Question 1

A gram-negative bacterium moves along a flat surface.  What is the maximum displacement of the bacterium during a 1-hour period if the bacterium moves at a constant speed of 25 µm/s?

Accepted Answer

11ecba2d_1317_4761_a3bf_339ac27106fb_MD0008_00 Velocity (v) is a variable of translational motion that expresses the displacement (Δx or x_f− x_i) of a moving object per unit time (t). Unlike speed, which is the magnitude of velocity, velocity is a vector quantity characterized by both magnitude and direction. Consequently, the speed of an object relates to distance, but the velocity of an object relates to displacement. Due to the relationship between velocity and displacement, the x- and y-components of displacement (Δx and Δy) for an object moving through an x,y-coordinate system can be evaluated by multiplying the x- and y-component velocities (v_x and v_y, respectively) by the interval of time for that motion: 11ecba2d_1317_6e72_a3bf_b3043cc2b595_MD0008_00 11ecba2d_1317_6e73_a3bf_4de5e6fe7067_MD0008_00 In this question, a gram-negative bacterium moves along a flat surface at a constant speed of 25 µm/s for 1 hour. Although the bacterium likely moves across the surface along a winding path, the maximum possible displacement from the origin would occur if the movement of the bacteria traces a straight path. In such a case, the constant speed of 25 µm/s would translate to a constant velocity of 25 µm/s because the bacterium moves in only one direction. After selecting an x,y-coordinate system oriented such that the motion of the bacterium takes place along only the x-axis (no y-axis displacement, v_y = 0), the maximum possible displacement of the bacterium over a span of 1 hour can be determined by substituting velocity and time into the equation for displacement: 11ecba2d_1317_6e74_a3bf_6bbe97b8d916_MD0008_00 Converting all values to standard units results in: 11ecba2d_1317_6e75_a3bf_cd6e63449031_MD0008_00 11ecba2d_1317_6e76_a3bf_f969e93037b2_MD0008_00 11ecba2d_1317_6e77_a3bf_c9e111fda42c_MD0008_00 Therefore, the maximum hourly displacement of a bacterium moving along a flat surface at a constant speed of 25 µm/s is 9 × 10⁻² m (Choice D). Educational objective: The displacement of an object is calculated as the average velocity of the object multiplied by the interval of time during which the object moves. The speed of an object is equal to the magnitude of the velocity of the object.

Question 2

Which of the following changes will increase the rate at which a mammalian organism loses body heat to the environment?

Accepted Answer

11ecba2d_1316_35ee_a3bf_fdcb61ad07c1_MD0008_00 Heat transfer is the transmission of thermal energy between two objects or systems by processes such as conduction and convection. In conduction, thermal energy passes between two objects (or domains) through molecule-to-molecule contact. During convection, molecules with higher kinetic energy (ie, temperature) move to a domain where molecules have lower kinetic energy. Heat transfer between two objects or regions occurs until the temperature equalizes. The physical dimensions of the transfer interface influence the rate of heat transfer (H) between objects. For example, the rate of heat transfer between two objects connected by a thermal conductor depends on the conductor length (L), conductor area (A), and difference between the temperature of the hotter object (T_H) and the temperature of the cooler object (T_C): 11ecba2d_1316_5cff_a3bf_3bbd37bb557f_MD0008_00 In biological contexts, heat transfer to the environment is facilitated by processes like ventilation (ie, inhalation and exhalation) and the flow of blood through superficial anatomical structures. The regulation of superficial blood flow via vasoconstriction and vasodilation adjusts the quantity of blood flowing near the (typically) cooler ambient air. Therefore, vasoconstriction decreases the rate of conductive heat loss to the environment and vasodilation increases it. Heat transfer to the environment through ventilation occurs through a similar mechanism except that conductive heat transfer to inhaled air is followed by convective heat transfer through exhalation. Therefore, increasing the rate of respiration increases the rate of heat loss to the environment. (Choice A) Vasoconstriction would reduce blood flow to superficial areas and diminish the rate of heat loss to the environment. (Choice B) Replacing ambient air with warmer air would either diminish or reverse the temperature gradient between the organism and the environment, decreasing the rate of heat loss to the environment. (Choice C) Replacing lean muscle mass with superficial fat would increase the thickness of the superficial structures that act as thermal insulators, decreasing the rate of heat loss to the environment. Educational objective: Heat transfer from an organism to the environment can be accomplished by increasing superficial blood flow (enhancing thermal conduction) or by increasing respiration (enhancing conduction and convection).

Question 3

The photoelectric effect refers to the ejection of electrons from a material when the material absorbs electromagnetic radiation of sufficient energy.  As the frequency of electromagnetic radiation increases, what happens to the kinetic energy of ejected electrons?

Accepted Answer

11ecba2d_1319_1c2b_a3bf_b714d3628a83_MD0008_00 The photoelectric effect describes the ejection of electrons from a substance due to the absorption of electromagnetic radiation. Although higher-intensity electromagnetic radiation exhibits greater electric field oscillations, some types of electromagnetic radiation do not cause the ejection of electrons in any case, regardless of intensity. This is due to the electric potential energy between positive charges (protons) and negative charges (electrons). For each electron there exists a discrete value of electric potential known as the work function (W), and the magnitude of energy absorbed through electromagnetic radiation must exceed W for the ejection of an electron to occur. The energy of electromagnetic radiation (E) is proportional to its frequency (f) via Planck's constant (h = 6.62 × 10⁻³⁴ m²∙kg/s), as given by: 11ecba2d_1319_1c2c_a3bf_1d8e23346807_MD0008_00 Accordingly, the ejection of an electron from a surface by incident electromagnetic radiation depends on the frequency of incident electromagnetic radiation. Furthermore, the conservation of energy dictates that the energy absorbed by an electron must contribute to either the ejection of the electron (overcoming the work function) or to the kinetic energy of the electron following ejection: 11ecba2d_1319_1c2d_a3bf_874e93e8099b_MD0008_00 Consequently, increasing the energy of electromagnetic radiation (ie, frequency) beyond the value of the work function will increase the kinetic energy of ejected electrons. (Choices A and B) Increasing the energy of electromagnetic radiation must increase the kinetic energy of ejected electrons because the work function of each electron is fixed, and the conservation of energy must be maintained. (Choice D) The kinetic energy of ejected electrons must obey the conservation of energy. Absorbed energy from electromagnetic radiation that does not contribute to surpassing the work function is converted to the kinetic energy of ejected electrons. Educational objective: The photoelectric effect describes the ejection of electrons from a substance due to the absorption of electromagnetic radiation with sufficient energy. Because the energy needed to eject an electron is fixed via its work function, increasing the energy of electromagnetic radiation will increase the kinetic energy of ejected electrons.

