Question 1

A 1-m spring is compressed to half its original length.  What is the potential energy stored within the spring?  (Note:  k = 40 N/m)

Accepted Answer

11ecba2d_131d_fe5e_a3bf_014e4036a092_MD0008_00 Potential energy refers to a form of stored energy that depends on the spatial position or configuration of objects. Essentially, potential energy is the capacity of an object within a system to do work in the future based on some work completed on it in the past. In mechanical systems, potential energy accumulates because of the work performed by a force applied over some distance. The type of potential energy stored within an object is related to the type of force that previously performed work on the object. For example, gravitational potential energy accumulates when the height of an object increases because a force must act against gravity to raise the object. Similarly, stretching or compressing a spring away from its equilibrium point (ie, its position at rest) increases its elastic potential energy (U_el) because displacing a spring requires doing work against the elastic forces resisting displacement. The potential energy stored within a compressed or stretched spring explains why harmonic oscillations take place when the spring is released after being compressed or stretched. The magnitude of potential energy stored within a compressed or stretched spring is a function of spring displacement (x) and the spring constant (k), a measure of the relative elasticity (stiffness) of the spring: 11ecba2d_131d_fe5f_a3bf_83243d783fcb_MD0008_00 In this question, a spring with a length of 1 m is compressed to 0.5 m by a force, which gives the spring a displacement of 0.5 m. The spring constant is 40 N/m, which indicates that maintaining a displacement of 1 m away from the equilibrium position of the spring requires 40 N of force. Consequently, the magnitude of potential energy stored within the spring from a 0.5-m displacement is: 11ecba2d_131e_2570_a3bf_95959616b7e4_MD0008_00 11ecba2d_131e_2571_a3bf_d3a2a44bcda4_MD0008_00 11ecba2d_131e_2572_a3bf_cfddadd09c18_MD0008_00 Therefore, compressing the 1-m spring to half its original length imparts a potential energy into the spring equivalent to 5.0 J (Choice B). Educational objective: Elastic potential energy refers to the potential energy of springs and other elastic objects. Elastic potential energy increases following the application of a stretching or compressing force that displaces a spring from its equilibrium position.

Question 2

Suppose that a simple circuit comprising one voltage source and one metallic resistor yields current I.  If the resistor were replaced with another resistor that is identical except that it has 75% lower conductivity, then I would:

Accepted Answer

11ecba2d_1319_915e_a3bf_1196cd4400f9_MD0008_00 Conductivity (σ) indicates the ease with which electrons flow within the molecular structure of a material. For example, metals conduct electricity more readily than nonmetals because many of the electrons contained within metals are very loosely associated with the positively charged nuclei. In contrast, the conductivity of electrolytic solutions is proportional to the molar concentration of charged atoms. Conductivity is inversely proportional to resistivity (ρ), a variable that quantifies the relative difficulty with which electrons flow through a material: 11ecba2d_1319_915f_a3bf_75e83a222f44_MD0008_00 Both resistivity and conductivity are intensive properties related to the behavior of materials rather than objects. Therefore, modifying the physical dimensions of an electric conductor may influence the rate at which current flows through the conductor, but not the underlying conductivity of the material from which the conductor is formed. Consequently, conductivity is directly proportional to the conductance of an electric conductor just as resistivity is directly proportional to resistance (R) of a resistor. In this question, a voltage source generates a current (I) through one resistor in a simple circuit. Because resistivity and conductivity are inversely proportional, replacing the resistor with another that has ¼ the conductivity of the original is equivalent to increasing the resistivity of the resistor by a factor of 4. Given that the resistor is otherwise identical (ie, the same physical dimensions), the resistance of the resistor will also increase by a factor of 4. Ohm's law relates the current generated by such a simple circuit to the voltage (V) and resistance: 11ecba2d_1319_b870_a3bf_c7e5e0545c4f_MD0008_00 Therefore, replacing the original resistor with another that has ¼ the conductivity (4 times the resistance and resistivity) of the original will decrease the current traveling through the circuit to ¼ its original value (Choice D). Educational objective: Conductivity is an intensive property that quantifies the ease with which current flows through a material acting as an electric conductor. Conductivity is inversely proportional to resistivity.

Question 3

A monoatomic ideal gas is sealed within a container featuring a piston fixed in place at one end.  How will the heat capacity C of the gas change if the piston is allowed to move freely?

Accepted Answer

11ecba2d_131c_9ebd_a3bf_4b3bfdf5f74f_MD0008_00 The molar heat capacity (C) is the amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Kelvin. As such, the heat (Q) associated with n moles of a substance undergoing a temperature change (ΔT) is given by: 11ecba2d_131c_9ebe_a3bf_5b58047af5d4_MD0008_00 Because the internal energy (U) of a monoatomic ideal gas depends on the gas temperature, the molar heat capacity at constant volume (C_V) is not equal to the molar heat capacity at constant pressure (C_P). At constant volume (V), the change in internal energy (ΔU) of the gas is equal to the heat energy: 11ecba2d_131c_c5cf_a3bf_45ae166653b2_MD0008_00 However, at constant pressure (P), ΔU depends on both heat and work (W), because the ideal gas law states that a temperature change from a heat transfer must produce a change in volume (ΔV) under constant pressure: 11ecba2d_131c_c5d0_a3bf_c166c04e7a7a_MD0008_00 11ecba2d_131c_c5d1_a3bf_e3b7cd53e7cd_MD0008_00 If the internal energy change (ie, temperature change) is assumed to be constant between constant volume and constant pressure conditions, the expression for ΔU_V can be substituted into the equation above to give: 11ecba2d_131c_c5d2_a3bf_c30497f0f2eb_MD0008_00 11ecba2d_131c_c5d3_a3bf_9bb3187ed67d_MD0008_00 Moreover, because the ideal gas constant R is equal to 11ecba2d_131c_c5d4_a3bf_23ee850a5abf_MD0008_00 , the equation simplifies to: 11ecba2d_131c_ece5_a3bf_3d7a1cd5c141_MD0008_00 This expression shows that C_V is less than C_P because some heat energy transferred into a gas stored at constant pressure may be converted to pressure-volume work during the expansion or compression of the gas. Therefore, allowing a previously fixed piston to move freely (to maintain constant pressure) will increase the molar heat capacity of a monoatomic ideal gas. (Choices B, C, and D) Heat may transfer into or out of the gas and change the temperature and internal energy of the gas whether the piston is allowed to move or not. However, once the piston becomes mobile, work can occur. As a result, the heat capacity cannot remain constant but will increase. Educational objective: The molar heat capacity of a gas is the amount of heat required to raise the temperature of 1 mole of the gas by 1 degree Kelvin. The molar heat capacity of a gas at constant pressure exceeds the molar heat capacity of a gas at constant volume.

