MCAT Physics and Math Missed Problems and Concept Checks

3. How does power relate to current, voltage, and resistance?

P = IV = (I^2)R = (V^2)/R

3. Why is the electrical potential at points along the perpendicular bisector of a dipole 0?

The perpendicular bisector of an electric dipole is an equipotential plane that is perpendicular to the axis of the dipole. As such, the equation V = kqd/r2 cos is necessarily equal to 0 because cos 90 = 0.

3. Draw the field lines for the electric field generated by an alpha particle (42He2+):

+2 charge with field lines radiating outward.

6. Given the cycle shown, what is the total work done by the gas during the cycle? (see Figure, #6 thermodynamics) A. -10 J B. 0 J C. 7.5 J D. 17.5 J

6. C The total work done by the cycle is the sum of the work of paths A, B, and C, or the area within the cycle. Because the area bounded by A, B, and C is a triangle with a base of 5 m3 and a height of 3 Pa, we can calculate the area as 1/2 (5 m3)(3 Pa) = 7.5 J. Clockwise loops tend to do positive work on the environment, while counterclockwise loops do negative work.

When a pitcher throws the baseball and releases it with spin, depending upon the orientation of this spin, the ball will "break" in some direction. In other words, a breaking ball is a pitch that does not travel straight like a fastball as it approaches the batter. Which of the following scenarios accurately describes the phenomenon of "breaking"? Choose 1 answer: A A baseball moving to the right and spinning vertically counterclockwise will experience an upward lift. B A baseball moving to the left and spinning horizontally counterclockwise will experience an upward lift. C A baseball moving to the right and spinning vertically clockwise will experience a deviation to the right of its original path. D A baseball moving to the left and spinning horizontally clockwise will experience a deviation to the left of its original path.

A baseball moving to the right will have the streamlines moving to the left around it and vice versa. Hint #22 / 5 If the baseball is spinning vertically, according to Bernoulli's, it will either experience an upward or downward lift, not leftward or downward. Only if the baseball is spinning horizontally can it experience a leftward or rightward shift. Hint #33 / 5 If the ball is moving to the right, the streamlines are moving to the left. By spinning counterclockwise, the spin and the streamlines match up to create a greater velocity on the top, but they cancel each other out on the bottom for a lesser velocity. Hint #44 / 5 Difference in velocity will result in difference in pressure. Hint #55 / 5 The baseball will experience a lower pressure on the top with the increased velocity and higher pressure from below with the reduced velocity, and hence the ball will experience an upward lift.

2. How will a charge that is placed at a point of zero electrical potential move relative to a source charge?

A charge will move in such a way to minimize its potential energy. Placing a charge at a point of zero electrical potential does not indicate that there is zero potential difference, so the charge may or may not move - and if it moves, it may move toward or away from the source charge depending on the sign of the source charge and test charge.

1. How does a change in electrical potential energy from -4 J to -7 J reflect on the stability of a system?

A decrease in potential energy indicates that the system has become more stable.

4. What is the behavior of an electric dipole when exposed to an external electric field?

A dipole will rotate within an external electric field such that its dipole moment aligns with the field.

2. A charge of 2 uC flows from the positive terminal of a 6 V battery, through a 100-ohm resistor, and back through the battery to the positive terminal. What is the total potential difference experienced by the charge? A. 0 V B. 0.002 V C. 0.2 V D. 6 V

A. Kirchhoff's loop rule states that the total potential difference around any closed loop of a circuit is 0 V. Another way of saying this is that the voltage gained in the battery (6 V) will be used up through the resistors. Because this charge both started and ended at the positive terminal, its total potential difference is therefore 0 V. 6 V, D, is the voltage gained in the battery as well as the voltage drop in the resistors - creating a net sum of 0 V.