Question 4

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

Accepted Answer

11ecba2d_130f_f42d_a3bf_6b7129f6b0ad_MD0008_00 In common terms, temperature (T) is an objective measure of the relative "heat" or "cold" contained with an object or system. Temperature influences important physical properties like the physical state and reactivity of matter. The absolute temperature scale is used to quantify the temperature of objects relative to absolute zero, the temperature at which matter achieves the lowest possible quantity of total energy (kinetic energy + potential energy). Absolute zero is considered "absolute" because it is the same for all matter, regardless of atomic structure or molecular configuration. The unit of absolute temperature is the Kelvin (K), and the gradations of the absolute temperature scale are equal in size to those of the centigrade scale. The scales differ only in the placement of the zero value. Consequently, the temperature in Kelvin (T_K) relates to the temperature in Celsius (T_C) through the following expression: 11ecba2d_130f_f42e_a3bf_8ff6eba6ce7e_MD0008_00 Fundamentally, kinetic energy is the key determinant of absolute temperature. Because temperature is typically sampled from multiple atoms or molecules, however, the temperature of matter reflects the average kinetic energy (KE) of a collection of atoms or molecules: 11ecba2d_130f_f42f_a3bf_c7df2896b9e0_MD0008_00 of each moleculeQuantity of molecules Therefore, the temperature of gas molecules moving throughout an enclosed container is determined not by the kinetic energy of any one gas molecule but rather by the average kinetic energy of all gas molecules. (Choice A) The quantity of gas molecules is directly proportional to the pressure and volume, but not the temperature, of a gas. (Choice B) Although significant intermolecular forces between gas molecules would influence the kinetic energy of those molecules, intermolecular forces are not observed between ideal gas molecules. (Choice D) Gases exhibit a range of possible kinetic energy values at all temperatures. However, temperature is not related to the kinetic energy of individual molecules at extreme kinetic energy values, but rather the average kinetic energy of all molecules. Educational objective: The absolute temperature scale quantifies temperature relative to absolute zero, the lowest possible total energy of matter. The absolute temperature of any system is directly proportional to the average kinetic energy of molecules within the system.

Question 5

Uniform magnetic fields created by advanced medical imaging devices most likely come from the:

Accepted Answer

11ecba2d_1310_9070_a3bf_1db9b8da7e00_MD0008_00 Magnetic fields are vector quantities representing the magnetic influence that electrical currents and magnetized materials would experience at a location in three-dimensional space. Common sources of magnetic fields include electromagnetic radiation and permanent magnets, materials in which sustained north and south magnetic poles are present intrinsically or formed through magnetic induction (ie, magnetization). Electric current is another source of magnetic fields. Current traveling along a straight wire generates magnetic field lines that encircle the wire lengthwise, the orientation of which can be determined by the right-hand rule. The magnitude of the magnetic field (_EMEM_) generated by electric current relates to the current (I), the distance from the axis of the wire (r), and the permeability constant (µ) of the medium: 11ecba2d_1310_9071_a3bf_cfc6ed0d430e_MD0008_00 Furthermore, current flowing along a circular wire generates unidirectional magnetic field lines within the interior of the coil. Among other applications, this principle is useful to medical imaging technologies. Specifically, the core of an MRI (magnetic resonance imaging) machine is composed of sequential conductive coils in which current flows in the same clockwise or counterclockwise direction. Therefore, the use of circular current generates a uniform magnetic field that interacts with anatomical structures to enable the collection of medical imaging data. (Choice A) Nuclear decay refers to the process by which the nuclear configuration or identity of an atom changes concurrent to the emission of radiation. The electromagnetic radiation associated with nuclear decay generates magnetic fields, but these fields oscillate and are not unidirectional. (Choice B) A charged particle generates an electric field that exerts forces on other surrounding charged particles. However, charged particles do not intrinsically generate magnetic fields. (Choice D) Capacitance is the ability of a device to store electric charges at small distances from one another, generating voltage. Charges stored by capacitors are fixed in place, and therefore do not generate magnetic fields. Educational objective: Magnetic fields are generated by electromagnetic radiation, permanent magnets, or the motion of charged particles. The direction of magnetic fields generated by moving charges can be determined using the right-hand rule.

Question 6

Thin-film interference is observed when polychromatic light is incident on an interface formed by two semitransparent media.  Which of the following best explains why thin-film interference generates a multicolored array when two semitransparent fluids are used?

