Introduction: The Nature of Science and Physics

In terms of radiation dose, what is the major difference between medical diagnostic uses of radiation and medical therapeutic uses?

A car is traveling at a speed of  $\mathbf{33}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s}$. (a) What is its speed in kilometres per hour? (b) Is it exceeding the $\mathbf{90}\mathbf{ }\mathbf{km}\mathbf{/}\mathbf{h}$ speed limit?

How does a model differ from a theory?

A system does 1.80×10⁸ J of work while 7.50×10⁸ J of heat transfer occurs to the environment. What is the change in internal energy of the system assuming no other changes (such as in temperature or by the addition of fuel)?

American football is played on a $\mathbf{100}\mathbf{-}\mathbf{yd}$ long field, excluding the end zones. How long is the field in meters? (Assume that  $\mathbf{1}\mathbf{ }\mathbf{meter}$ equals $\mathbf{3}\mathbf{.}\mathbf{281}\mathbf{ }\mathbf{feet}$ .)

If a galaxy is \({\rm{500 Mly}}\) away from us, how fast do we expect it to be moving and in what direction?

Soccer fields vary in size. A large soccer field is 115 m  long and 85 m  wide. What are its dimensions in feet and inches? (Assume that  1 meter  equals  3.281 feets).

What is the height in meters of a person who is \({\bf{6}}{\rm{ }}{\bf{ft}}{\rm{ }}{\bf{1}}.{\bf{0}}{\rm{ }}{\bf{in}}\) tall? (Assume that \({\bf{1}}{\rm{ }}{\bf{meter}}\) equals \({\bf{39}}.{\bf{37}}{\rm{ }}{\bf{in}}\).)

Identify the type of energy transferred to your body in each of the following as either internal energy, heat transfer, or doing work: (a) basking in sunlight; (b) eating food; (c) riding an elevator to a higher floor

Mount Everest, at \({\bf{29}},{\bf{028}}\)feet, is the tallest mountain on the Earth. What is its height in kilometres? (Assume that \({\bf{1}}{\rm{ }}{\bf{kilometre}}\) equals \({\bf{3}},{\bf{281}}{\rm{ }}{\bf{feet}}\).)

(a) A woman climbing the Washington Monument metabolizes \[6.00 \times {10^2}{\rm{ }}kJ\] of food energy. If her efficiency is \({\bf{18}}{\bf{.0\% }}\) , how much heat transfer occurs to the environment to keep her temperature constant? (b) Discuss the amount of heat transfer found in (a). Is it consistent with the fact that you quickly warm up when exercising? 

Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of\({\bf{4}}.{\bf{0}}{\rm{ }}{{{\rm{cm}}} \mathord{\left/ {\vphantom {{{\rm{cm}}} {{\rm{year}}}}} \right. \\} {{\rm{year}}}}\). (a) What distance does it move in \({\rm{1 s}}\) at this speed? (b) What is its speed in kilometers per million years?

An infant’s pulse rate is measured to be $\mathbf{130}\mathbf{\pm }\mathbf{5}\mathbf{ }\mathbf{beats}\mathbf{/}\mathbf{min}$. What is the percent uncertainty in this measurement?

What is the relationship between the accuracy and uncertainty of measurement?

What is the relationship between the accuracy and uncertainty of measurement?

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m  . What is its percent uncertainty?

Prescriptions for vision correction are given in units called dioptres (D). Determine the meaning of that unit. Obtain information (perhaps by calling an optometrist or performing an internet search) on the minimum uncertainty with which corrections in dioptres are determined and the accuracy with which corrective lenses can be produced. Discuss the sources of uncertainties in both the prescription and accuracy in the manufacture of lenses.

Find the components of \({v_{tot}}\) along a set of perpendicular axes rotated \(30^\circ \) counterclockwise relative to those in Figure 3.55.

Figure: The two velocities \({{\rm{v}}_{\rm{A}}}\) and \({{\rm{v}}_{\rm{B}}}\) add to give a total \({{\rm{v}}_{{\rm{tot}}}}\)

a) A car speedometer has a \(5.0\% \)uncertainty. What is the range of possible speeds when it reads \(90{\rm{ }}{{km} \mathord{\left/{\vphantom {{km} {hr}}} \right. \\} {hr}}\)? (b) Convert this range to miles per hour. \(\left( {1{\rm{ }}km = 0.6214{\rm{ }}mi} \right)\)

A real process may be nearly adiabatic if it occurs over a very short time. How does the short time span help the process to be adiabatic?

An infant’s pulse rate is measured to be $\mathbf{130}\mathbf{ }\mathbf{\pm }\mathbf{5}\mathbf{ }\mathbf{beats}\mathbf{/}\mathbf{min}$. What is the percent uncertainty in this measurement?

(a) Suppose that a person has an average heart rate of  $\mathbf{72}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{beats}\mathbf{/}\mathbf{min}$ beats/ min. How many beats does he or she have in 2.0 y ? (b) In  2.00 y ?  (c) In 2.000 y ?

What is the net work output of a heat engine that follows path ABDA in the figure above, with a straight line from B to D? Why is the work output less than for path ABCDA? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.

State how many significant figures are proper in the results of the following calculations: (a) $\left(106.7\right)\left(98.2\right)\mathbf{/}\left(46.210\right)\left(1.01\right)$ (b) ${\left(18.7\right)}^{\mathbf{2}}$ (c) $\left(1.60\times {10}^{-19}\right)\left(3712\right)$.

What are the advantages and disadvantages of connecting batteries in series? In parallel?