A constant electric field moves a positive point charge from one position to another position so that the change in electric potential is -450V. Which of the following must increase during this movement? Choose 1 answer: A The charge's velocity B The charge's potential energy C The charge's electric potential D The charge's acceleration

According to the question stem, there is an electric potential difference between the two positions. Hint #22 / 4 The negative change in electric potential indicates that the point charge moves from a position of higher electric potential to a position of lower electric potential. Hint #33 / 4 The point charge displacement as a result of a constant electric field indicates that the point charge moves to a more favorable, downstream position. This indicates that the charge loses potential energy and gains kinetic energy during the movement. Hint #44 / 4 Just like a ball dropped from a height due to the force of gravity, the point charge moves to its new location due to the force generated by the electric field on the charge. In both situations, the object being moved will increase in velocity during its movement. A

2. To which properties of a sound do amplitude and frequency correspond?

Amplitude: Sound level (volume) Frequency: Pitch

14. A moving negative charge placed in an external magnetic field circulates counterclockwise in the plane of the paper. In which direction is the magnetic field pointing? A. Into the page B. Out of the page C. Toward the center of the circle D. Tangent to the circle

B This problem is an application of the right-hand rule. The velocity vector v is always tangent to the circle. The magnetic force must always point radially toward the center of the circle. Consider when the negative charge is at the "12 o'clock" position in its circle and apply the right-hand rule. Your thumb points to the left, tangent to the circle at this point. The back of your hand, which represent the force on a negative charge, points down the page, radially toward the center of the circle. Your fingers must point out of the page to get your hand into this position. Therefore, the direction of the magnetic field must be out of the page.

7. In an adiabatic compression process, the internal energy of the gas: A. increases because the work done on the gas is negative B. increases because the work done on the gas is positive C. decreases because the work done on the gas is negative D. decreases because the work done on the gas is positive

B. To answer this question, make sure you understand all the terms. An adiabatic process means there is no exchange of heat; in other words, Q = 0. When a gas is compressed, positive work is being done on the gas (rather than by the gas), so the value for work done by the gas will be negative (W < 0). Based on this, we can determine how the internal energy of the gas changes by using the first law of thermodynamics (deltaU = Q - W). If Q = 0 and W is negative, then deltaU is positive.

9. In some forms of otosclerosis, the stapedial foot plate, which transmits vibrations from the bones of the middle ear to the fluid within the cochlea, can become fixed in position. This limits the displacement of the stapedial foot plate during vibration. Based on this mechanism, which of the following symptoms would most likely be seen in an individual with otosclerosis? A. An increase in the perceived volume of sounds B. A decrease in the perceived volume of sounds C. An increase in the perceived pitch of sounds D. A decrease in the perceived pitch of sounds

B. Saying that the stapedial footplate has limited displacement during vibration is another way of stating that the amplitude of the vibration has been decreased. Because amplitude is related to intensity, and intensity is related to sound level, the perceived sound level (volume) will be decreased as well. Pitch is related to the frequency of a sound, not its amplitude.

13. Shock waves have the greatest impact when the source is traveling: A. just below the speed of sound B. exactly at the speed of sound C. just above the speed of sound D. well above the speed of sound

B. Shock waves are the buildup of wave fronts as the distance between those wave fronts decreases. This occurs maximally when an object is traveling at the same speed as the wave is traveling (the speed of sound). Once an object moves faster than the speed of sound, some of its effects of the shock wave are mitigated because all the wave fronts will trail behind the object, destructively interfering with each other.

4. If the electric field at a distance r away from charge Q is 36 N/C, what is the ratio of the electric fields at r, 2r, and 3r? A. 9:3:1 B. 36:9:4 C. 36:18:9 D. 36:18:12

B. The first step in answering this question is to remember that the magnitude of the electric field is inversely proportional to the square of the distance: E = kQ/r2 E is proportional to 1/r2 Therefore, if the electric field at radius r, Er, is 36 N/c, then the electric field at radius 2r will be E2r : 1/(2r)2 = 1/4r2 = Er/4 = 36 N/C /4 = 9 N/C Similarly, the electric field at radius 3r is equal to E3r : 1/(3r)2 = 1/9r2 = Er/9 = (36 N/C)/9 = 4 N/C Therefore, the ratio of Er:E2r:E3r is 36:9:4.