Accepted Answer

11ecba2d_1318_7fea_a3bf_6f863feddfb5_MD0008_00 Thin-film interference refers to the multicolored arrays generated by the reflection events that occur within a system composed of two layers of semitransparent media. The relative intensity of the colors seen within the multicolored array depends on the constructive and destructive interference among waveforms of polychromatic (variable wavelength) light. Interference that occurs within a thin-film system results from differences in the travel path of the light. Some light that is incident on the two-media system will reflect off the surface of the first medium (thin film), and some light will transmit through the first medium before reflecting off the media interface. When light reflected off the surface of the first medium constructively interferes with light reflected off the media interface, an observer perceives bright light. Conversely, when light reflects off the surface of the first medium and destructively interferes with light reflected off the media interface, an observer perceives darkness. Thin-film interference is influenced by the thickness of the film because light waves of a specific wavelength (ie, color) that interfere constructively or destructively at one film thickness may no longer interfere in the same fashion at a different thickness. Therefore, surface tension and other effects that locally distort the surface of a fluid may also cause multicolored arrays to appear on the surface as light that emerges from adjacent segments of the thin film varies in color composition. (Choices A and C) Variations in fluid density and osmolarity cannot explain changes to the interference pattern of light that are necessary to produce multicolored arrays. Furthermore, the fluid density and osmolarity of each medium would not be expected to vary within the same two-media system. (Choice D) Layering two semitransparent fluids increases the frequency of reflection events, enabling the waveform interference that generates multicolored arrays. Educational objective: Thin-film interference describes the multicolored array generated when polychromatic light is incident on an interface formed by two semitransparent media. Localized discrepancies within the thickness of a thin film (top media) contribute to variable interference patterns that produce the colorful array.

Question 7

A cable with a tension of 45 N is used to suspend a 5 kg mass M against a wall.  What is the magnitude and direction of the force of friction between the mass and the wall?

Accepted Answer

11ecba2d_130e_bb9d_a3bf_03764543d973_MD0008_00 Any object may be acted on by multiple translational forces of different origin, magnitude, and direction. For example, an object located in two-dimensional space will accelerate when the sum of all forces acting along one or both axes of the xy-coordinate system does not equal zero. Because forces acting along the same axis can be either antagonistic or cooperative, free-body diagrams can be used to assess the balance of forces along each axis provided that the vector components of each force are known: 11ecba2d_130e_e2ae_a3bf_25411bb3d705_MD0008_00 11ecba2d_130e_e2af_a3bf_891f1dcfef9e_MD0008_00 When the sum of all forces acting on a mass along each axis of the xy-coordinate system is equal to zero, the object is said to be in equilibrium such that no acceleration occurs: 11ecba2d_130e_e2b0_a3bf_415cee99d458_MD0008_00 11ecba2d_130e_e2b1_a3bf_f9d7f6f5f489_MD0008_00 In contrast to an equilibrium in which an object is moving, static equilibrium results when the balance of forces acting on an object maintains the absence of motion by that object. In the prompt, a 5 kg mass is suspended in static equilibrium by a cable with a tension of 45 N. Isolating only the vertical (y-axis) forces, the magnitude of the gravitational force acting on the object can be determined by the simple equation for weight: 11ecba2d_130e_e2b2_a3bf_495e406f8342_MD0008_00 Because this downward (−y) gravitational force acting on the mass is greater than the 45 N tension force pulling the block upward (+y), it can be concluded that the frictional force acting on the mass must act in an opposing, upward (+y) direction to maintain the static equilibrium. Using the equation for static equilibrium, the magnitude of the frictional force (F_f) between the mass and the wall can be calculated: 11ecba2d_130f_09c3_a3bf_8f04903e6d82_MD0008_00 11ecba2d_130f_09c4_a3bf_590d1fbe07ed_MD0008_00 11ecba2d_130f_09c5_a3bf_4791b680f06e_MD0008_00 11ecba2d_130f_09c6_a3bf_81a491d7b8e2_MD0008_00 N and oriented in an upward (+y) direction (Choice A). Educational objective: Static equilibrium occurs when the sum of all forces acting on a motionless object is equal to zero. Free-body diagrams are used to illustrate the directional components of translational forces.

Question 8

Two transverse waveforms (A and B) travel through the same medium with a phase difference of 180°.  If the amplitude of the waveforms is ±100 m, what is the combined displacement of both waveforms as waveform A reaches maximum displacement?

Accepted Answer

11ecba2d_1312_6539_a3bf_e3ad8d87cbfe_MD0008_00 Mechanical waves transmit energy by displacing matter through temporary, periodic oscillations (ie, vibrations). Transverse mechanical waves are modeled by sinusoidal functions that express the momentary displacement of the propagation medium (y-axis) through a cyclical interval (x-axis). Sinusoidal functions are used to model mechanical waves because each function contains terms analogous to the fundamental properties of waves (eg, frequency, amplitude, periodicity). In particular, sinusoidal functions used to model mechanical waves repeat every 360° (or 2π radians), which is one complete cycle. For example, a wave function yielding a maximum displacement at 90° will once again yield maximum displacement at 450° following another complete cycle (90° + 360° = 450°). Phase difference (or phase shift) refers to the degree to which the cyclical nature of two equal-frequency waveforms are aligned. For example, a phase difference of 0° indicates that both wave functions are fully overlaid and reach minimum or maximum displacement together at the same point in the waveform cycle. Conversely, a phase difference of 180° (half a cycle) indicates that the maximum of one wave function occurs concurrent to the minimum of the other waveform. As a result, phase difference expresses the degree of constructive and destructive interference between two waveforms. In this question, waveforms A and B are out of phase by 180°. Therefore, when waveform A reaches its maximum displacement (+100 m) waveform B reaches its minimum displacement (-100 m). The expression for total displacement caused by two interfering waveforms is the sum of the individual relative displacements (y-axis values) of each waveform: Total displacement = Waveform A displacement + Waveform B displacement Total displacement = (100 m + -100 m) = 0 m Therefore, the combined displacement of both waveforms as waveform A reaches maximum is 0 m. Educational objective: Phase difference relates the alignment of two equal-frequency waveforms to one another. Phase differences can result in constructive interference, destructive interference, or no interference.

Question 9

An ideal fluid flows within a fixed tube with decreasing cross-sectional area.  Assuming constant height and volumetric flow rate, which of the following graphs best illustrates the relationship between fluid pressure and the increase in fluid velocity?