Question 4

A marble rolls down a slope at a velocity of 10 m/s.  If the kinetic energy of the marble is 2 J, what is the mass of the marble?

Accepted Answer

11ecba2d_1323_a3ce_a3bf_85b629fac99b_MD0008_00 Gravitational potential energy and kinetic energy are two forms of energy that an object may possess in mechanical systems. Gravitational potential energy is energy that is stored based on an object's position relative to a reference point within a gravitational field. Consequently, potential energy is often referred to as the "energy of position." Kinetic energy is the energy possessed by an object in motion, whether that object is rotating or moving through space via translational motion. Consequently, kinetic energy may be referred to as the "energy of motion," and the magnitude of the kinetic energy (KE) is determined by the mass (m) and velocity (v) of a moving object: 11ecba2d_1323_a3cf_a3bf_95807c306edf_MD0008_00 The SI unit for energy is the joule (J), where 1 joule is equal to the product of mass (kg) and velocity (m/s) squared (1 J = 1 kg·m²·s⁻²). Certain mechanical processes may convert energy from one form to another. For example, an object falling from a height loses gravitational potential energy and gains kinetic energy. However, the total energy of an object is always conserved. In this question, a marble has 2 J of kinetic energy as it rolls down a slope at a velocity of 10 m/s. Provided that no forces other than gravity act on the marble to cause motion, it can be assumed that all of this kinetic energy was attained through the conversion of its gravitational potential energy. The mass of the marble can be determined by substituting given values and solving for mass in the equation for the kinetic energy of an object: 11ecba2d_1323_cae0_a3bf_1bf1d73edc2f_MD0008_00 11ecba2d_1323_cae1_a3bf_57052f04cef7_MD0008_00 11ecba2d_1323_cae2_a3bf_73754793e31e_MD0008_00 Therefore, the marble has a mass of 0.04 kg, or 40 g (Choice B). Educational objective: Kinetic energy (often expressed in SI units using the joule) is a form of mechanical energy that has a magnitude directly proportional to the mass and the square of the velocity of an object.

Question 5

Blood flows through a vessel in the leg at an average velocity of 10 cm/s. How much glucose passes by a segment of the blood vessel each second if the radius of the blood vessel is 0.20 cm and each 1.0 cm³ of blood contains 1.0 mg of dissolved glucose?

Accepted Answer

11ecba2d_1325_c6cb_a3bf_61834bd391ed_MD0008_00 Fluid flow describes the motion of liquid or gas molecules. For a fluid traveling through a closed conduit (eg, pipe), the volume of fluid flowing past a fixed point per unit time is the volumetric flow rate (Q). Q is equal to the product of the velocity of the fluid (v) and the cross-sectional area (A) of the conduit at a given point: 11ecba2d_1325_eddc_a3bf_13654f673ecb_MD0008_00 Fluid flow may be further characterized by the movement of fluid mass per unit time. For a noncompressible, ideal fluid with constant density (ρ), the mass flow rate (m_f) quantifies the amount of mass flowing past a point within the conduit per unit time: 11ecba2d_1325_eddd_a3bf_e7ee8b54b8e8_MD0008_00 MassTime=VolumeTime⋅MassVolume 11ecba2d_1325_edde_a3bf_eff0d1f46c7d_MD0008_00 The concept of mass flow rate may also be extended to solutes within a fluid, provided that solutes are uniformly distributed through the fluid. In this question, blood with a glucose mass concentration of 1 mg/cm³ (ie, 1 cm³of blood contains 1mg of glucose) flows through a blood vessel with a radius (r) of 0.20 cm. Accordingly, the cross-sectional area of the artery is: 11ecba2d_1325_eddf_a3bf_731b48447a32_MD0008_00 11ecba2d_1325_ede0_a3bf_3dc67fe3c1c1_MD0008_00 Given a blood velocity of 10 cm/s, Q is: 11ecba2d_1325_ede1_a3bf_e925389a7454_MD0008_00 Furthermore, the mass flow rate of glucose (m_glucose) at a segment of the artery is equal to the product of the volumetric flow rate and the blood glucose mass concentration: 11ecba2d_1325_ede2_a3bf_1789ab7749fa_MD0008_00 11ecba2d_1325_ede3_a3bf_694eef678527_MD0008_00 Therefore, 1.3 mg of glucose passes by a segment of the artery each second (Choice D). Educational objective: A mass flow rate refers to the quantity of fluid or solute mass that flows past a fixed point per unit time. For solutes uniformly dissolved within fluids, the mass flow rate of the solute is equal to the product of volumetric flow rate and mass concentration of the solute (ie, mass of solute per unit volume of fluid).

Question 6

The suspension of mass M within a two-pulley system requires a force F.  If pulley B is removed from the system, what is the ratio of the original value of the force with two pulleys to the new value of the force with one pulley?