9. A large cylinder is filled with equal volumes of two immiscible fluids. A balloon is submerged in the first fluid; the gauge pressure in the balloon at the deepest point in the first fluid is found to be 3 atm. Next, the balloon is lowered all the way to the bottom of the second fluid, where the hydrostatic pressure in the balloon reads 8 atm. What is the ratio of the gauge pressure accounted for by the first fluid to the gauge pressure accounted for by the second fluid? A. 1:3 B. 3:4 C. 3:5 D. 3:8

B. The first step to answering this question is defining the different types of pressures. Atmospheric pressure is the pressure at the top of the first fluid exerted by air (at sea level, it is equal to 1 atm). Gauge pressure is the pressure inside the balloon above and beyond atmospheric pressure; gauge pressure is the total (absolute or hydrostatic) pressure inside the balloon minus the atmospheric pressure. Gauge pressure depends on the density of the fluid, the constant of gravity, and the depth at which the object is submerged. Hydrostatic or absolute pressure is the total pressure in the balloon (that is, the gauge pressure and the atmospheric pressure together). Because we are given the gauge pressure at the bottom of the first fluid as 3 atm, our task is now to calculate the gauge pressure accounted for by the second fluid. The hydrostatic pressure at the bottom of the cylinder is 8 atm. One of these atmospheres is atmospheric pressure pushing on the fluids. Another 3 atmospheres are accounted for by the first fluid that is pushing on the second fluid. Thus, the gauge pressure due to the second fluid is 8 - 1 - 3 = 4 atm. The ratio of the gauge pressures is therefore 3:4.

Blood takes about 1.0 seconds to pass through a 1.0 millimeter long capillary in the human circulatory system. If the diameter of the capillary is 8.00 μm and the pressure drop is 2.0 kPa, what is the viscosity of the blood, assuming laminar flow? Choose 1 answer: A 4 μPa·s B 4 mPa·s C 40 mPa·s D 40 μPa·s

B. Use Poiseuille's law to relate the pressure drop to the vessel radius, vessel length, blood flow rate, and blood viscosity: \DeltaΔdeltaP=\dfrac{8{\eta}L}{{\pi}r^4} πr 4 8ηL ​ Q = (\piπpir^4 4 start superscript, 4, end superscript\DeltaΔdeltaP/8LQ) Hint #22 / 6 Volume flow rate is Q = Av, where Q =\piπpir2v. Hint #33 / 6 Plug into original equation to get: =(r^2 2 start superscript, 2, end superscript\DeltaΔdeltaP/8Lv) Hint #44 / 6 Convert all your units and do the math watching out for the exponents:=(r^2 2 start superscript, 2, end superscript\DeltaΔdeltaP/8Lv) =(4 x 10^{-6} −6 start superscript, minus, 6, end superscript m)^2 2 start superscript, 2, end superscript(2.0 x 10^3 3 start superscript, 3, end superscript Pa)/8(1 x 10^{-3} −3 start superscript, minus, 3, end superscriptm)(1 x 10^{-3} −3 start superscript, minus, 3, end superscriptm/s) Hint #55 / 6 The numerator will become (16 x 10^{-12} −12 start superscript, minus, 12, end superscript m)(2.0 x 10^3 3 start superscript, 3, end superscript Pa)and the denominator will become (8 x 10^{-6} −6 start superscript, minus, 6, end superscript m·m/s), which equals (32 x 10^{-9} −9 start superscript, minus, 9, end superscript)/(8 x 10^{-6} −6 start superscript, minus, 6, end superscript) Hint #66 / 6 The correct answer is 4 x 10^{-3} −3 start superscript, minus, 3, end superscript Pa·s or 4 mPa·s.

Which of the following scenarios would produce a magnetic force? Choose 1 answer: A An electron moving with a velocity to the right in a magnetic field pointing to the left B An positron moving perpendicular to a changing electric field C A current-carrying wire lying beside another current-carrying wire D A high-speed neutron entering a magnetic field perpendicular to the plane of the page

C To figure out which scenario would produce a magnetic force, refer to the Lorentz force formula: F=qvB sin(θ) q cannot be zero, so there must be a charge. A high-speed neutron entering a magnetic field perpendicular to the plane of the page would not produce a magnetic force. v cannot be zero, so a charge must be moving. B sin(θ) cannot be zero, so the magnetic field cannot be either parallel or antiparallel to the motion of the charge. An electron moving to the right while a magnetic field points to the left would not produce a magnetic field since they are antiparallel and sin180 is zero. Additionally, there must be a magnetic field. A changing electric field will produce a magnetic field, so a positron moving perpendicular to a changing electric field would not produce a magnetic force. A current-carrying wire lying beside another current-carrying wire would produce a magnetic force. A wire with current has moving charges, which produces a magnetic field. That field will produce a magnetic force for the adjacent wire since that wire also has moving charges.