Accepted Answer

11ecba2d_1315_7294_a3bf_611380c6ad4a_MD0008_00 One application of Bernoulli's equation relates to the travel of fluids between two points (A and B) within a fixed conduit (a pipe or channel through which a fluid passes). Each side of Bernoulli's equation contains three terms, the first of which is pressure (P), a measure of energy per unit volume. The second and third terms reflect the potential and kinetic energy of a fluid, which both differ from the potential and kinetic energy of solids by being related to fluid density (ρ) rather than to mass: 11ecba2d_1315_7295_a3bf_6b4f8bbbebbc_MD0008_00 PA+ ρghA+12ρvA2=PB+ρghB+12ρvB2 Bernoulli's equation is useful in modeling the flow of ideal fluids because ideal fluids are non-compressible (ie, unchanging density). Fluid incompressibility requires that changes in conduit geometry (ie, cross-sectional area) cause changes in fluid velocity because the volumetric flow rate through interconnected segments of a conduit must be equal. Consequently, changes in conduit geometry are accompanied by changes in fluid pressure or potential energy, maintaining the conservation of energy. In this question, an ideal fluid flows through a fixed tube with a decreasing cross-sectional area. Because the height (h) remains constant, the potential energy terms can be eliminated from Bernoulli's equation: 11ecba2d_1315_7296_a3bf_6fbee9c18408_MD0008_00 11ecba2d_1315_7297_a3bf_55338d0ec176_MD0008_00 Further rearrangement of the remaining terms yields an expression that relates the difference in pressure at both points to the difference in kinetic energy at both points: 11ecba2d_1315_7298_a3bf_e7e9791af00d_MD0008_00 Because the cross-sectional area of the conduit decreases while the volumetric flow rate remains constant, fluid velocity must increase: 11ecba2d_1315_99a9_a3bf_434c5070e0d3_MD0008_00 11ecba2d_1315_99aa_a3bf_c1d0e7ebf06e_MD0008_00 Substituting this inequality into the previous arrangement of Bernoulli's equation yields an expression for pressure: 11ecba2d_1315_99ab_a3bf_0b8e485a431c_MD0008_00 11ecba2d_1315_99ac_a3bf_4150997535fb_MD0008_00 11ecba2d_1315_99ad_a3bf_839fd6702d92_MD0008_00 Therefore, the pressure of ideal fluid in motion will decrease as fluid velocity increases (Choice A), a phenomenon known as the Venturi effect. The Venturi effect has relevance to practical scenarios (eg, aviation, blood flow) and can be observed using a device known as a Venturi tube. Educational objective: The Venturi effect describes the decrease in pressure observed concurrent to an increase in fluid velocity. The Venturi effect is modeled by Bernoulli's equation, which describes the conservation of energy in fluids.

Question 10

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

Accepted Answer

11ecba2d_1317_e3a8_a3bf_e953be222a4b_MD0008_00 A diffraction grate is a diffractive array composed of numerous slits with near-zero width similar to the wavelength of incident light. Like the band patterns produced through single-slit diffraction and double-slit diffraction, dark bands that result from light passing through a diffraction grate are caused by destructive interference between light waves. Conversely, light bands are caused by constructive interference between light waves. Compared to other diffractive phenomena, the band pattern caused by grated diffraction is characterized by relatively sharp and narrow peaks (ie, thin peaks with highly variable amplitude). This band pattern occurs because constructive and destructive interference occurs not only between waves emerging from adjacent slits (eg, double-slit diffraction) but also between waves emerging from slits separated from each other by other slits. Light bands (regions of maximum light intensity) from the diffraction grating occur when diffracted light waves pass through the slits at angles (θ) that are a function of the distance separating each slit (d) and an integer multiple (m = ±1, ±2, ±3…) of the wavelength: 11ecba2d_1318_0ab9_a3bf_2d504061eaad_MD0008_00 The sharp, narrow peaks of the band pattern produced by a diffraction grating are useful in analyzing the properties of the light that enters the slit. For example, long-wavelength light diffracts more than short-wavelength light. Consequently, transmitting polychromatic light composed of light waves with different wavelengths (eg, white light) through a diffraction grate will produce a series of multicolored arrays (eg, rainbows) that enables an analysis of wavefront composition. (Choices A and B) Compared to grated diffraction, the band patterns produced by single- and double-slit diffraction are relatively diffuse. Therefore, single- and double-slit diffractions are not helpful in analyzing the individual components of light wavefronts. (Choice D) In contrast to polychromatic white light, monochromatic light is composed of only one color (ie, one wavelength). Consequently, the wavelength of monochromatic light can be detected without the use of diffraction. Educational objective: Diffraction grating refers to passage of light through an array consisting of numerous slits. Diffraction grating may be used to determine the components of polychromatic (eg, white) light and other mixed electromagnetic wavefronts.

Question 11

Ultrasonic shock wave devices may be used in medical settings to disrupt disease structures located deep in the body.  Among other variables, the device user can control the frequency of emitted waveforms.  The adjustment of waveform frequency:

Accepted Answer

11ecba2d_1313_4f9e_a3bf_45bb1d31a0be_MD0008_00 Ultrasonic sound waves (ie, ultrasound) are mechanical waves that propagate at a frequency above the upper bound of the human auditory spectrum (~20 kHz). Ultrasonic sound waves behave much like audible sound waves that can be detected by the human ear. However, the relatively small wavelength of ultrasonic waves allows them to propagate through body tissues without diffracting significantly. Propagation without diffraction enables the use of ultrasound waves in medical imaging contexts. Unlike ultrasound techniques used for medical imaging, shock wave ultrasound is a non-imaging treatment modality in which the mechanical energy of ultrasonic sound waves is transmitted to structures associated with human disease. Shock wave absorption by these tissues causes high-amplitude vibrations that contribute to tissue destruction. Although standing wave vibrations may take place in any object following perturbation, vibrations that occur in non-acoustic objects are generally inaudible because the amplitude (A) of the vibrations is too small or because the resonance frequency (f₀) falls outside the audible range. The high-amplitude vibrations associated with shock wave ultrasound, for example, occur only because the shock wave frequency (f) approaches (or is equal to) the resonance frequency of the target structure. The resonance frequency of disease structures may change in accordance with size and material composition. Shock wave therapy devices must therefore allow the user to adjust the frequency of the emitted shock waves to ensure effectiveness in destroying particular tissue types. (Choice A) Shock wave ultrasound utilizes ultrasonic waves that transmit at frequencies beyond the human auditory spectrum, making direct auditory feedback from the device to the user impossible. (Choice C) Regardless of frequency, all sound waves attenuate (ie, lose intensity) somewhat when propagating through a medium. Furthermore, attenuation may occur as sound waves pass between media. (Choice D) Doppler ultrasound is a specialized imaging technique that allows for the characterization of dynamic structures. However, shock wave ultrasound is typically used to destroy static structures. Educational objective: Shock wave therapies like shock wave ultrasound utilize high-frequency waves to cause destructive, high-amplitude vibrations within target structures. For maximum effectiveness, the frequency of the shock waves should match the resonance frequency of the target structure.

