Physical quantities：練習題

A student uses a micrometer to measure the diameter of a thin wire. The readings obtained are \( 0.22 \text{ mm} \), \( 0.21 \text{ mm} \), \( 0.22 \text{ mm} \), and \( 0.23 \text{ mm} \). The manufacturer states the diameter is \( 0.25 \pm 0.01 \text{ mm} \).
Which statement best describes the student's measurements?

A student estimates the power output of a human heart. If the heart pumps approximately \(70\text{ ml}\) of blood per beat, beats \(70\text{ times per minute}\), and does work against an average blood pressure of \(13\text{ kPa}\), what is the best estimate for the power in S.I. base units?

A student is asked to estimate the total number of protons in a standard \(330\text{ ml}\) can of water. Which of the following is the most reasonable order of magnitude for this estimate? (Assume the density of water is \(1000\text{ kg m}^{-3}\) and its molar mass is approximately \(18\text{ g mol}^{-1}\))

A physical quantity \( X \) is calculated from the expression \( X = \frac{a^3 b}{c^2} \). If the percentage uncertainties in \( a \), \( b \), and \( c \) are \( 1\% \), \( 2\% \), and \( 3\% \) respectively, what is the percentage uncertainty in \( X \)?

The power \( P \) dissipated in a resistor is given by the formula \( P = \frac{V^2}{R} \). If the percentage uncertainty in the potential difference \( V \) is \( 3\% \) and the percentage uncertainty in the resistance \( R \) is \( 2\% \), what is the percentage uncertainty in the power \( P \)?

Estimate the order of magnitude of the number of atoms in a solid copper cube with a side length of \(1\text{ cm}\), assuming the volume of a single atom is approximately \(10^{-30}\text{ m}^3\).

(a) The kilowatt-hour (kW h) is a unit of energy. Show that \( 1 \text{ kW h} = 3.6 \text{ MJ} \).
(b) A student is investigating the power of a motor. The motor lifts a mass of \( 500 \text{ g} \) through a vertical height of \( 1.20 \text{ m} \). The time taken for the lift is measured as \( 0.80 \pm 0.05 \text{ s} \). The height is measured to the nearest millimeter.
(i) Calculate the average power output of the motor.
(ii) Calculate the percentage uncertainty in the power value.
(iii) Identify whether the timing error or the height measurement error contributes more significantly to the uncertainty in power.