Accepted Answer

11ecba2d_1321_a7ea_a3bf_3930d92108cd_MD0008_00 Mechanical advantage describes the phenomenon by which forces are amplified using a mechanical device or system. One way to achieve mechanical advantage is by using a pulley system comprising a rope and one or more pulleys (ie, a wheel located on an axle) that may be configured to significantly reduce the force required to transport or support the weight (W) of an object. Pulley systems can include both fixed and load-sharing pulleys. Fixed pulleys do not contribute to mechanical advantage but redirect forces acting along the vertical axis. For example, an upward force may be converted into a downward force as a rope bends around a fixed pulley attached to the ceiling. In contrast, load-sharing pulleys are typically free to move up and down in accordance with the motion of the supported object, and the mechanical advantage of a pulley system is related to the number of load-sharing pulleys that are present. In this question, a force (F_original) is required to support the weight of mass M using a two-pulley system. Pulley A is fixed to the ceiling and therefore redirects the tension within the portion of the rope held by the user. Conversely, pulley B moves freely and acts to split the weight of the mass into two equal tension forces (T₁ and T₂). Tension force T₁ acts on the portion of the rope attaching pulley B to the ceiling, while tension force T₂ acts on the portion of the rope between pulley B and the user such that: 11ecba2d_1321_cefb_a3bf_73ec4ee08678_MD0008_00 As a result, the inclusion of pulley B within the system yields a mechanical advantage of two. Consequently, removing pulley B from the system will double the magnitude of force required to support the weight of the mass. 11ecba2d_1321_cefc_a3bf_0b850fcd460a_MD0008_00 Therefore, the ratio of the original force to the ratio of the new force (F_new) is 1:2 (Choice B). Educational objective: Mechanical advantage describes the force amplification that occurs through the use of a mechanical system or device. The mechanical advantage of pulley systems is related to the number of load-sharing pulleys but unrelated to the number of fixed pulleys that redirect forces.

Question 7

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

Accepted Answer

11ecba2d_131a_a2d5_a3bf_c562407588ac_MD0008_00 Multiple translational forces, each with unique magnitude and direction, may simultaneously act on the same object. According to Newton's second law, an object will accelerate if the net force acting along each axis of the x,y-coordinate system is a nonzero quantity. Conversely, equilibrium occurs when the net force acting along each axis of the x,y-coordinate system equals zero such that the object does not accelerate. Dynamic equilibrium is a special type of equilibrium that describes an object moving at a constant velocity without acceleration. Like other forms of equilibria, dynamic equilibrium may result from either the absence of translational forces or a perfect balance between antagonistic forces. Provided that the x- and y-components of each force vector are known, free-body diagrams can be used to assess equilibrium resulting from multiple forces, where: 11ecba2d_131a_c9e6_a3bf_99a81dd76ad7_MD0008_00 11ecba2d_131a_c9e7_a3bf_f32674b3f74d_MD0008_00 For example, a mass sliding down an incline at constant velocity is acted on by multiple forces. To simplify the analysis of the forces, the vector components of force can be classified as acting either parallel (||) or perpendicular (⊥) to the surface of the incline, such that: 11ecba2d_131a_c9e8_a3bf_4139627e2174_MD0008_00 11ecba2d_131a_c9e9_a3bf_e954949ef349_MD0008_00 Accordingly, for a block to slide down an incline with nonzero friction at constant velocity requires that the frictional force (F_f) resisting motion be equal and opposite to the component of the gravitational force that acts parallel to the surface of the incline (F_||): 11ecba2d_131a_c9ea_a3bf_5932ccf2ebe5_MD0008_00 11ecba2d_131a_c9eb_a3bf_5b382839bee2_MD0008_00 Furthermore, the component of gravitational force that acts parallel to the surface of the incline may be expressed in terms of the weight of the object (M∙g) and the angle of incline (θ) as: 11ecba2d_131a_f0fc_a3bf_e14026c3cd39_MD0008_00 11ecba2d_131a_f0fd_a3bf_bd93ccef06b4_MD0008_00 Therefore, the frictional force acting on a mass sliding down an incline in dynamic equilibrium is equal in magnitude to the weight of the object multiplied by the sine of the incline angle (Choice A). Educational objective: Dynamic equilibrium occurs when the sum of all forces acting on an object in motion is equal to zero (ie, the object moves but does not accelerate). Free-body diagrams are used to assess the directional components of translational forces.

Question 8

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?

Accepted Answer

11ecba2d_131d_6217_a3bf_5195d0ee8e59_MD0008_00 Mechanical work refers to the transfer of energy in or out of a system that occurs as the result of the application of a force (F) over some distance (d): 11ecba2d_131d_6218_a3bf_87c5461d43ad_MD0008_00 The SI unit for work is the joule (J), where 1 J is equal to 1 newton (N) of force exerted over 1 meter (m) of distance (1 J = 1 N∙m). In a graph of force versus distance, the area under the curve is equal to work associated with the displacement because the F ∙ d component of the above equation is equal to a y-axis value (a force) multiplied by an x-axis value (a distance). In this question, the graph shows a variable force being applied to the end of a spring to stretch it from a length of 15 cm to a length of 35 cm. When stretching the spring from 20 cm to 30 cm long, the variable force acts over a distance of 10 cm. Converting this distance to standard units results in: 11ecba2d_131d_8929_a3bf_899f746f487d_MD0008_00 In the graph of force versus distance, the area under the curve can be calculated by visualizing the total area as the sum of the areas (A) of two geometric shapes (one triangle and one rectangle) that both have a base 0.10 m in length. The combined area of these two shapes yields the work: 11ecba2d_131d_892a_a3bf_6172f6aa129f_MD0008_00 11ecba2d_131d_892b_a3bf_7778bb141dd7_MD0008_00 11ecba2d_131d_892c_a3bf_fdd3db785014_MD0008_00 11ecba2d_131d_892d_a3bf_9768a42686c3_MD0008_00 Therefore, stretching the spring from a length of 20 cm to 30 cm through the application of a variable force is associated with mechanical work equal to 25 J in magnitude (Choice A). Educational objective: Work describes the energy transfer into or out of a system that takes place as the result of a force acting through a distance. In a graph of force versus distance, the work associated with a given displacement can be derived from the graph by evaluating the total area under the curve.

Question 9

The figure above shows a board placed on top of a fulcrum that is balanced by three masses (M₁, M₂, and M₃). If the mass of M₁ and M₂ are 60 kg and 30 kg, respectively, what is the mass of M₃?

Accepted Answer

11ecba2d_1322_6b3e_a3bf_9b62af2e2341_MD0008_00 Torque is the tendency of an applied force to cause the rotation of an object around a pivot point located at some radial distance from where the force is applied. The magnitude of torque (τ) is expressed in terms of the magnitude of the applied force (F), the radial distance (r), and the angle (θ) between F and r: 11ecba2d_1322_6b3f_a3bf_3fffe1511db9_MD0008_00 τ = r⋅F sinθ Because torque increases as a force of equal magnitude is applied at greater distances from the pivot point, a mechanical advantage is observed in the context of rotational forces applied to a lever arm. However, when the sum of all torques acting on an object is equal to zero, an object is in rotational equilibrium (no rotation occurs): 11ecba2d_1322_6b40_a3bf_09a6bdd0a9c7_MD0008_00 ∑Torques=0 In this question, a board placed on a fulcrum is balanced by three separate masses. Each mass exerts a force on the board due to its weight. The resulting torque exerted on the left side of the fulcrum by the weight of M₁ is counterbalanced by the two torques exerted on the right side of the fulcrum by the weights of M₂ and M₃: 11ecba2d_1322_6b41_a3bf_e3f5cb1952c5_MD0008_00 Substituting the expressions for torque into the summation equation gives: 11ecba2d_1322_6b42_a3bf_613ec98c15a1_MD0008_00 Representing each torque as a product of weight and radial distance from the fulcrum yields: 11ecba2d_1322_6b43_a3bf_1d6af5b060ca_MD0008_00 Because the acceleration due to gravity g cancels from all terms and because all angles are equal to 90° (sin 90° = 1), the expression simplifies to: 11ecba2d_1322_9254_a3bf_d19e2e9d48d7_MD0008_00 11ecba2d_1322_9255_a3bf_a53386193195_MD0008_00 Using the values of M₁, M₂, r₁, and r₂ provided in the question yields: 11ecba2d_1322_9256_a3bf_293e4c739678_MD0008_00 11ecba2d_1322_9257_a3bf_01fed4b24a91_MD0008_00 11ecba2d_1322_9258_a3bf_55113e49a4d8_MD0008_00 11ecba2d_1322_b969_a3bf_7bbcc50683e4_MD0008_00 Therefore, the mass of M₃ must be approximately 17 kg for the board to remain in rotational equilibrium (Choice B). Educational objective: Torque is the tendency of an applied force to cause an object to rotate around a pivot point located at some radial distance from where the force is applied. Rotational equilibrium occurs when the sum of all torques acting on an object is equal to zero and results in no rotation.

Question 10

Compared to other diffraction techniques, the advantage of x-ray diffraction is that it enables:

Accepted Answer

11ecba2d_1320_6f66_a3bf_bb5b1f73ac91_MD0008_00 Not all forms of electromagnetic radiation undergo diffraction when incident upon one or more slits. For example, x-rays are a form of electromagnetic radiation that cannot undergo classic slit diffraction because the wavelengths of x-rays range from 1 × 10⁻¹¹ m to 10 × 10⁻¹¹ m, which is always exceeded by the lengths of industrially fabricated slits. However, the wavelength of some x-rays is comparable to the typical distance between atoms within the molecular structure of most materials. Consequently, exposing a sample of a purified and crystallized material to x-ray radiation may produce a diffraction pattern unique to that particular substance. When two x-ray waveforms approach and depart a crystalline lattice at an identical incident angle, the waveforms may constructively interfere such that a bright spot is observed on a piece of film distant to the material. The occurrence of constructive interference is a function of the incident angle (θ), the distance between atoms (d), and an integer multiple (n = ±1, ±2, ±3…) of the x-ray wavelength (λ): 11ecba2d_1320_9677_a3bf_8f97570f6d0e_MD0008_00 Because the crystalline lattice of many materials exceeds the complexity of simple crystals, the pattern of bright spots produced on the photographic film is indicative of a molecule's three-dimensional structure and its packing orientation within the crystal lattice. (Choice B) Calculating the kinetic energy of electrons ejected due to the absorption of energy from incident light is applicable in modeling the photoelectric effect, but x-ray diffraction does not cause the ejection of electrons. (Choice C) Using a reference substance with known three-dimensional structure might allow the wavelength of x-ray waveforms to be determined experimentally using x-ray crystallography. However, other diffractive techniques can more easily determine the wavelength of incident light. (Choice D) Electromagnetic radiation can be passed through a linear polarization filter to reveal the original polarization. However, this phenomenon does not involve diffraction and is not specific to x-rays. Educational objective: X-rays diffract within molecules because the space between atoms is comparable to the wavelength of x-rays. X-ray diffraction through a sample of a purified and crystallized material can be used to determine its three-dimensional molecular structure and packing.

Question 11

Which of the following expressions correctly compares the energies of visible light (E_visible), microwaves (E_microwave), and radio waves (E_radio)?

Accepted Answer

11ecba2d_131c_2989_a3bf_05cc8646d6f9_MD0008_00 Electromagnetic radiation refers to oscillating electric and magnetic fields that propagate radiant energy through a medium. The electromagnetic spectrum describes classifications of electromagnetic radiation that differ from one another in terms of waveform characteristics, occurrence in the natural world, and technological utility. The electromagnetic spectrum is typically arranged in order of frequency (f) or wavelength (λ). Because the frequency and wavelength of electromagnetic radiation are inversely proportional, arranging the electromagnetic spectrum from largest wavelength (radio waves) to smallest wavelength (gamma rays) is equivalent to arranging the electromagnetic spectrum from smallest frequency to largest frequency. Alternately, the electromagnetic spectrum may also be ordered in terms of the energy (E) associated with a given electromagnetic waveform, which can be expressed in terms of either electromagnetic frequency or wavelength using Planck's constant (h) and the speed of light (c) as: 11ecba2d_131c_298a_a3bf_37bb0f5c3471_MD0008_00 Accordingly, the energy of electromagnetic radiation is inversely proportional to wavelength and directly proportional to frequency. Consequently, the order of electromagnetic radiation types arranged from lowest energy to highest energy is: 11ecba2d_131c_298b_a3bf_2bf0c91e352b_MD0008_00 adio waves(Choice B). Educational objective: The electromagnetic spectrum consists of radiation types with different wavelengths, frequencies, and energies. Ordering the electromagnetic spectrum in terms of decreasing wavelength is equivalent to ordering the electromagnetic spectrum in terms of increasing energy.

Question 12

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?

Accepted Answer

11ecba2d_1326_6315_a3bf_0b91326e1f62_MD0008_00 The sign (positive or negative) and quantity of electric charge influences the way charged particles interact. For example, charges with the same sign exert repulsive forces against each other whereas charges with opposite signs are attracted to one another. Coulomb's law states that the electric force (F) between two charges is directly proportional to the charge of each particle (q₁, q₂) but inversely proportional to the square of the distance (r) separating the charges. This relationship is expressed as an equation via Coulomb's constant (k = 8.99 × 10⁹ N·m²·C⁻²): 11ecba2d_1326_6316_a3bf_856743113d7e_MD0008_00 In this question, each of the four charges fixed along the line experiences an electric force from the other three nearby charges. Depending on the sign of each charge, the multiple electric forces within this setup are either attractive or repulsive. Specifically, particle B experiences three forces: a repulsive electric force from particle A (F_AB) and attractive electric forces from both particle C (F_BC) and particle D (F_BD). Each of the forces acting on particle B is oriented along the same line toward particles C and D (ie, to the right). Furthermore, F_AB has the largest magnitude in this setup because the charges of particles A and B (+4q and +3q, respectively) are relatively large and the distance between particles A and B (r_AB) is relatively small. Consequently, the sum of electric forces acting on particle B is the largest in magnitude such that particle B accelerates most rapidly once the charges are released. (Choice A) Particle A will not accelerate to the left as rapidly as particle B accelerates to the right because particle A is also attracted to particles C and D, which are located to the right of particle A. (Choices C and D) Neither particle C nor D will accelerate as rapidly as particle B because the electric charges of particles C and D are smaller in magnitude than the charges of particles A and B. Educational objective: The magnitude and direction of the attractive or repulsive forces exerted between electric charges are directly proportional to the charge of each particle but inversely proportional to the square of the distance separating the charges.

Question 13

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?

Accepted Answer

11ecba2d_1323_2e9a_a3bf_8158e98cfcde_MD0008_00 Unlike scalar quantities, vectors contain both a magnitude and a direction. Vectors may be added to or subtracted from other vectors. Consequently, a vector located within a two-dimensional coordinate system can be represented as two vector components in which one vector component is oriented along the x-axis and the other is oriented along the y-axis. Mathematically, the overall (resultant) vector is the hypotenuse (longest side) of a right triangle in which the x- and y-components of the vector form the adjacent and opposite sides. Furthermore, the angle (θ) between the overall vector and its adjacent, horizontal (x-axis) component can be used with trigonometric ratios to calculate the magnitude of the horizontal component (V_x) and vertical component (V_y) of the initial vector (V): 11ecba2d_1323_2e9b_a3bf_5700359cce4a_MD0008_00 11ecba2d_1323_2e9c_a3bf_930696815fce_MD0008_00 In this question, the cannonball is launched with an initial speed of 30 m/s from a cannon angled 60° above the horizontal (ie, the ground). When a convenient orientation is selected for an xy-coordinate system in which the ground is parallel to the x-axis, the cannonball's velocity vector (V) vector is oriented 60° above the x-axis with a magnitude (length) of 30 m/s. Accordingly, the magnitudes of the horizontal (V_x) and vertical components (V_y) of velocity can be calculated as: 11ecba2d_1323_55ad_a3bf_934fb9d8d2f2_MD0008_00 Therefore, the horizontal component of the cannonball's initial velocity has a magnitude of 15 m/s, and the vertical component of the cannonball's initial velocity has a magnitude of 25 m/s (Choice C). Educational objective: Vector quantities can be separated into fundamental component vectors using trigonometric ratios. The horizontal and vertical components of an object's velocity can be calculated using the magnitude of the velocity and its angle above the horizontal.

Question 14

Ideal fluids are used to model the behavior of fluids both in motion and at rest.  Which one of the following assumptions does NOT apply to an ideal fluid?

Accepted Answer

11ecba2d_131f_36e3_a3bf_c9ca68bf0771_MD0008_00 Fluids are substances that have no fixed shape and readily conform to the dimensions of the container in which they are placed. Fluids that are considered ideal share the following attributes: No viscosity: Friction between fluid molecules is negligible such that applied shearing forces (ie, gravity acting on a fluid pouring out of a glass) cause instantaneous, uniform acceleration of the fluid (Choice C). Laminar flow: The fluid flows in parallel layers, each with equal velocity. No interaction between each layer occurs, ensuring uniform velocity within the fluid at all points (Choice A). Incompressible: The density of the fluid is modified by neither external forces nor its own weight when oriented in a fluid column (Choice D). Ideal fluid behavior serves as a model for many practical applications of fluids. For example, water and mercury are both relatively incompressible, which allows both fluids to be used within a simple fluid barometer to reliably measure atmospheric pressure (P_atm). Furthermore, ideal fluid behavior is essential for the application of Bernoulli's equation, which mathematically describes the conservation of energy in fluids in terms of fluid pressure (P), density (ρ), and velocity (v) between two points (A and B) within a conduit (ie, the container through which a fluid flows): 11ecba2d_131f_36e4_a3bf_0b1349274ff4_MD0008_00 Bernoulli's equation predicts changes in fluid flow and pressure that occur following a change in fluid height (h) or conduit geometry. For example, Bernoulli's equation dictates that the pressure of an ideal fluid will decrease as fluid velocity increases and the height remains constant. Consequently, changes in fluid kinetic energy must be accompanied by changes in pressure energy so that overall energy is conserved. Therefore, the statement that fluid pressure is not influenced by fluid velocity is not true for an ideal fluid. Educational objective: Ideal fluids are totally nonviscous and incompressible; they exhibit smooth, laminar flow without viscosity. Bernoulli's equation dictates that an increase in the velocity of an ideal fluid is accompanied by a decrease in fluid pressure.

Question 15

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

Accepted Answer

11ecba2d_1321_32b8_a3bf_c99aba32d895_MD0008_00 The primary optical components of the eye are the cornea and lens, both of which form a biological converging lens that focuses incoming light rays onto the retina, a structure analogous to the film or sensor within a camera. Refractive errors occur when the eye is unable to focus incoming light rays onto the retina, producing unclear images. Refractive errors are caused by a mismatch between the physical dimensions (eg, length) and optical properties of the eye. For example, hyperopia (ie, farsightedness) is a condition that results when the optical power (S) of the eye is insufficient to refract light rays from nearby objects. A hyperopic eye cannot sufficiently refract light rays that approach the eye at an angle (eg, light rays from nearby objects), producing an image of nearby objects that is sharpest at a location behind the retina. Hyperopia is corrected by placing a converging lens in front of the eye, forming an optical system with greater optical power. Consequently, images of nearby objects shift closer to the lens and onto the retina after a corrective lens is placed in front of the hyperopic eye. (Choice A) Myopia (ie, nearsightedness) describes a visual condition in which the eye forms an image of distant objects at a focal point in front of the retina. Correcting myopia (not hyperopia) shifts the image away from the lens. (Choice C) Spherical aberration refers to the optical deficiencies of lenses with perfectly spherical surfaces. The surfaces of the cornea or lens are not perfectly spherical, so no spherical aberration occurs. (Choice D) Placing a converging lens in front of the eye increases the optical power of the eye, allowing it to properly focus light rays emitted from or reflected off of nearby objects. Educational objective: Hyperopia describes the refractive error that results in an individual being unable to see nearby objects. Hyperopia is caused by the optical power of the eye being insufficient relative to the length of the eye; the condition is corrected by placing a converging lens in front of the eye.

Question 16

A concave mirror has a 4-m radius of curvature.  This mirror will focus distant objects at a location that is approximately:

Accepted Answer

11ecba2d_131a_2da1_a3bf_27fed621c1e8_MD0008_00 Spherical mirrors are a specific class of curved reflective surfaces shaped like a portion of a sphere. Spherical mirrors are further classified as concave (converging) or convex (diverging). The reflective surface of concave (converging) mirrors curves inward, away from the object and incident (incoming) light. Conversely, the reflective surface of convex (diverging) mirrors curves outward, toward the object and incident light. The focal length (f) of a concave mirror is the distance in front of the mirror at which reflected light rays converge to form an image. Concave mirrors will form an inverted, real image when the reflected object is located outside of the focal length, but when the object is placed inside the focal length of a concave mirror, an upright, virtual image is formed. In contrast, convex mirrors always form an upright, virtual image. Ignoring spherical aberrations, the focal length of a spherical mirror is equal to half the radius of curvature (r) (Choice A), where r is the distance between the midpoint of the mirror surface and the center of the imaginary sphere of which the mirror surface is only a portion: 11ecba2d_131a_2da2_a3bf_434fb2bf692e_MD0008_00 The equation for focal length is identical for both convex and concave mirrors. Consequently, a concave mirror and a convex mirror with the same radius of curvature will have identical focal length magnitudes. However, the point of focus is positioned in front of a concave mirror and behind a convex mirror (Choices B and D). This question introduces a concave mirror with a radius of curvature of 4 m. The focal length of the concave mirror may be calculated as: 11ecba2d_131a_2da3_a3bf_3d0ed51577b3_MD0008_00 Because concave mirrors converge distant objects to form real, inverted images beyond the focal length of the mirror, this concave mirror will focus the light rays emanating from a distant object at a location that is at least 2 m in front of the mirror. Educational objective: Concave (converging) spherical mirrors create real, inverted images of objects placed outside of mirror focal length. The focal length of a concave spherical mirror is half the radius of curvature and is positioned in front of the mirror.

Question 17

That the spherical aberration of a converging lens is corrected by reducing the thickness of the lens periphery means that the light rays emerging from aberrant converging lenses:

Accepted Answer

11ecba2d_131f_d325_a3bf_0db831587e5d_MD0008_00 An ideal lens generates an image of an object at a single focal point, regardless of the locations at which the light rays enter and exit the lens. Spherical aberration describes the phenomenon by which real lenses' perfectly rounded (ie, spherical) surfaces do not produce an image at a single point, but rather at a series of focal points. In converging lenses, the location of each focal point is related to the distance from the principal axis (ie, the lens center) at which light enters and exits the lens. Spherical aberration is most pronounced among rays entering and exiting the lens periphery (ie, distant from the principal axis). Furthermore, correcting spherical aberration in converging lenses requires using an aspherical lens in which the thickness of the lens periphery is decreased relative to a perfectly rounded lens. Because reducing the thickness of the lens periphery will lead to less refraction of light, light rays exiting the periphery of a spherical converging lens can be said to refract excessively, converging on a focal point that is too close to the lens. (Choice A) Spherical aberration in a converging lens is characterized by refractive events that focus light emerging at the lens periphery more dramatically than light emerging closer to the lens center. Therefore, light is excessively, not insufficiently, refracted at the lens periphery. (Choice B) All lens and mirror aberrations describe a failure of optical instruments to converge or diverge light rays uniformly. (Choice D) Chromatic dispersion describes the failure of a lens to focus multicolored light onto a single point. Chromatic dispersion in converging lenses is corrected by using a diverging lens to increase the thickness of the lens periphery. Educational objective: Spherical aberration occurs when lenses with perfectly rounded surfaces focus light at multiple focal points. Spherical aberration is most pronounced among light rays entering and exiting the periphery of converging lenses.

Question 18

A large number of monoatomic ideal gas molecules are stored within a closed container at a temperature of 200 K. What is the average translational kinetic energy of the individual gas molecules? (Note: Use Boltzmann's constant k = 1.381 × 10⁻²³ J/K.)

Accepted Answer

11ecba2d_1324_4013_a3bf_8d60a42bea57_MD0008_00 The kinetic molecular model describes macroscopic characteristics of gases that are related to the constant motion of freely moving gas molecules. The kinetic molecular model assumes that a rigid, closed container contains a large number N of monoatomic ideal gas molecules. The total kinetic energy (K_tr) of all gas molecules is related to the mass (m) of each molecule and the average value of velocity squared 11ecba2d_1324_4014_a3bf_7b264f15ad5b_MD0008_00 : 11ecba2d_1324_4015_a3bf_dd5a59e4d39f_MD0008_00 Applying the kinetic molecular model to a rigid cubic container allows the pressure (P) of the gas to be stated in terms of the total kinetic energy of all gas molecules and the container volume (V): 11ecba2d_1324_4016_a3bf_7bccec532dbb_MD0008_00 11ecba2d_1324_4017_a3bf_2df991023c43_MD0008_00 Furthermore, Boltzmann's constant (k = 1.381 × 10⁻²³ J/K) may be used to restate the ideal gas law in terms of the behavior of individual gas molecules as: 11ecba2d_1324_6728_a3bf_a9a4164ff4a7_MD0008_00 Combining the kinetic molecular model's expressions for ideal gas behavior and pressure produces an expression for the average kinetic energy 11ecba2d_1324_6729_a3bf_31d32f7e823a_MD0008_00 of an individual gas molecule at a given temperature in Kelvin (K): 11ecba2d_1324_672a_a3bf_69d0d30093ad_MD0008_00 11ecba2d_1324_672b_a3bf_b316041932d4_MD0008_00 11ecba2d_1324_672c_a3bf_8b7b43e2277b_MD0008_00 In this question, ideal gas molecules are stored within a fixed container at a temperature of 200 K. Therefore, the average translational kinetic energy of an individual monoatomic ideal gas molecule is: 11ecba2d_1324_672d_a3bf_c5c05d4c26dd_MD0008_00 11ecba2d_1324_8e3e_a3bf_2bfdd0d6b55f_MD0008_00 11ecba2d_1324_8e3f_a3bf_c3586ddaa3da_MD0008_00 11ecba2d_1324_8e40_a3bf_672c7dbc6dfe_MD0008_00 Therefore, the average kinetic energy of an ideal gas molecule stored within a closed container at 200 K is 4.2 × 10⁻²¹ J (Choice D). Educational objective: The kinetic molecular model uses the behavior of individual gas molecules to explain the macroscopic characteristics of gases. Boltzmann's constant can be used to determine the average translational kinetic energy of a single ideal gas molecule at a given temperature.

Question 19

Two identical balls of equal mass m₁ and m₂ are placed at rest at the top of separate hills. How do the velocities v₁ and v₂ of the balls compare, measured after each has rolled down to the bottom of its respective hill? (Note: Assume the absence of friction and negligible rotational kinetic energy.)

Accepted Answer

11ecba2d_1325_0372_a3bf_b5fdc9fa616e_MD0008_00 In mechanical systems, the total energy (U) of an object is quantified by the sum of kinetic energy (KE) and potential energy (PE): 11ecba2d_1325_0373_a3bf_8bb6bf8b9759_MD0008_00 KE describes the energy of translational or rotational motion. Specifically, translational kinetic energy refers to the energy associated with the motion of an object through three-dimensional space and relates to the mass (m) and velocity (v) of an object: 11ecba2d_1325_2a84_a3bf_3108d42293d7_MD0008_00 PE describes the stored energy associated with an object's configuration (eg, a compressed spring) or relative position. Gravitational potential energy describes the energy an object possesses when placed at some distance above the Earth's surface, and it relates to the object mass (m), gravitational constant (g = 10 m/s²), and height (h): 11ecba2d_1325_2a85_a3bf_df87675aff33_MD0008_00 Conservation of energy requires that an object's total energy observed between two points (A and B) remains the same, but contributions from potential energy may convert to kinetic energy (or vice versa) within mechanical systems: 11ecba2d_1325_2a86_a3bf_357e50550825_MD0008_00 In this question, each of two balls of equal mass (m₁ and m₂) is at rest at the top of a hill, each with a different height (h and 2h). Based on the conservation of energy, all the potential energy stored within the balls at the top of the hills is converted into kinetic energy as the balls reach the bottom of the hills (ie, the earth's surface) such that: 11ecba2d_1325_2a87_a3bf_672c40aafc52_MD0008_00 The velocity of each ball may be determined by rearranging and canceling terms within the equations above: 11ecba2d_1325_2a88_a3bf_b90febbea148_MD0008_00 Consequently, the ratio between the velocity of each ball is: 11ecba2d_1325_5199_a3bf_8933ef1eb02c_MD0008_00 11ecba2d_1325_519a_a3bf_f3cff9a3a7a3_MD0008_00 Therefore, placing a ball on a hill at half the half the height of an equal ball results in the first ball having 70% of the velocity of the second ball upon reaching the bottom of the hill (Choice B). Educational objective: Translational kinetic energy is the energy of motion whereas gravitational potential energy describes the energy of position. Due to the conservation of energy, in the absence of friction, the total energy of an object along a path remains constant, but contributions from potential energy may convert to kinetic energy (or vice versa).

Question 20

A cube with a side length of 5 cm floats on the surface of water. If 4/5 of the cube volume floats above the surface of the water, what is the density of the cube? (Note: Density of water = 1,000 kg/m³.)

Accepted Answer

11ecba2d_131b_662e_a3bf_edc6133c9477_MD0008_00 Archimedes' principle states that the magnitude of the buoyant force (F_B) that acts on a floating object is equal to the weight of the fluid displaced by the object. Consequently, the buoyant force can be expressed in terms of the acceleration of gravity (g) and the displaced fluid's density (ρ_fluid) and volume (V_fluid): 11ecba2d_131b_662f_a3bf_63d555e1b53b_MD0008_00 Furthermore, the buoyant force has an equal magnitude and opposite direction to the weight (W_O) of the floating object such that: 11ecba2d_131b_8d40_a3bf_b7fc9eb72209_MD0008_00 11ecba2d_131b_8d41_a3bf_e954c96108f1_MD0008_00 Given that the mass of the floating object (m_object) can be expressed as a product of the object density (ρ_object) and object volume (V_object), it follows that: 11ecba2d_131b_8d42_a3bf_c16222f599f5_MD0008_00 11ecba2d_131b_8d43_a3bf_9d30ef08ec63_MD0008_00 Rearranging the equation above yields an expression that relates the ratio of the object and fluid densities to the ratio of the displaced fluid volume and the object volume: 11ecba2d_131b_8d44_a3bf_9367148e82fd_MD0008_00 Because V_fluid depends on the buoyancy of the object, V_fluid = x · V_object, where x is the fraction of the object volume that is submerged in the fluid. Therefore, the V_fluid/V_object ratio equals x. 11ecba2d_131b_8d45_a3bf_f5f47536d596_MD0008_00 In this question, 4/5 of the cube volume floats above the surface of the water. This means that 1/5 of the cube volume is submerged below the surface of the water, and the cube displaces a volume of water that is 1/5 its own volume: 11ecba2d_131b_b456_a3bf_e1d6d037539a_MD0008_00 Given that the density of water is 1,000 kg/m³, the density of the object can be calculated as: 11ecba2d_131b_b457_a3bf_5d31b8b1da6b_MD0008_00 11ecba2d_131b_b458_a3bf_f17c028901bc_MD0008_00 Therefore, the density of a floating cube that displaces 1/5 its volume in water is 200 kg/m³ (Choice A). Educational objective: Archimedes' principle states that the buoyant force acting on a floating object is equal to the weight of the fluid displaced by the object. The fraction of the object submerged is related to the density of the object and the density of the fluid on which the object floats.

Exam 7: Physics

A 1-m spring is compressed to half its original length. What is the potential energy stored within the spring? (Note: k = 40 N/m)

Suppose that a simple circuit comprising one voltage source and one metallic resistor yields current I. If the resistor were replaced with another resistor that is identical except that it has 75% lower conductivity, then I would:

A monoatomic ideal gas is sealed within a container featuring a piston fixed in place at one end. How will the heat capacity C of the gas change if the piston is allowed to move freely?

A marble rolls down a slope at a velocity of 10 m/s. If the kinetic energy of the marble is 2 J, what is the mass of the marble?

Blood flows through a vessel in the leg at an average velocity of 10 cm/s. How much glucose passes by a segment of the blood vessel each second if the radius of the blood vessel is 0.20 cm and each 1.0 cm³ of blood contains 1.0 mg of dissolved glucose?

The suspension of mass M within a two-pulley system requires a force F. If pulley B is removed from the system, what is the ratio of the original value of the force with two pulleys to the new value of the force with one pulley?

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

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?

The figure above shows a board placed on top of a fulcrum that is balanced by three masses (M₁, M₂, and M₃) . If the mass of M₁ and M₂ are 60 kg and 30 kg, respectively, what is the mass of M₃?

Compared to other diffraction techniques, the advantage of x-ray diffraction is that it enables:

Which of the following expressions correctly compares the energies of visible light (E_visible) , microwaves (E_microwave) , and radio waves (E_radio) ?

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?

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?

Ideal fluids are used to model the behavior of fluids both in motion and at rest. Which one of the following assumptions does NOT apply to an ideal fluid?

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

A concave mirror has a 4-m radius of curvature. This mirror will focus distant objects at a location that is approximately:

That the spherical aberration of a converging lens is corrected by reducing the thickness of the lens periphery means that the light rays emerging from aberrant converging lenses:

A large number of monoatomic ideal gas molecules are stored within a closed container at a temperature of 200 K. What is the average translational kinetic energy of the individual gas molecules? (Note: Use Boltzmann's constant k = 1.381 × 10⁻²³ J/K.)

A cube with a side length of 5 cm floats on the surface of water. If 4/5 of the cube volume floats above the surface of the water, what is the density of the cube? (Note: Density of water = 1,000 kg/m³.)

Exam 7: Physics

A 1-m spring is compressed to half its original length. What is the potential energy stored within the spring? (Note: k = 40 N/m)

Suppose that a simple circuit comprising one voltage source and one metallic resistor yields current I. If the resistor were replaced with another resistor that is identical except that it has 75% lower conductivity, then I would:

A monoatomic ideal gas is sealed within a container featuring a piston fixed in place at one end. How will the heat capacity C of the gas change if the piston is allowed to move freely?

A marble rolls down a slope at a velocity of 10 m/s. If the kinetic energy of the marble is 2 J, what is the mass of the marble?

Blood flows through a vessel in the leg at an average velocity of 10 cm/s. How much glucose passes by a segment of the blood vessel each second if the radius of the blood vessel is 0.20 cm and each 1.0 cm3 of blood contains 1.0 mg of dissolved glucose?

The suspension of mass M within a two-pulley system requires a force F. If pulley B is removed from the system, what is the ratio of the original value of the force with two pulleys to the new value of the force with one pulley?

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

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?

The figure above shows a board placed on top of a fulcrum that is balanced by three masses (M1, M2, and M3) . If the mass of M1 and M2 are 60 kg and 30 kg, respectively, what is the mass of M3?

Compared to other diffraction techniques, the advantage of x-ray diffraction is that it enables:

Which of the following expressions correctly compares the energies of visible light (Evisible) , microwaves (Emicrowave) , and radio waves (Eradio) ?

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?

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?

Ideal fluids are used to model the behavior of fluids both in motion and at rest. Which one of the following assumptions does NOT apply to an ideal fluid?

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

A concave mirror has a 4-m radius of curvature. This mirror will focus distant objects at a location that is approximately:

That the spherical aberration of a converging lens is corrected by reducing the thickness of the lens periphery means that the light rays emerging from aberrant converging lenses:

A large number of monoatomic ideal gas molecules are stored within a closed container at a temperature of 200 K. What is the average translational kinetic energy of the individual gas molecules? (Note: Use Boltzmann's constant k = 1.381 × 10−23 J/K.)

A cube with a side length of 5 cm floats on the surface of water. If 4/5 of the cube volume floats above the surface of the water, what is the density of the cube? (Note: Density of water = 1,000 kg/m3.)

Blood flows through a vessel in the leg at an average velocity of 10 cm/s. How much glucose passes by a segment of the blood vessel each second if the radius of the blood vessel is 0.20 cm and each 1.0 cm³ of blood contains 1.0 mg of dissolved glucose?

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

The figure above shows a board placed on top of a fulcrum that is balanced by three masses (M₁, M₂, and M₃) . If the mass of M₁ and M₂ are 60 kg and 30 kg, respectively, what is the mass of M₃?

Which of the following expressions correctly compares the energies of visible light (E_visible) , microwaves (E_microwave) , and radio waves (E_radio) ?

A large number of monoatomic ideal gas molecules are stored within a closed container at a temperature of 200 K. What is the average translational kinetic energy of the individual gas molecules? (Note: Use Boltzmann's constant k = 1.381 × 10⁻²³ J/K.)

A cube with a side length of 5 cm floats on the surface of water. If 4/5 of the cube volume floats above the surface of the water, what is the density of the cube? (Note: Density of water = 1,000 kg/m³.)