Exam 7: Physics

The resistance of an object acting as a resistor is directly proportional to its:resistivity.cross-sectional area.length.

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. -To test the integrity of the capacitor, researchers maintained a voltage of 50 mV across the parallel portion of the circuit for several minutes.  During this time, how much energy was stored in the capacitor?

A circuit is constructed from two voltage sources (V₁ and V₂) and three resistors (R₁, R₂, and R₃). If the potential of each voltage source is 10 V and the resistance of each resistor is 5 Ω, what is the current exiting Point A?

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. -Which of the following wave characteristics would be observed to increase if the bubbles are flowing toward the Doppler ultrasonic flow meter?

Passage The effects of gravity are effectively negated if an object is in free fall.  For example, an object orbiting the Earth experiences an apparent weightlessness known as microgravity.  Because the human body evolved under the influence of Earth's gravity, human physiology undergoes several changes in microgravity environments.  Puffy face syndrome (PFS) occurs when an astronaut's extracellular fluid shifts toward upper body regions, resulting in facial bulging and leg shrinkage.  Elongation of the spinal column also occurs as intervertebral discs (spinal cartilage) decompress, making astronauts up to 6 cm taller.Researchers simulated microgravity-induced spinal elongation on Earth by suspending 50 volunteers by the arms, holding each above the ground in an upright position.  The thickness of each intervertebral disc was measured prior to and following 10 minutes of suspension.  Researchers then compared the percentage change in intervertebral disc thickness to similar measurements recorded in microgravity, as shown in Figure 1. Figure 1  Percentage change in intervertebral disc thicknessIn theory, spinal elongation would also occur in reduced-gravity environments like the surface of the Moon, where the acceleration of gravity is one-sixth that observed on the Earth's surface. -An astronaut drifts through space alongside the edge of a spaceship.  The astronaut moves as a rigid body with constant velocity and no rotation.  Which of the following occurs when the astronaut strikes a protruding portion of the spaceship with her foot?  The astronaut:

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. -To simplify calculations, mathematical models of DSGR can be generated that replace R_E and R_D in Figure 1 with an equivalent resistor R_eq.  The mathematical expression for R_eq is:

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. -The diameter of a segment of an artery is reduced by a factor of two due to an obstruction.  Assume that the flow is incompressible and laminar.  Compared to an unobstructed segment of the artery, the velocity of blood in the obstructed segment of the artery is:

Passage A traumatic brain injury (TBI) is a form of brain injury caused by an external physical force.  In addition to direct injury at the site of an impact, the rapid acceleration-deceleration of the head may cause the brain to move within the skull and result in injury to the part of the brain opposite the impact site.  This is known as a contrecoup injury.If an impact to the head also results in a skull fracture, the injury is classified as an open TBI.  If there is no skull fracture, the injury is classified as a closed TBI.  The type of TBI can be predicted from the collision duration and the average acceleration of the head.  The thresholds for open and closed TBI are shown in Figure 1. Figure 1  Thresholds for open and closed TBIIn an experiment to study head collisions with projectiles, researchers equipped the head of a crash test dummy with sensors that measured acceleration on multiple axes.  The crash test dummy was stationary before its head was subjected to controlled collisions with incoming projectiles of varying mass and impact velocity.  The linear acceleration of the crash test dummy's head was recorded during and after the impact.  The results for a trial in which the impact lasted for 10 ms are shown in Figure 2. Figure 2  The acceleration of the head during and after a 10-ms collision -When a stationary head is hit by a moving projectile, a contrecoup injury is likely to occur due to:

Which of the following will occur if a corrective lens is placed in front of an eye that is unable to form a clear image of a nearby object?

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 -The earliest stethoscope was simply a wooden pipe open at both ends.  The fundamental frequency of a 0.25-m stethoscope will cause resonance at approximately what distance along the basilar membrane from its base?  (Note: Use 350 m/s for the speed of sound in air.)

A dielectric material is introduced into the empty space between the two plates of a parallel plate capacitor.  How will the capacitance (C) change if the value of the dielectric constant (κ) for the material is 1.5?

Atmospheric pressure on a distant planet causes water to rise to a height of 10 m inside an evacuated tube with its open end immersed in a container of water open to ambient pressure. What is the atmospheric pressure?  (Note: The density of water is 10³ kg/m³ and the gravitational acceleration is 20 m/s²)

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. -Blood flows toward and later passes by a doppler ultrasound probe that is fixed in place.  Relative to the probe, the velocity of blood changes from negative to positive.  Which of the following best illustrates the relationship between blood velocity v_B and the frequency shift of returning waveforms Δf?

Passage Black holes have played an important part in astrophysics for the last half-century.  A black hole is a region of space where the force of gravity is especially strong and gravitational potential energy U is very large.  Analogous to the electrostatic potential energy associated with electrical charges, U is defined as the work required to move an object of mass m from an infinite distance to a point at radial distance r within the gravitational field of a second mass M as given by Equation 1where G is the gravitational constant.  Near a black hole, the gravitational potential energy can become so negative that not even light has enough energy to escape the black hole's gravity.Escape velocity can be determined by launching an object of mass m with velocity v to an infinite radial distance from the surface of a central mass M (eg, a star or a planet) with radius R.  For a black hole to exist, the escape velocity must be equal to the speed of light.Scientists have thoroughly studied the physics of black holes.  Stars near the center of our galaxy have been observed to orbit an extremely massive, invisible object (millions of times more massive than our Sun) that is almost certainly a black hole.  The orbital angular velocity ω of a star is defined as ω=360°⋅fEquation 2where f is the frequency of rotation in hertz (Hz).  Likewise, black holes are not merely static masses but are often observed to rotate about their own axis.  The interaction between the rotation of a black hole and matter falling into the hole is suspected to form powerful beams (jets) of ionized matter that project away from the black hole along its axis of rotation.  Nevertheless, many aspects of how these jets are formed remains a mystery.  Black holes will remain a fruitful area for research far into the future. -Matter falling in the gravitational field of a central mass can form a hot, charged fluid.  The fluid matter orbiting some stars radiates infrared light, but the matter orbiting black holes emits x-rays.  Which of the following explains this discrepancy?  The matter orbiting black holes must:

A 10-kg block is suspended in air by a single string that passes through a pulley and is attached on the other side to a 35-kg block that is on the verge of sliding on the ground. What is the coefficient of static friction between the larger block and the ground?  (Note: The magnitude of the vertical force the small block exerts on the large block is 87 N.)

Which of the following graphs best illustrates how the intensity of sound varies as a detector is moved further and further from a stationary source projecting sound in all directions? (Note: Ignore the Doppler effect)

The absolute temperature of ideal gas molecules stored in a container is directly proportional to the:

Passage Nitrogen is extremely cold in its liquid phase.  It is used in the cryopreservation of small tissue samples and in cryosurgery to freeze and destroy diseased tissues.  Liquid nitrogen can be produced from nitrogen gas using the Hampson-Linde cycle (Figure 1). Figure 1  Hampson-Linde cycle apparatus used to liquefy nitrogenThe cycle begins by compressing nitrogen gas and forcing it through a coil in an external cooler that contains dry ice.  The gas proceeds to a heat exchanger, where it cools further due to the countercurrent heat exchange with colder nitrogen gas returning from a later stage of the cycle; this process is known as regenerative cooling.  The gas is subsequently forced through a narrow valve, where it expands and cools significantly upon exiting.  As a result, a portion of the gas becomes liquefied.The temperature change of the gas exiting the valve is described by the Joule-Thomson effect, which occurs without heat transfer with the surroundings.  Finally, the liquefied nitrogen is collected, and the remaining gas is sent through the regenerative cooler back to the compressor to reenter the cycle.  The physical properties of nitrogen are given in Table 1.Table 1  Thermal Properties of Nitrogen -Based on the passage, a feature of the Joule-Thomson effect is that it occurs:

Relative to the angle of incidence, how will angle of refraction (θ₂) change when a monochromatic ray of light enters a medium of greater refractive index?

The band pattern produced by light passing through a single slit depends on the:refractive index of the medium.slit width.wavelength.