Question 12

An 8-F parallel plate capacitor generates a voltage of 5 V when fully charged.  How much charge is stored by the capacitor?

Accepted Answer

11ecba2d_130e_4668_a3bf_21bf30b78493_MD0008_00 A capacitor is a common component of electrical circuits that stores electric charge between equally but oppositely charged conductive surfaces (plates) separated by a fixed distance (d). A capacitor is charged when it is connected to a source of electric current. As electric current flows, an electric field develops across the capacitor, which causes positive charge to accumulate on the plate of the capacitor closest to the positive (+) node of the current source. Conversely, negative charge accumulates on the capacitor plate closest to the negative (−) node. Storing equal but opposite charges in proximity to one another generates an electric potential energy (voltage) from the mutual attraction between the positive and negative charges. Because movement of charge between the plates (leakage) would diminish the stored charge, capacitor strength is assessed by the quantity of charge (Q) that can be stored relative to the voltage (V) generated. As such, capacitor strength is quantified by capacitance (C), which is expressed through the equation: 11ecba2d_130e_4669_a3bf_6b7a7b43843e_MD0008_00 Capacitance is generally stated in units of farads (F), where 1 farad is equal to 1 coulomb (C) of charge stored per volt (V) of electric potential generated. In this question, an 8-F parallel plate capacitor generates 5 V of electric potential by storing an unknown quantity of charge. To identify the amount of charge stored, the equation for capacitance must be rearranged as: 11ecba2d_130e_466a_a3bf_756262e40be3_MD0008_00 Substituting the values for capacitance and voltage into the equation gives: 11ecba2d_130e_6d7b_a3bf_1d006cd48379_MD0008_00 Therefore, an 8-F parallel plate capacitor that generates 5 V of electric potential has stored 40 C of charge (Choice C). Educational objective: Capacitors generate electric potential (voltage) by storing charge. The quantity of charge stored by a capacitor is a product of capacitance (capacitor strength) and the voltage generated by charge storage.

Question 13

Light from an incandescent lightbulb passes through an ideal linear polarizer.  The intensity of the light is 100 lm before passing through the filter, but 50 lm immediately after.  Which of the following explains this discrepancy?

Accepted Answer

11ecba2d_1311_2cb2_a3bf_7b46c78128cb_MD0008_00 Polarization refers to the alignment of transverse wave oscillations in a particular orientation within the x,y,z-coordinate system. For example, a transverse wave traveling along the x-axis causes oscillations that may occur exclusively along the y- or z-axis, or at some angle between the y- and z-axes. Polarization is unique to transverse waves because only transverse waves cause oscillations perpendicular to the direction of propagation. Consequently, electromagnetic radiation can be polarized but sound cannot. A waveform is said to be linearly polarized if waveform oscillations take place within only one plane of the coordinate system. By standard convention, the overall orientation of electromagnetic radiation is the same as the orientation of the electric field component. Polarization filters are optical devices that reorient the polarization of electromagnetic radiation so that radiation exiting the filter is polarized in only one orientation. A linear polarization filter, for example, allows for the transmission of electromagnetic radiation oriented parallel to the axis of polarization but inhibits the passage of radiation oriented perpendicular to this axis. Most light sources emit unpolarized light comprising waveforms oriented in all directions. Even for unpolarized light, however, approximately half of the intensity of electromagnetic radiation is polarized along one of two perpendicular axes. Because only electromagnetic radiation with an electric field oriented parallel to the axis of polarization passes through, the total intensity of light will therefore decrease by 50% when nonpolarized light passes through a linear polarization filter. (Choices A and D) The reflection and refraction of light are important to an optical phenomenon related to a discrepancy between the refractive index of two media. However, polarizers are designed to facilitate the passage of light unrefracted and unreflected. (Choice B) Light waves with magnetic fields oriented perpendicular to the axis of polarization have electric fields parallel to the axis of polarization. Such waves are transmitted through the polarizer and are not absorbed. Educational objective: Linearly polarized waveforms are associated with oscillations that occur in a particular orientation of the x,y,z-coordinate system. A linear polarization filter blocks electric fields aligned perpendicular to the axis of polarization (ie, 50% of total intensity).

Question 14

The table above gives the angle of refraction measured when light encounters three unique smooth interfaces. In each case, the refractive index of the new medium and the angle of refraction are identical. Some light reflects off the media interface in each condition. How does the angle of reflection θ_r in the high refractive index condition compare to the angle of reflection in the low refractive index condition?

Accepted Answer

11ecba2d_1314_d64e_a3bf_114c4a469a8d_MD0008_00 Reflection is a phenomenon in which light that arrives at the interface between two media re-enters the original media with modified direction. Models of reflection assume that light is comprised of individual rays rather than dispersed wavefronts. This simplification allows for accurate predictions about the pathway that light will take during reflection events. Specifically, the pathway of light following a reflection event is described in terms of the angle that light rays make with the normal, an imaginary line perpendicular to the interface between media. For example, the angle of incidence (θ₁ or θ_i) refers to the angle (relative to the normal) at which light approaches the interface between two media. When light strikes a media interface, some light may pass through the first medium, enter the second medium, and undergo refraction. However, the remaining light does not enter the second medium and instead reflects back into the first medium at the angle of reflection (θ_r). One principle characteristic of reflection is that the angle of reflection is always equal to the angle of incidence, irrespective of the refractive index on either side of the media interface: 11ecba2d_1314_d64f_a3bf_5be02b6e7654_MD0008_00 Consequently, light rays approaching equally smooth interfaces at different angles of incidence will reflect away from each interface at different angles of reflection. Therefore, light rays that approach a smooth interface at an angle of 12° (high refractive index condition) will reflect away from the interface at half the angle of light rays approaching the interface at an angle of 24° (low refractive index condition) (Choice B). Educational objective: Light reflects from an interface between media and travels in a new direction within the original medium. For smooth media interfaces, the angle of reflection is equal to the angle of incidence.

Question 15

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?

Accepted Answer

11ecba2d_130f_7ef7_a3bf_0d9174a74e8d_MD0008_00 In some cases, determining the total quantity of work (W) done on or by a system is sufficient for describing the transfer or expenditure of energy. However, most energy-related phenomena do not occur instantaneously. Therefore, power (P) is used to quantify the magnitude of energy transfer or expenditure over time (t): 11ecba2d_130f_7ef8_a3bf_3597f0dafad4_MD0008_00 The SI unit for power is the watt (W), where 1 W is equal to 1 joule (J) of energy expended per second (s) of time. In the context of translational motion, power can be restated in terms of the change in energy per unit of time caused by the application of a force (F) over a distance (d): 11ecba2d_130f_7ef9_a3bf_9bb438ba24de_MD0008_00 The above expression relating power to mechanical work may also be rearranged and expressed in terms of the velocity (v) of the object acted on by the force: 11ecba2d_130f_7efa_a3bf_e9d4f7443171_MD0008_00 Therefore, the power expenditure associated with the motion of an object is equal to the product of the force required to move the object and the velocity at which the object moves. In the prompt, a 50 N force propels a wheelchair forward at a constant velocity. Because the wheelchair is displaced 0.5 m each second, the velocity of the wheelchair is equal to 0.5 m/s. Using this velocity, the power expenditure associated with the motion of the wheelchair is calculated as follows: 11ecba2d_130f_a60b_a3bf_198210831c33_MD0008_00 Because 1 N·m is equal to 1 J, the power required to propel the wheelchair forward is therefore: 11ecba2d_130f_a60c_a3bf_bdb30dbd6a34_MD0008_00 Educational objective: Power is the rate of energy transfer into or out of a system. In the context of translational motion, power is equal to the product of force and velocity.

Question 16

Circularly polarized light results from the vector sum of the electric field oscillations of two linearly polarized transverse waves traveling along the same axis.  To achieve circular polarization, the two transverse waves must be out of phase to one another.  The necessary phase difference is:

Accepted Answer

11ecba2d_1316_d230_a3bf_55615a648c6a_MD0008_00 Polarization is a property unique to transverse waves (eg, electromagnetic radiation) in which the wave oscillations are aligned in a particular spatial orientation within the x,y,z-coordinate system. When two polarized waves combine, a new wave is formed with a different polarization. For example, a wave polarized along the x-axis totally in-phase with a wave polarized along the y-axis produces a combined wave that is polarized between the x- and y-axes at a 45° angle. When the polarization of a combined wave rotates around the axis of propagation, the wave is said to be circularly polarized. If the polarization of the combined wave rotates in a clockwise direction when viewed facing the direction of propagation, the waveform is right-polarized; if the polarization rotates in a counterclockwise direction, the waveform is left-polarized. Circular polarization occurs when two wave forms with equal amplitude and perpendicular linear polarization (ie, polarized along different axes) propagate 90° out of phase to one another (ie, one waveform yields zero displacement when the other waveform is yielding a peak or a trough). The mismatch in phase causes each contributing wave to generate momentary oscillations that are different at every point in time. This results in a continuous rotation in the orientation of the combined wave. A 90° phase difference is required for circular polarization because only a 90° phase shift yields both the positive and negative oscillations along each axis and the symmetry necessary to produce a circular polarization pathway. (Choices A and D) Phase differences of 0° and 360° both reflect waveforms that are traveling completely in phase with one another. The polarization of two waves traveling in phase with one another is fixed and will not rotate. (Choice C) A phase shift of 180° represents waves traveling completely out of phase and will result in a polarization oriented in a fixed orientation at a 45° angle to the axis of polarization of each contributing wave. Educational objective: Circular polarization refers to the rotation of polarization observed when two transverse waves with equal amplitude and perpendicular linear polarization propagate out of phase with one another by 90°.

Question 17

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

Accepted Answer

11ecba2d_1312_da6a_a3bf_d3ea7d476b1a_MD0008_00 Like other acoustic objects, physically perturbed pipes generate standing waves that form in accordance with the shape and dimensions of the perturbed object. The multiple standing waves elicited in pipes develop in a fixed series known as harmonics. For example, the unique acoustic qualities of a wind instrument (ie, a musical instrument built from an open or closed pipe) are derived from the unique harmonic series of that particular instrument. The wavelength of the first harmonic (λ₁) corresponds to the soundwave of the longest wavelength that may be produced within a pipe. The first harmonic is typically the most intense standing wave elicited by physical perturbations of the pipe. Furthermore, higher harmonics have smaller wavelengths and higher frequencies than those of the first harmonic. For a pipe closed at one end, the wavelength of each harmonic is proportional to object length (L) and harmonic number (n = 1, 3, 5…): 11ecba2d_1312_da6b_a3bf_e5d985f28660_MD0008_00 Pipes closed at one end cannot produce even-numbered harmonics (n = 2, 4, 6…), as no displacement of air takes place at the closed end. In other words, the closed end of the pipe is always a node (ie, a point of minimum displacement) and the open end of the pipe is always an antinode (ie, a point of maximum displacement). Nevertheless, even-numbered harmonics retain a place within the harmonic series. Consequently, the harmonic number associated with the second-longest standing wave of a pipe closed at one end is not 2 but 3. In such a case, the expression that gives the wavelength of the third harmonic is: 11ecba2d_1312_da6c_a3bf_610c86d23db2_MD0008_00 Therefore, the expression that gives the wavelength of the third harmonic for a 1.5 m pipe that is closed at one end is: 11ecba2d_1312_da6d_a3bf_5545ddf32355_MD0008_00 Educational objective: Standing waves can be elicited within open and closed pipes. There are no even-numbered harmonics in the harmonic series of a pipe closed at one end because the closed end of a pipe is always a node and the open end is always an antinode.

