Exam 7: Physics

Passage In mass spectrometry, a sample's molecules are ionized in a vacuum and then exposed to a uniform electric field created by a high-voltage plate in the acceleration chamber.  The electric field accelerates the ions until they arrive at the next section of the device, designated as the separation chamber.  In this section, the drifting ions are sorted by their mass-to-charge ratio (m/q).The separation chamber in a time-of-flight mass spectrometer (TOF-MS) is linear and has no electric or magnetic fields.  The ions travel at a constant velocity through the chamber until they reach the detector.  The time it takes for an ion to reach the detector depends on its m/q ratio. Figure 1  Time-of-flight mass spectrometerA magnetic sector mass spectrometer (MS-MS) has a curved separation chamber where a magnetic field is generated.  The magnetic field exerts a centripetal force on drifting ions, bending their trajectories into curved paths.  The radius of the curvature depends on the ion's m/q. Figure 2  Magnetic sector mass spectrometerThe centripetal force (F) acting on a particle can be determined from its mass (m) and velocity (v) and the radius (r) of the curved path:F = mv²/rEquation 1 -Which expression gives the ion's radius of curvature in a magnetic field EM_/_ for an ion with a mass of m, charge of q, and velocity of v?

A tennis ball is thrown and bounced off a wall twice.  The displacement of the tennis ball over time is shown. Which point on the plot corresponds to the greatest instantaneous velocity?

Passage Ultrasound is a technique that uses the propagation properties of high-frequency sound waves to construct images of internal organs or to measure blood flow velocity.  The shape and position of internal organs are resolved by measuring the return time of reflected ultrasound waves.  Similarly, blood flow velocity is resolved by measuring the Doppler shift of reflected ultrasound waves.  An ultrasound device consists of an array of piezoelectric crystals and an acoustic lens.  The piezoelectric crystals generate sound when an alternating voltage is applied, and the acoustic lens increases the transmission efficiency from the device to the body by reducing sound reflection at the skin.Ultrasound is performed using frequencies in the range of 2-15 MHz.  The lower ultrasound frequencies are used for deep abdomen and obstetric/gynecological imaging due to their greater penetrating ability.  The higher ultrasound frequencies have less penetrating ability but provide higher resolution, and therefore are used for blood flow measurements and the imaging of more superficial structures.  Detailed ultrasound penetration data is shown in Figure 1. Figure 1  Penetration in soft tissue for three different ultrasound frequenciesSound waves propagate through soft tissue at an average speed of 1,500 m/s and through blood at 1,570 m/s. -Which of the following is NOT a property of sound?

Passage Ultrasound is a technique that uses the propagation properties of high-frequency sound waves to construct images of internal organs or to measure blood flow velocity.  The shape and position of internal organs are resolved by measuring the return time of reflected ultrasound waves.  Similarly, blood flow velocity is resolved by measuring the Doppler shift of reflected ultrasound waves.  An ultrasound device consists of an array of piezoelectric crystals and an acoustic lens.  The piezoelectric crystals generate sound when an alternating voltage is applied, and the acoustic lens increases the transmission efficiency from the device to the body by reducing sound reflection at the skin.Ultrasound is performed using frequencies in the range of 2-15 MHz.  The lower ultrasound frequencies are used for deep abdomen and obstetric/gynecological imaging due to their greater penetrating ability.  The higher ultrasound frequencies have less penetrating ability but provide higher resolution, and therefore are used for blood flow measurements and the imaging of more superficial structures.  Detailed ultrasound penetration data is shown in Figure 1. Figure 1  Penetration in soft tissue for three different ultrasound frequenciesSound waves propagate through soft tissue at an average speed of 1,500 m/s and through blood at 1,570 m/s. -Laser Doppler flowmetry uses an infrared laser to measure blood flow velocity.  Compared to ultrasound, the observed frequency shift using this technique is:

Passage Positron emission tomography (PET) is a medical imaging technique used for the detection of tumors and the evaluation of neurological functions.  A radiopharmaceutical (radioactive tracer) injected into a patient undergoes positive beta decay and emits a positron.  The positron undergoes an annihilation event with a nearby electron (<1 mm away), which emits a pair of 511 keV gamma ray photons traveling in opposite directions.  The gamma rays are detected by a ring of scintillation detectors surrounding the patient, as shown in Figure 1.  The difference in detection time between the two gamma rays from the same annihilation event is used to determine its location.  An image is constructed from data collected from multiple emission events. Figure 1  Basic setup and process of positron emission tomographyScintillation, the emission of detectable light when excited electrons return to their ground state, occurs in crystals within the detectors due to the transfer of energy from the high energy gamma rays.  The wavelength of the emitted light depends exclusively on the type of scintillation material used (Table 1).Table 1  Common PET Scintillating Crystal Materials The electrons in the scintillating crystals are excited through Compton scattering, a process in which a gamma ray photon acts as a particle, and transfers energy to an electron via collision.  Subsequently, the photon scatters (travels in a new direction) and its wavelength changes.  The percent change in the wavelength of the photon due to the energy loss is Equation 1where θ is the angle between the scattered photon and electron.  Equation 1 is represented in Figure 2. Figure 2  Percent change in photon wavelength due to Compton scattering -Which scintillation crystal emits light with a wavelength outside the visible spectrum?