Question: (a) Calculate the number of photoelectrons per second ejected from a \(1.00\,{\rm{m}}{{\rm{m}}^{\rm{2}}}\) area of sodium metal by \(500\,{\rm{nm EM}}\) radiation having an intensity of \(1.30\,{\rm{kW/}}{{\rm{m}}^{\rm{2}}}\) (the intensity of sunlight above the Earth’s atmosphere). (b) Given that the binding energy is\(2.28\,{\rm{eV}}\), what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?

(a) How many significant figures are in the numbers 99 and  100 ? (b) If the uncertainty in each number is  1 , what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties? 

(a) If your speedometer has an uncertainty of 2.0 km/h  at a speed of  90 km/h, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads  60  km/h , what is the range of speeds you could be going?

(a) What is the final speed of an electron accelerated from rest through a voltage of \(25.0{\rm{ }}MV\) by a negatively charged Van de Graaff terminal? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

(a) A person’s blood pressure is measured to be $\mathbf{120}\mathbf{\pm }\mathbf{2}\mathbf{ }\mathbf{mm}\mathbf{ }\mathbf{Hg}$. What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of  80  mm  Hg?

A person measures his or her heart rate by counting the number of beats in 30 s . If  $\mathbf{40}\mathbf{\pm }\mathbf{1}\mathbf{ }\mathbf{beats}$ are counted in $\mathbf{30}\mathbf{.}\mathbf{0}\mathbf{\pm }\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{s}$, what is the heart rate and its uncertainty in beats per minute?

Does the second law of thermodynamics alter the conservation of energy principle?

What is the area of a circle 3.102 cm in diameter?

Explain why heat pumps do not work as well in very cold climates as they do in milder ones. Is the same true of refrigerators?

(a)-What is the efficiency of a cyclical heat engine in which 75.0 kJ of heat transfer occurs to the environment for every 95.0 kJ of Heat transfer into the engine (b) How much work does it produce for 100.0 kJ of heat transfer into the engine?

An automobile starter motor has an equivalent resistance of \({\rm{0}}{\rm{.0500 \Omega }}\) and is supplied by a \({\rm{12}}{\rm{.0}}\;{\rm{V}}\) battery with a \({\rm{0}}{\rm{.0100}}\;{\rm{\Omega }}\) internal resistance.

(a) What is the current to the motor?

(b) What voltage is applied to it?

(c) What power is supplied to the motor?

(d) Repeat these calculations for when the battery connections are corroded and add 0.0900 Ω to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)

A marathon runner completes a 42.188 km  course in 20h, 30 min  and 12 s . There is an uncertainty of 25 m  in the distance travelled and uncertainty of  1 s  in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

The wavelength of the four Balmer series lines for hydrogen are found to be 410.3, 434.2, 486.3, and 656.5 nm. What average percentage difference is found between these wavelength numbers and those predicted by\[\frac{{\bf{1}}}{{\bf{\lambda }}}{\bf{ = R}}\left( {\frac{{\bf{1}}}{{{\bf{n}}_{\bf{f}}^{\bf{2}}}}{\bf{ - }}\frac{{\bf{1}}}{{{\bf{n}}_{\bf{i}}^{\bf{2}}}}} \right){\bf{?}}\]It is amazing how well a simple formula (disconnected originally from theory) could duplicate this phenomenon. 

The sides of a small rectangular box are measured to be \({\bf{1}}.{\bf{80}} \pm {\bf{0}}.{\bf{01}}{\rm{ }}{\bf{cm}}\), \({\bf{2}}.{\bf{05}} \pm {\bf{0}}.{\bf{02}}{\rm{ }}{\bf{cm}}\), and \({\bf{3}}.{\bf{1}} \pm {\bf{0}}.{\bf{1}}{\rm{ }}{\bf{cm}}\) long. Calculate its volume and uncertainty in cubic centimeters.

What do the quark compositions and other quantum numbers imply about the relationships between the \[{{\rm{\Delta }}^{\rm{ + }}}\]and the proton? The \[{{\rm{\Delta }}^{\rm{0}}}\]and the neutron?

Find the volume of the given solid. Bounded by the planes \(z = x,y = x,z = 0,x + y = 2\) 

A car engine moves a piston with a circular cross-section of \({\bf{7}}.{\bf{500}}{\rm{ }} \pm {\rm{ }}{\bf{0}}.{\bf{002}}{\rm{ }}{\bf{cm}}\) diameter a distance of \({\bf{3}}.{\bf{250}}{\rm{ }} \pm {\rm{ }}{\bf{0}}.{\bf{001}}{\rm{ }}{\bf{cm}}\) to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters. (b) Find the uncertainty in this volume.

A generation is about one-third of a lifetime. Approximately how many generations have passed since the year \({\bf{0}}\) AD?

How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10^-22s

Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10^-27 kg and the mass of a bacterium is on the order of 10^-15 kg.) 

a) What energy photons can pump chromium atoms in a ruby laser from the ground state to its second and third excited states? 

(b) What are the wavelengths of these photons? Verify that they are in the visible part of the spectrum.

Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to Earth. It is reasonable to assume that the echo time equals the time necessary for the radio wave to travel from the Earth to the Moon and back (that is, neglecting any time delays in the electronic equipment). Calculate the distance from Earth to the Moon given that the echo time was 2.56 s and that radio waves travel at the speed of light (\({\bf{3 \times 1}}{{\bf{0}}^{\bf{8}}}\;{\bf{m/s}}\)).

(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?

(a) Write the complete α decay equation for ²²⁶Ra . (b) Find the energy released in the decay.

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?