Question 18

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

Accepted Answer

11ecba2d_130d_d136_a3bf_a5ae79185436_MD0008_00 Diffraction is broadly defined as the bending of light around edges or objects. Classic slit diffraction occurs as a uniform wavefront of monochromatic light arrives at a slit (ie, confined gap) in which the width of the slit (a) is comparable to the wavelength of the light (λ), resulting in the dispersed propagation of light away from the center of the slit. Diffraction through a single slit produces a pattern of dark and bright bands on a flat background surface distant to the slit. Bands occur when the bending of light causes the distance (path length) traveled by some waves to be longer than that of others. When the path lengths of two light waves differ by λ/2, the waves arrive at the background out-of-phase (ie, the peak of one waveform coincides to a trough of the other). As a result, destructive interference occurs such that dark bands in the diffraction pattern are produced. Conversely, light bands result from zero or minimal destructive interference. Dark bands (minimum light intensity) due to destructive interference occur when diffracted light waves pass through the slit at angles (θ) that are a function of the slit width and an integer multiple (m = ±1, ±2, ±3…) of the wavelength: 11ecba2d_130d_d137_a3bf_e17c1934c724_MD0008_00 sin θ=mλa According to this relationship, decreased slit width or increased wavelength tends to widen the band pattern such that greater distances are present between light and dark bands. Conversely, increased slit width or decreased wavelength results in a relatively narrow band pattern. Therefore, both slit width and wavelength influence the angle of propagation associated with the dark and light bands in the pattern of diffracted light (Numbers II and III). (Number I) The refractive index of the medium is relevant to refraction, dispersion, and other optical phenomena related to the passage of light between two media. However, the refractive index is not relevant to diffraction. Educational objective: Single-slit diffraction is an optical phenomenon that demonstrates the waveform nature of light. The band pattern associated with a given diffraction event is related to slit width and the wavelength of light.

Question 19

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?

Accepted Answer

11ecba2d_1313_ebe0_a3bf_1d7853edba50_MD0008_00 In contrast to simple circuits, complicated circuits are structured such that current flows through two or more loops (ie, closed pathways) sharing only some circuit components. Junctions are points along a complicated circuit at which three or more circuit elements meet. Junctions bridge two or more circuit loops to one another, and the sum of current entering the junction (I_enter) must be equal to the current exiting that junction (I_exit): 11ecba2d_1313_ebe1_a3bf_732b1309c723_MD0008_00 Ienter=Iexit In other words, charge cannot accumulate or disappear at junctions and must pass on to other circuit elements. Furthermore, the total voltage drop (V) within each loop is related to the resistance (R) of and current traveling across all resistors within the loop: 11ecba2d_1314_12f2_a3bf_0391d50ad7e6_MD0008_00 Vn=I1R1+I2R2…+InRn In the prompt, current flows through a complicated circuit with two voltage sources (V₁ and V₂) and three resistors (R₁, R₂, and R₃). Two loops are present within each circuit, the first of which is composed of voltage source V₁ and resistors R₁ and R₃. The second loop is composed of voltage source V₂ and resistors R₂ and R_3. One current unique to each loop (I_A and I_B) enters Point A and another current shared by both loops exits Point A (I_exit): 11ecba2d_1314_12f3_a3bf_0d3a4d22880e_MD0008_00 11ecba2d_1314_12f4_a3bf_79ff5bdfa949_MD0008_00 11ecba2d_1314_12f5_a3bf_edb2be69b773_MD0008_00 The question states that each loop is composed of a 10-V source connected to two resistors, each with a resistance of 5 Ω: 11ecba2d_1314_12f6_a3bf_fd9efc5f131f_MD0008_00 11ecba2d_1314_12f7_a3bf_3dec36b8d600_MD0008_00 11ecba2d_1314_3a08_a3bf_db75c5add4eb_MD0008_00 11ecba2d_1314_3a09_a3bf_23941187c67d_MD0008_00 Because both loops that converge on Point A and are identical, I_exit must be twice the value of I_A and I_B: 11ecba2d_1314_3a0a_a3bf_973bdbd14740_MD0008_00 11ecba2d_1314_3a0b_a3bf_13e1f2736104_MD0008_00 11ecba2d_1314_3a0c_a3bf_79aa5db9ba39_MD0008_00 Consequently, the quantity of current exiting Point A must be 4/3 C/s (Choice C) because charge cannot accumulate or disappear within circuit junctions. Educational objective: Circuits composed of multiple loops contain junctions, points on the circuit at which three or more elements meet. The current entering any junction must be equal to the current exiting the junction.

Question 20

A battery is connected to a circuit joining it to a lightbulb as shown.  Increasing the internal resistance of the battery will:

Accepted Answer

11ecba2d_1311_a1e4_a3bf_3186ceaee0a3_MD0008_00 In electronics, the flow of charge (current) through a circuit requires the establishment of a gradient of electric potential energy (voltage) that is typically maintained by an electrical generator. Despite its name, the electromotive force 11ecba2d_1311_c8f5_a3bf_e7b5d38f00ed_MD0008_00 is the energy per unit of charge that is supplied by a battery or other generator to move charge through a circuit. In principle, the electromotive force represents an intrinsic electric potential gradient within the battery, which produces an observed terminal voltage (V) that affects circuit components external to the battery (eg, resistors, conductors, capacitors). For an ideal battery, the observed terminal voltage is equal to the electromotive force: 11ecba2d_1311_c8f6_a3bf_59fd4b132861_MD0008_00 However, in real systems a battery uses chemical reactions to physically segregate positive and negative charges in a process that is not perfectly efficient. As a result, internal resistance (r) within the battery dissipates some of the electric potential energy as charges are transported as current (I) to the appropriate battery terminals. The voltage that is "lost" (V_loss) due to internal resistance within the battery is expressed by application of Ohm's law: 11ecba2d_1311_c8f7_a3bf_c763eab97acf_MD0008_00 Accordingly, the discrepancy between electromotive force and the observed terminal voltage is: 11ecba2d_1311_c8f8_a3bf_53e97e0e800f_MD0008_00 Consequently, the magnitude of the electromotive force is the theoretical upper limit of the terminal voltage, although this limit is not achieved in practical contexts. Therefore, increasing the internal resistance of the battery connected to the circuit powering a light bulb will not change the magnitude of the intrinsic electromotive force; however, it will decrease the observed terminal voltage. (Choices A and B) The electromotive force is intrinsically related to the physical dimensions and composition of the battery; however, the magnitude of electromotive force is independent of internal resistance. Increasing internal resistance will not influence the magnitude of the electromotive force. (Choice D) For the observed terminal voltage to increase, the internal resistance of the battery would have to decrease, not increase. Educational objective: The electromotive force quantifies the capacity of electrical generators to establish an electric potential energy gradient. Due to internal resistance within the electrical generator, the observed terminal voltage is less than the electromotive force.

Exam 7: Physics

A gram-negative bacterium moves along a flat surface. What is the maximum displacement of the bacterium during a 1-hour period if the bacterium moves at a constant speed of 25 µm/s?

Which of the following changes will increase the rate at which a mammalian organism loses body heat to the environment?

The photoelectric effect refers to the ejection of electrons from a material when the material absorbs electromagnetic radiation of sufficient energy. As the frequency of electromagnetic radiation increases, what happens to the kinetic energy of ejected electrons?

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

Uniform magnetic fields created by advanced medical imaging devices most likely come from the:

Thin-film interference is observed when polychromatic light is incident on an interface formed by two semitransparent media. Which of the following best explains why thin-film interference generates a multicolored array when two semitransparent fluids are used?

A cable with a tension of 45 N is used to suspend a 5 kg mass M against a wall. What is the magnitude and direction of the force of friction between the mass and the wall?

Two transverse waveforms (A and B) travel through the same medium with a phase difference of 180°. If the amplitude of the waveforms is ±100 m, what is the combined displacement of both waveforms as waveform A reaches maximum displacement?

An ideal fluid flows within a fixed tube with decreasing cross-sectional area. Assuming constant height and volumetric flow rate, which of the following graphs best illustrates the relationship between fluid pressure and the increase in fluid velocity?

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

Ultrasonic shock wave devices may be used in medical settings to disrupt disease structures located deep in the body. Among other variables, the device user can control the frequency of emitted waveforms. The adjustment of waveform frequency:

An 8-F parallel plate capacitor generates a voltage of 5 V when fully charged. How much charge is stored by the capacitor?

Light from an incandescent lightbulb passes through an ideal linear polarizer. The intensity of the light is 100 lm before passing through the filter, but 50 lm immediately after. Which of the following explains this discrepancy?

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?

Circularly polarized light results from the vector sum of the electric field oscillations of two linearly polarized transverse waves traveling along the same axis. To achieve circular polarization, the two transverse waves must be out of phase to one another. The necessary phase difference is:

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

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

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?

A battery is connected to a circuit joining it to a lightbulb as shown. Increasing the internal resistance of the battery will:

Exam 7: Physics

A gram-negative bacterium moves along a flat surface. What is the maximum displacement of the bacterium during a 1-hour period if the bacterium moves at a constant speed of 25 µm/s?

Which of the following changes will increase the rate at which a mammalian organism loses body heat to the environment?

The photoelectric effect refers to the ejection of electrons from a material when the material absorbs electromagnetic radiation of sufficient energy. As the frequency of electromagnetic radiation increases, what happens to the kinetic energy of ejected electrons?

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

Uniform magnetic fields created by advanced medical imaging devices most likely come from the:

Thin-film interference is observed when polychromatic light is incident on an interface formed by two semitransparent media. Which of the following best explains why thin-film interference generates a multicolored array when two semitransparent fluids are used?

A cable with a tension of 45 N is used to suspend a 5 kg mass M against a wall. What is the magnitude and direction of the force of friction between the mass and the wall?

Two transverse waveforms (A and B) travel through the same medium with a phase difference of 180°. If the amplitude of the waveforms is ±100 m, what is the combined displacement of both waveforms as waveform A reaches maximum displacement?

An ideal fluid flows within a fixed tube with decreasing cross-sectional area. Assuming constant height and volumetric flow rate, which of the following graphs best illustrates the relationship between fluid pressure and the increase in fluid velocity?

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

Ultrasonic shock wave devices may be used in medical settings to disrupt disease structures located deep in the body. Among other variables, the device user can control the frequency of emitted waveforms. The adjustment of waveform frequency:

An 8-F parallel plate capacitor generates a voltage of 5 V when fully charged. How much charge is stored by the capacitor?

Light from an incandescent lightbulb passes through an ideal linear polarizer. The intensity of the light is 100 lm before passing through the filter, but 50 lm immediately after. Which of the following explains this discrepancy?

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?

Circularly polarized light results from the vector sum of the electric field oscillations of two linearly polarized transverse waves traveling along the same axis. To achieve circular polarization, the two transverse waves must be out of phase to one another. The necessary phase difference is:

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

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

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?

A battery is connected to a circuit joining it to a lightbulb as shown. Increasing the internal resistance of the battery will:

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?