Passage For a person with perfect vision, light from an object is properly refracted by the eye lens to converge on a single point at the retina, forming a clear image of the object.  Vision defects result from eye shape abnormalities or errors in the refractive power of the eye lens.  Myopia (nearsightedness) occurs when light from a distant object is incorrectly focused in front of the retina.  Hyperopia (farsightedness) occurs when light rays from a nearby object are focused beyond the retina.Many optical techniques are available to measure the refractive error of an individual to determine the necessary correction.  Photorefraction is a photographic technique often used with young children because it does not require the individual to be still for a lengthy duration.  When the patient is looking at the camera, a flash photograph is taken of the eye to determine the amount of light that is reflected off the retina and captured by the camera lens.In healthy eyes, all the light from the flash that enters the eye is reflected off the retina and returns back to the camera's light source.  Because the camera lens does not receive this light, the pupil is completely dark in the resulting image.  A myopic eye cannot properly focus the light at the retina.  Due to the geometry of the eye and its lens, some of the light is reflected to the top portion of the camera lens.  The camera captures an image of a pupil with a crescent of light at the top.  In a hyperopic eye, the crescent appears at the bottom of the pupil.  Ray diagrams for photorefraction are shown in Figure 1. Figure 1  Paths of light in photorefraction for different eyes:  (A) Healthy, (B) Myopic, and (C) Hyperopic. HC. Howland, "Optics of photorefraction: orthogonal and isotropic methods." ©1983 Optical Society of America. -An object is located at a distance of 2 focal lengths from the center of a converging lens.  What is the ratio of the height of the image to the height of the object?

When the side of an open tank filled with water is punctured, water flows out according to Bernoulli's equation: P1+12ρv12+ρgy1=P2+12ρv22+ρgy2where P is the external pressure, ρ is the density of water (10³ kg/m³), v is the flow velocity, g is gravitational acceleration (10 m/s²), and y is the elevation.  If water flows out at a rate of 6 m/s, what is the height of the water above the hole?

Passage For a person with perfect vision, light from an object is properly refracted by the eye lens to converge on a single point at the retina, forming a clear image of the object.  Vision defects result from eye shape abnormalities or errors in the refractive power of the eye lens.  Myopia (nearsightedness) occurs when light from a distant object is incorrectly focused in front of the retina.  Hyperopia (farsightedness) occurs when light rays from a nearby object are focused beyond the retina.Many optical techniques are available to measure the refractive error of an individual to determine the necessary correction.  Photorefraction is a photographic technique often used with young children because it does not require the individual to be still for a lengthy duration.  When the patient is looking at the camera, a flash photograph is taken of the eye to determine the amount of light that is reflected off the retina and captured by the camera lens.In healthy eyes, all the light from the flash that enters the eye is reflected off the retina and returns back to the camera's light source.  Because the camera lens does not receive this light, the pupil is completely dark in the resulting image.  A myopic eye cannot properly focus the light at the retina.  Due to the geometry of the eye and its lens, some of the light is reflected to the top portion of the camera lens.  The camera captures an image of a pupil with a crescent of light at the top.  In a hyperopic eye, the crescent appears at the bottom of the pupil.  Ray diagrams for photorefraction are shown in Figure 1. Figure 1  Paths of light in photorefraction for different eyes:  (A) Healthy, (B) Myopic, and (C) Hyperopic. HC. Howland, "Optics of photorefraction: orthogonal and isotropic methods." ©1983 Optical Society of America. -The image of an object projected onto a fixed screen through a lens using red light is clear and focused.  Using the same set-up, the image is slightly unfocused when violet light is used.  This is because violet light:

Passage When present in the bloodstream above a threshold partial pressure, a general anesthetic blocks the sensation of pain, induces a state of unconsciousness, and causes muscle paralysis.  Many anesthetic agents are administered in their gaseous phase and are absorbed into the bloodstream through the lungs.  The rate of diffusion V_gas of an anesthetic across the alveolar membrane with a surface area A and a thickness T is described by the Fick law of diffusion: Vgas=DAΔPTEquation 1where D is the diffusion coefficient specific for the gas and ΔP is the partial pressure difference across the membrane.An inhaled anesthetic is described by its blood-gas partition coefficient, the ratio of the anesthetic's concentration in the blood to its concentration in the lungs when the partial pressures are equal.  The concentration C of an anesthetic gas dissolved in blood is described by the Henry law of solubility: C=kHPgasEquation 2where k_H is the solubility constant specific for the gas and P_gas is the partial pressure of the gas.Due to the paralytic effects of general anesthetics, mechanical ventilators are usually necessary to assist a patient's breathing during surgery.  Positive-pressure ventilators are noninvasive and use external pumps to induce inspiration by forcing air into the lungs through a ventilation mask.  Despite the paralytic effects of general anesthesia, patients are often capable of expiration without the active aid of a mechanical ventilator. -Many inhalational anesthetics are thought to increase surface tension effects in the alveoli.  Water with greater surface tension:

Passage The humerus bone in the upper arm and the radius bone in the lower arm can be modeled as a lever with the elbow joint as the pivot point.  Movement about the elbow results from a combination of internal and external forces acting on these bones.  The primary internal force is generated from contractions of skeletal muscles; a 1-cm² cross-sectional area of skeletal muscle can generate a maximum of 7 × 10⁶ dynes of force (1 dyn = 1 g⋅cm/s²).  Friction between the humerus and the radius at the elbow is another internal force that can affect arm movements.  As people age, cartilage degeneration decreases the lubrication between bones, which increases the coefficients of static and kinetic friction.The contraction of the biceps, a skeletal muscle in the upper arm, exerts a pulling force on the radius in the lower arm.  If the torque generated by this muscle exceeds that of any opposing internal and external forces, the arm curls about the elbow.  This specific type of movement is known as a concentric muscle contraction.The following experiments were performed with a 30-year-old male subject.  Electrodes were placed around the subject's biceps and attached to an electromyograph, a device that measures the electrical activity of skeletal muscle contractions.  The estimated weight of the subject's lower arm is 45 N, and the subject's lower arm segments to the elbow are shown in Table 1.Table 1  Lower Arm Segment Lengths  Experiment 1The subject kept his entire arm stationary and in a fixed position while holding balls of varying masses.  The upper arm was perpendicular to the ground, and the lower arm was parallel to the ground (Figure 1). Figure 1  The fixed position of the arm during Experiment 1Experiment 2The subject kept his upper arm stationary and perpendicular to the ground while lifting and lowering balls of varying masses. Adapted from N. Ozkaya, Fundamentals of Biomechanics. (C) 2016 Springer. -Suppose the subject is holding a 4-kg ball during Experiment 1.  Ignoring friction, what is the force exerted by the biceps?  (Note: Use g = 10 m/s².)

Passage The electric capacitance of biological tissues serves as the basis for numerous medical technologies.  For example, dielectric spectroscopy glucose reading (DSGR) is a noninvasive diagnostic technique that uses the electric capacitance of blood to estimate blood glucose levels.A DSGR device records the electric current that results from applying a voltage source to the skin and underlying blood vessels.  DSGR can be modeled by the circuit shown in Figure 1, in which V represents the applied potential, C_B represents the capacitance of the blood, and R_E, R_D, and R_B represent the electrical resistances of the epidermis, the dermis, and the blood, respectively. Figure 1  DSGR circuit model including skin and superficial blood vesselThe capacitance of charged blood may be explained by red blood cell membranes acting as physical barriers that separate electrons introduced into the blood from positively charged ions in the red blood cell cytoplasm.  The dielectric constant k of red blood cell membranes varies with glucose concentration (Figure 2) because glucose uptake by red blood cells alters the activity of membrane-bound proteins that regulate the flow of ions into and out of the cell. Figure 2  Blood dielectric constant vs blood glucose concentrationDSGR readings vary with blood glucose concentration because the time needed to fully charge the blood is related to total blood capacitance.  However, interpreting DSGR readings may be complicated by changes in biological variables other than blood capacitance.  For example, the resistivity of blood varies in accordance with osmolarity such that changes in diet or hydration status influence the current measured by DSGR devices. Livshits, L. et al.  Dielectric response of biconcave erythrocyte membranes to D- and L-glucose.  J. Phys. D: Appl. Phys. 40 (2007), 15-19. -When dietary sodium intake increases, the electric current measured by a DSGR device also increases.  Current increases because:

Passage Cable theory is a mathematical model used to calculate currents and voltages along and across axon membranes.  The model treats small sections of the membrane as the resistor-capacitor circuit shown in Figure 1.  An electric neuronal signal enters the circuit through the input node.  A portion of the signal remains inside the axon and continues to the next section of membrane via Output 1, and the rest of the signal exits to the extracellular fluid via Output 2. Figure 1  Circuit unit used to model axon membranesResearchers studied cable theory by recreating the circuit in Figure 1 using a 2 μF capacitor for C_M, a 200 Ω resistor for R_M, and a 1,000 Ω resistor for R_L.  The researchers sent an electrical signal through the input and discovered that the capacitor acted as a resistor whose resistance varied with the signal's frequency, as shown in Figure 2. Figure 2  Capacitor equivalent resistance vs. signal frequency for C_M Adapted from Tuckwell H, Introduction to Theoretical Neurobiology 2006 SIAM. -A voltmeter is placed across R_L.  If a charge of 0.1 C flows into the input node every 2 s, what will be the reading on the voltmeter?

Passage Laparoscopy is a minimally invasive surgical procedure where small surgical instruments are inserted into the body through cannulas (hollow tubes 0.5 to 1.0 cm in diameter).  A cannula is inserted into the skin while sleeved around a trocar (Figure 1).  The skin incision can be made directly with a sharp-tipped trocar as it is being inserted with the cannula.  If a blunt-tipped trocar is used, the incision is made beforehand with a surgical blade.  After insertion, the trocar is removed, leaving the cannula as an access point for laparoscopic procedures. Figure 1  Cannula, trocar, and two types of tipsLow-friction trocars increase surgical precision and reduce postoperative scarring.  Friction between the skin and trocar tip is tested with synthetic skin and a stationary ramp whose surface is made of the same material as the trocar.  For testing, the synthetic skin is pressed against the ramp's surface by a load, weighted to allow the skin to slide down at a constant speed (Figure 2).  In this setup, the weight of the synthetic skin layer is negligible. Figure 2  Experimental setup to test the friction between trocar and skin Adapted from W. Firme-Gustavo et al., (C)2015 Society of Laparoendoscopic Surgeons. -After the load leaves the ramp, it slides on a horizontal table with a coefficient of kinetic friction μ_k of 0.1 and a coefficient of static friction μ_s of 0.3.  If the direction of the load's velocity is positive, what is the acceleration of the load?  (Note:  Use g = 10 m/s².)

Passage During deep underwater dives, scuba divers must overcome the external ambient pressure in order to expand their chests to inhale.  To assist underwater breathing, air from scuba tanks is administered at high pressures to keep divers' lungs inflated.  Scuba tanks are often filled with a mixture of N₂ and O₂ gas.  Due to the increased pressure of the gases in the lungs, a greater amount of the gases are dissolved into the bloodstream during underwater dives.  At a body temperature of 37°C, the solubility of N₂ gas in blood is 6.0 × 10⁻³ mol/L⋅atm and the solubility of O₂ gas is 1.3 × 10⁻² mol/L⋅atm.If a diver ascends too quickly after an extended dive, there is an increased risk of vascular bubble formation.  Due to the decrease in ambient pressure, the excess gas dissolved in the blood may come out of solution as gas bubbles and cause a number of adverse effects.  This condition is known as decompression sickness, or "the bends."  To avoid this problem, scuba divers limit their rate of ascension to allow the excess gas dissolved in their blood to be safely removed through respiration.  Because gas bubbles are good reflectors of sound, these bubbles can be detected using Doppler ultrasonic flowmetry after the diver has surfaced. Adapted from M. Spencer, Journal of Applied Physiology. ©1976 American Physiology Society. -An underwater diver is able to shine a laser onto the underwater portion of a distant boat.  However, the diver is unable to shine the laser onto the portion of the boat above the surface.  Which of the following best explains this phenomenon?

Passage In the event of end-stage heart failure, a left ventricular assist device (LVAD) can be used as a heart transplant bridge to keep a patient alive.  The first iterations of LVADs were pulsatile and mimicked the physiological pumping action of the heart (Figure 1). Figure 1  A pulsatile-flow LVAD schematicA pulsatile-flow LVAD assists ventricular systole by mechanically pumping blood from a weakened left ventricle into the aorta through a pair of one-way valves.  The pressure differential ΔP generated by the pump is related to cardiac output (CO) and vascular resistance (VR):ΔP = CO × VREquation 1The efficiency and performance of the heart (or LVAD) can be determined by the patient's cardiac pressure-volume (PV) loop.  A cardiac PV loop plots the pressure and volume of the blood in the left ventricle throughout a single cardiac cycle (Figure 2). Figure 2  Cardiac PV Loop of a pulsatile-flow LVADBlood pressure is often represented by only two numbers:  arterial systolic and diastolic pressures.  A more detailed representation of blood pressures is shown in a blood pressure profile, which graphs the blood pressure throughout the length of the different vessel groups (Figure 3).  Multiple pressure fluctuations are shown within a vessel because the pressure is traced across multiple cardiac cycles. Figure 3  Blood pressure profile of the different vessels -The mean arterial pressure (MAP) is used to approximate the average blood pressure of an individual's arteries:MAP = DP + (SP - DP)/3where DP is diastolic pressure and SP is systolic pressure.  What is the MAP for the blood pressure profile shown in Figure 3?

