Problem: A person measures his or her heart rate by counting the number of beats in 30 s. If 40±1 beats are counted in 30±0.5 s, what is the heart rate and its uncertainty in beats per minute?
Solution:
In order to compute for the heart rate in beats per minute, we need to solve for the base. The base is
A=\frac{40\:\text{beats}}{30\:\text{sec}\:}\times \frac{60\:\text{sec}}{1\:\text{min}}=80\:\text{beats/min}Then we compute for the percent uncertainty by combining the uncertainties of the number of beats and time. That is
\begin{align*}
\text{\%\:uncertainty} & =\left( \frac{1\:\text{beat}}{40\:\text{beats}}\times 100\% \right)+ \left(\frac{0.5\:\text{s}}{30.0\:\text{s}}\times 100\% \right)\\
&=2.5\%+1.7\% \\
& =4.2\% \\
\end{align*}Based on this percent uncertainty, we compute for the tolerance
\begin{align*}
\delta _A & =\frac{\text{\%\:uncertainty}}{100\:\%}\times A \\
& = \frac{4.2 \%}{100 \%} \times 80 \ \text{beats/min} \\
& =3.4\:\text{beats/min}\\
\end{align*}Therefore, the heart rate is
\displaystyle 80\pm 3\:\text{beats/min} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)College Physics Chapter 1 Problems

College Physics 2nd Edition Solutions Table of Contents
Chapter 1: Introduction: The Nature of Science and Physics
Chapter 3: Two-Dimensional Kinematics
Chapter 4: Dynamics: Force and Newton’s Law of Motion
Chapter 5: Further Applications of Newton’s Laws: Friction, Drag, and Elasticity
Chapter 6: Uniform Circular Motion and Gravitation
Chapter 7: Work, Energy, and Energy Resources
Chapter 8: Linear Momentum and Collisions
Chapter 10: Rotational Motion and Angular Momentum
Chapter 12: Fluid Dynamics and Its Biological and Medical Applications
Chapter 13: Temperature, Kinetic Theory, and the Gas Laws
Chapter 14: Heat and Heat Transfer Methods
Chapter 16: Oscillatory Motion and Waves
Chapter 17: Physics of Hearing
Chapter 18: Electric Charge and Electric Field
Chapter 19: Electric Potential and Electric Field
Chapter 20:
Electric Current, Resistance, and Ohm’s Law
Chapter 21: Circuits and DC Instruments
Chapter 23: Electromagnetic Induction, AC Circuits, and Electrical Technologies
Chapter 24: Electromagnetic Waves
Chapter 26: Vision and Optical Instrument
Chapter 28: Special Relativity
Chapter 29: Introduction to Quantum Physics
Chapter 31: Radioactivity and Nuclear Physics
You must be logged in to post a comment.