} \)).
(c) If the power station operates at an efficiency of \( 85\% \) and outputs a constant power of \( 400 \text{ MW} \), estimate the order of magnitude of the time, in days, that the reservoir could sustain this output before running empty. Assume no water enters the reservoir during this period.