A block with mass M slides down an incline of angle θ at constant velocity v. Which of the following expressions is equal to the magnitude of frictional force between the block and the incline? (Note:  The acceleration of gravity g = 10 m/s².)

Passage Sound waves propagate through many conducting structures in the ear before they are transduced into neuronal signals.  When sound waves reach the fluid-filled cochlea, they are detected by hair cells lining the basilar membrane.  The cochlear spiral can be modeled as a resonator system because each section of the basilar membrane is sensitive to a specific frequency (Figure 1). Figure 1  Amplitude pattern of the basilar membrane for different frequenciesPresbycusis (age-related hearing loss) results from a combination of factors that lessens an individual's mechanical and/or neurological sensitivity to sound.  Pure tone audiometry (PTA) is used to determine an individual's ability to detect different sound frequencies and can be used to evaluate presbycusis.  A "pure" tone is characterized by a single sinusoidal waveform.  An audiogram plots the relative intensity required of a given frequency to be detected by the individual (Figure 2). Figure 2  Audiogram of an elderly patient exhibiting presbycusis -A sound wave used in PTA that causes resonance close to the apex of the basilar membrane has a relatively:

Passage The flow of blood through the human body is typically laminar, but in certain conditions, as when blood flows through the aorta during a period of heightened physical activity, the flow can become turbulent.  Blood flow can also become turbulent in abnormal cases in which the passage of blood is obstructed by constrictions within the blood vessel.  The energy generated by blood turbulence creates sound vibrations that can be heard with a stethoscope.Using the technique of laser Doppler velocimetry, researchers recorded the blood velocity v at a point in the aorta of an experimental subject at different times during aerobic exercise.  Table 1 shows the blood velocities observed over a 400 ms time interval.Table 1  Blood Velocity within the Aorta of an Experimental Subject (mean velocity v̅ = 101 cm/s) Turbulent kinetic energy (TKE) is the kinetic energy per unit mass associated with turbulence within flowing fluids and is defined as: Equation 1where σ_v is the standard deviation of the fluctuating fluid velocities at a point within the turbulent flow.Reynolds number Re is the quantity that ultimately measures whether a flow is turbulent or laminar.  Re is defined in terms of the fluid density ρ, mean velocity of the flow v̅, conduit diameter d, and dynamic viscosity η of the fluid, as given by: Equation 2In the context of blood flow, d is the diameter of the blood vessel, and blood has a fluid density of about 1,060 kg∙m⁻³ with a dynamic viscosity of about 0.003 kg∙m⁻¹∙s⁻¹. -A fluid is stirred until it becomes turbulent.  After the stirring stops, the fluid gradually returns to its original static state.  The turbulent flow does not continue indefinitely because:

Passage Cable theory is a mathematical model used to calculate currents and voltages along and across axon membranes.  The model treats small sections of the membrane as the resistor-capacitor circuit shown in Figure 1.  An electric neuronal signal enters the circuit through the input node.  A portion of the signal remains inside the axon and continues to the next section of membrane via Output 1, and the rest of the signal exits to the extracellular fluid via Output 2. Figure 1  Circuit unit used to model axon membranesResearchers studied cable theory by recreating the circuit in Figure 1 using a 2 μF capacitor for C_M, a 200 Ω resistor for R_M, and a 1,000 Ω resistor for R_L.  The researchers sent an electrical signal through the input and discovered that the capacitor acted as a resistor whose resistance varied with the signal's frequency, as shown in Figure 2. Figure 2  Capacitor equivalent resistance vs. signal frequency for C_M Adapted from Tuckwell H, Introduction to Theoretical Neurobiology 2006 SIAM. - An ammeter is added to the circuit as shown.  The voltage across the capacitor is kept constant while the frequency is increased from 200 Hz to 400 Hz.  Through this change, the value shown by the ammeter:

An observer perceives a sound to be lower in frequency when the sound source is moving away from the observer.  This shift in the frequency of the perceived sound occurs because: