Exam 7: Physics

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. -Ignoring any attachments between the spinal discs and vertebrae, how would static friction between these anatomical structures compare for a person standing on the surface of the Moon to a person standing on the surface of the Earth?

In the presence of an external magnetic field (not shown), a proton initially traveling upward is deflected into the path labeled as A in the following figure. What would be the expected path for an electron in the same magnetic field?

What expression gives the wavelength of the third harmonic for a 1.5 m pipe that is closed at one end?

A spring is extended 15 cm from its equilibrium point.  If the spring constant k is 75 N/m, the magnitude and direction of the elastic force F_el are described by which of the following?

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 -If the pulsatile-flow LVAD in Figure 2 pumps with a frequency of 1.5 Hz, what is the volumetric flow rate of blood throughout the systemic circulatory system?

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. -Which of the following graphs best depicts the anesthetic partial pressure along the length of the pulmonary capillaries when it is first administered?

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. -While underwater, divers designate their position with a buoy that floats at the surface above them.  Assuming the buoy is not pulled by the diver, what is the mass of a floating buoy that experiences a buoyancy force of 10 N and is 20% submerged?

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 -Which of the following best describes the type of heat transfer that occurs after the compression stage of the Hampson-Linde cycle is completed?

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. -A patient's eye lens has a focal length of 2 cm.  When the patient wears a pair of prescription eyeglasses with an optical power of −4 D, the combined strength of the lenses is approximately:

Passage In hemodynamics, blood flow through the cardiovascular system can be modeled as an electric circuit in which the blood serves as electricity, the blood vessels as resistive wires, and the heart as a battery (see Figure 1). Figure 1  Cardiovascular circuit modelOhm's law states that the voltage drop ΔV across each element, the current I flowing through it, and its electrical resistance R are related by ΔV = IR.  In a blood vessel, pressure difference between one vessel and the next ΔP replaces ΔV, volumetric blood flow Q replaces I, and vascular resistance R replaces electrical resistance.  Therefore, Ohm's law for blood flow in a vessel isΔP = QREquation 1Vascular resistance is due to the blood's viscosity η and the dimensions of the vessel through which it flows.  Assuming blood vessels are cylinders, R can be approximated as Equation 2where L is the length of the vessel, and r is its inner radius.  If Equation 2 is combined with Equation 1, the resulting equation is Poiseuille law.In a study of the circulatory system in rats, researchers measured the intravascular blood pressure of the mesenteric blood vessels.  The mesentery is the set of tissues that holds the intestines in place.  Blood flows in the following order:  aorta, superior mesenteric artery (SMA), arterial arcade, venous arcade, superior mesenteric vein (SMV).For the procedure, catheters with pressure transducers were inserted into each vessel via laparotomy.  Laparotomy is an invasive procedure that involves a surgical incision into the abdominal cavity.  Blood pressure measurements were taken simultaneously at the proximal end (beginning) of each blood vessel. Figure 2  Mesenteric blood pressure profile of rats (Note: SMA = superior mesenteric artery; SMV = superior mesenteric vein.) -Which of the following can be used as units for η in Equation 2?

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. -Ignoring the weight of the arm, what is the mechanical advantage of the biceps when it is lifting a ball in Experiment 2?

Passage Hydrostatic weighing is a technique used to determine an individual's overall body density.  The weight of the individual is measured when their body is completely submerged in water.  Because the volume of air in the respiratory system affects the measured underwater weight, the individual must exhale completely before entering the water.  However, residual volume, the volume of air that always remains in the respiratory system, must also be accounted for.By comparing an individual's in-air weight to their underwater weight, their total body volume can be determined.  The density of the body D_b excluding any air in the respiratory system is calculated with the in-air mass of the individual m_air, the individual's total body volume V_total, and an estimate of residual volume V_res by: Db=mairVtotal-VresEquation 1Body density can be used to calculate an individual's body fat composition, the percentage of total body mass that is made up of fatty tissue.  Human fatty tissue has an average density of 0.9 kg/L, and the density of water is 1 kg/L.  The acceleration due to gravity is 10 m/s². Adapted from Siri, WE, Body composition from fluids spaces and density. Nutrition 1956 Springer Nature. -An individual that weighs 700 N in air has an apparent weight of 40 N when submerged in water.  What is the volume of the displaced water?

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. -Which of the following units can be used to express Reynolds number?

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. -For equally sized trocar-cannula systems, incisions made for blunt-tipped trocars are smaller than those made by sharp-tipped trocars, forcing the skin to stretch more around the cannula.  This option better prevents slipping after the cannula is inserted because:

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. -What is the change in pressure when a diver descends from 10 m to 100 m below the water's surface?  (Note:  The density of water is 1,000 kg/m³.)

A cannonball is launched at a speed of 30 m/s and at an angle of 60° above the horizontal.  What are the magnitudes of the horizontal and vertical components of the cannonball's initial velocity, respectively?

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. -A 10-L scuba tank is initially filled with 2,800 g of N₂ gas.  At room temperature (25°C), what is the pressure in the tank?  (Note:  Use R = 0.0821 L⋅atm/mol⋅K.)

The electric force generated by two point charges separated by Distance A is 4 times greater than the electric force generated when separated by Distance B.  How does Distance A compare to Distance B?

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 -What is the frequency of the gamma rays emitted in PET?  (Note:  Use h = 4 × 10⁻¹⁵ eV⋅s.)

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 of the following best describes the high voltage plate if it accelerates positive ions away from it?