Exam 7: Physics

A scientist studying capillary fluid exchange in a laboratory environment can most effectively increase the filtration of fluid out of capillaries by doing which of the following?

Passage Osteoporosis is a degenerative bone condition in which healthy bone degenerates into porous bone.  Because bone provides the structural integrity that allows the musculoskeletal system to bear weight, osteoporosis is associated with a higher risk of bone fracture.Researchers conducted an experiment designed to assess the strength and elasticity of osteoporotic bone relative to normal bone.  Osteoporotic and normal bone samples with identical physical dimensions were collected and placed within an pneumatic compression device, as shown in Figure 1. Figure 1  Bone compression device loaded with a bone sampleThe force required to compress the bone samples longitudinally (lengthwise) by a given distance was measured, with the results shown in Figure 2. Figure 2  Relationship between force and compression for normal and osteoporotic bonesResearchers observed that bone samples returned to their original dimensions for deformations not exceeding 1% of the original length L₀.  For each deformation, the associated strain ε is defined as the change in length of an object ΔL divided by the object's original length (Equation 1). Equation 1Based on these observations, researchers concluded that both osteoporotic bone and normal bone behaved as an elastic material under a wide range of applied forces. -If maintaining the maximal compression of an osteoporotic bone sample for 5 s requires 80 J of energy, what is the power expended by the compression machine?

A 4-μF capacitor is added in series with both capacitors shown in the circuit above.  What is the ratio of the new equivalent capacitance to the original equivalent capacitance?

Which of the following procedures best describes the use of diffractive phenomena in separating the individual components of an electromagnetic wavefront?

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. -A bone sample (specific gravity = 3) completely immersed in isopropyl alcohol (specific gravity = 0.8) is subject to a buoyant force of 4 N.  What buoyant force would the same bone sample experience when immersed in water?

The relationship between the length of a spring and the force required to stretch the spring is shown below. What is the work done when the spring length is increased from 20 cm to 30 cm?

Passage A student performed an experiment to determine the energy content of a sample of potato chips.  The chips were blended and then freeze-dried to remove moisture from the sample.  Freeze-drying, or lyophilisation, is the preferred dehydration process for food calorimetry due to its minimal impact on nutritional content.  Lyophilisation removes water from frozen food samples at low pressure through sublimation.  The water is later collected in a cooled condensation chamber to prevent damage to any electric components.After freeze-drying, the sample was ground into a dry homogenous powder.  A 1-g sample of the powder was placed in a bomb cell, an enclosed steel-walled container, and pressurized to 25 atm with pure oxygen to ensure complete combustion.  The bomb cell was submerged in 500 g of water at room temperature (25°C) in an enclosed and thermally insulated calorimetry device.  The sample was combusted using an electric fuse.  The temperature of the surrounding water was measured with a glass thermometer every 30 s for several minutes (Figure 1). Figure 1  Temperature of the water in the bomb calorimeterThe energy content of food is given in units of dietary calories (Cal), which is equal to 4.185 kJ, or 1,000 gram calories (cal).  A gram calorie is the amount of energy required to increase 1 g of water by 1°C. Adapted from Jumpertz R, Venti CA, Le DS, et al., Food label accuracy of common snack foods. Obesity 2013 Wiley-Blackwell. -If the student repeated the experiment by replacing the water in the calorimetry device with an ice bath at 0°C, how would the experimental results differ?

Four charged particles of equal mass are initially fixed in place along a straight line, as shown above.  If all the charged particles are released at the same time, which particle would initially accelerate most rapidly?

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 area enclosed by the cardiac PV loop is:

Which of the following color transitions best describes what may take place as a light-emitting object begins releasing electromagnetic waves of progressively higher energy?

Passage A student performed an experiment to determine the energy content of a sample of potato chips.  The chips were blended and then freeze-dried to remove moisture from the sample.  Freeze-drying, or lyophilisation, is the preferred dehydration process for food calorimetry due to its minimal impact on nutritional content.  Lyophilisation removes water from frozen food samples at low pressure through sublimation.  The water is later collected in a cooled condensation chamber to prevent damage to any electric components.After freeze-drying, the sample was ground into a dry homogenous powder.  A 1-g sample of the powder was placed in a bomb cell, an enclosed steel-walled container, and pressurized to 25 atm with pure oxygen to ensure complete combustion.  The bomb cell was submerged in 500 g of water at room temperature (25°C) in an enclosed and thermally insulated calorimetry device.  The sample was combusted using an electric fuse.  The temperature of the surrounding water was measured with a glass thermometer every 30 s for several minutes (Figure 1). Figure 1  Temperature of the water in the bomb calorimeterThe energy content of food is given in units of dietary calories (Cal), which is equal to 4.185 kJ, or 1,000 gram calories (cal).  A gram calorie is the amount of energy required to increase 1 g of water by 1°C. Adapted from Jumpertz R, Venti CA, Le DS, et al., Food label accuracy of common snack foods. Obesity 2013 Wiley-Blackwell. -The bomb cell and the calorimetry device used in the experiment are what types of thermodynamic systems?

Passage A student performed an experiment to determine the energy content of a sample of potato chips.  The chips were blended and then freeze-dried to remove moisture from the sample.  Freeze-drying, or lyophilisation, is the preferred dehydration process for food calorimetry due to its minimal impact on nutritional content.  Lyophilisation removes water from frozen food samples at low pressure through sublimation.  The water is later collected in a cooled condensation chamber to prevent damage to any electric components.After freeze-drying, the sample was ground into a dry homogenous powder.  A 1-g sample of the powder was placed in a bomb cell, an enclosed steel-walled container, and pressurized to 25 atm with pure oxygen to ensure complete combustion.  The bomb cell was submerged in 500 g of water at room temperature (25°C) in an enclosed and thermally insulated calorimetry device.  The sample was combusted using an electric fuse.  The temperature of the surrounding water was measured with a glass thermometer every 30 s for several minutes (Figure 1). Figure 1  Temperature of the water in the bomb calorimeterThe energy content of food is given in units of dietary calories (Cal), which is equal to 4.185 kJ, or 1,000 gram calories (cal).  A gram calorie is the amount of energy required to increase 1 g of water by 1°C. Adapted from Jumpertz R, Venti CA, Le DS, et al., Food label accuracy of common snack foods. Obesity 2013 Wiley-Blackwell. -What is the order of the phase changes of water throughout the lyophilisation process after freezing?

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. -At 200 Hz, the current in C_M is 0.7 A.  What is the current in R_M?

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. -A positive pressure mechanical ventilator most likely inflates the lungs by directly:

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. -Suppose that a 5-mL blood sample with a glucose concentration of 10 mM has capacitance C.  How will C change if the concentration of blood glucose is reduced to 2.5 mM?

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. -If the voltage across the parallel portion of the circuit is 2 V, how much power is dissipated from C_M at 400 Hz?

Performing a medical examination assessing the conduction of nerves, a physician sends an electric impulse down the forearm of a patient.  What is the average velocity of the electric signal if it arrives at an electrode 25 cm away from its initial position following 5 ms of travel?

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. -What is the camera lens' refractive index if incident light 50° from the normal is refracted to 35° from the normal?

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. -An inhalational anesthetic administered to a patient has a rate of diffusion V_gas.  If the partial pressure difference is doubled and the membrane thickness is also doubled, what will be the new rate of diffusion?

A force of 50 N is used to push a wheelchair forward at constant velocity.  If the wheelchair is displaced 0.5 m each second, what is the mechanical power expended when transporting the wheelchair?