4. What is the final temperature of a 5-kg silver pendant that is left in front of an electric heater, absorbing heat energy at a rate of 100 W for minutes? Assume the pendant is initially at 20 C and that the specific heat of silver is 233 J/kg*K. A. 29 C B. 59 C C. 72 C D. 100 C

C. To answer this question, first remember that watts are equal to joules per second; in other words, power is energy transfer over time. In 10 minutes, the pendant absorbs the following amount of energy: E = P x t = (100 W)(10 min)(60s/1 min) = 6x 104 J Now we can find the temperature from this equation: q=mc(deltaT) 6 x 104 J = (5 kg)(233 J/kg*K)(deltaT) 52 C = deltaT The final temperature is thus 20 + 52 = 72 C.

15. A dipole is placed in an electric field and is allowed to come to equilibrium. How would the dipole react if the direction of the electric field is suddenly reversed? A. It rotates to align with the new field. B. It accelerates linearly along the field lines. C. It experiences no rotational or linear movement. D. It both rotates to align with the new field and accelerates linearly along the field lines.

C. Torque is a function of both force applied and the angle at which it is applied. A dipole paced in an electric field will experience a torque until it comes to rest oriented within the field, at which point the angle between the plane of the dipole and the electric field is 0 degrees. Once this point is reached, inverting the electric field has no impact on the dipole because it will now have an angle of 180 degrees, the sine of which is still 0. Note, however, that this is an unstable setup; any deviation in the dipole from its rest position will immediately result in torque on the dipole and force it to realign with the new field.

15. Which of the following processes is LEAST likely to be accompanied by a change in temperature? A. The kinetic energy of a gas is increased through a chemical reaction. B. Energy is transferred to a solid via electromagnetic waves C. A boiling liquid is heated on a hot plate. D. A warm gas is mixed with a cold gas.

C. If a substance is undergoing a phase change, any added heat will be used toward overcoming the heat of transformation of the phase change. During the phase change, the temperature will remain constant. Temperature is a measure of the kinetic energy of the molecule in a sample, so a change in kinetic energy, A, is essentially the same thing as a change in temperature. The heat transfer by radiation described in B will change the temperature of the solid as long as it is not in the process of melting. D describes heat transfer by convection, in which the warm gas will transfer heat to the cold gas until they both reach an intermediate temperature.

11. A 10-ohm resistor carries a current that varies as a function of time as shown (see figure). How much energy has been dissipated after 5 s? A. 40 J B. 50 J C. 120 J D. 160 J

C. Power is energy dissipated per unit time; therefore, the energy dissipated is E = Pdelta. In the five-second internval during which the resistor is active, it has a 2 A current for three of those seconds. The power dissipated by a resistor R carrying a current I is P = I2R. Therefore, the enrgy dissipated is E = I2R = (2 A)2(10 ohm)(3 s) = 4 x 10 x 3 = 120 J.

The average height of an American adult is 1.70 m. When an individual of this height is standing, by how much will the blood pressure at the bottom of the feet differ from the blood pressure at the top of the head? (Densityblood = 1060 kg/m3) A2000 Pa B 6000 Pa C 10000 Pa D 18000 Pa

Choice D is correct. The pressure in a static fluid varies with depth h according to P = Pair + ρgh, where the ρgh term arises from the weight of the fluid. In this case, the pressure at the top isn't from the air, but the same principle applies: Pfeet = Phead + ρgh. The pressure difference is thus ρgh = 1060×9.8×1.7 = 17660 Pa, which rounds to 18000 Pa. Since the answers are not particularly close to each other, the multiplication can easily be approximated as ρgh ≈ 1000×10×1.7 = 17000 Pa, which is closest to choice D. Choices A, B, and C are various options that could be obtained via multiplication errors or mistakes made in choosing which quantities to multiply, and are all incorrect.

Atmospheric gases absorb more energy than they emit. If we consider a gas to be a closed system, which of the following is true? Choose 1 answer: A. The internal energy of the gas increases. B The work done on the gas is equal to the change in internal energy and the heat absorbed by the gas. C The change in volume of the gas is negative. D The heat absorbed by the gas is positive.

D

13. Which of the following will most likely increase the electric field between the plates of a parallel plate capacitor? A. Adding a resistor that is connected to the capacitor in series B. Adding a resistor that is connected to the capacitor in parallel C. Increasing the distance between the plates D. Adding an extra battery to the system

D. The electric field between two plates of a parallel plate capacitor is related to the potential difference between the plates of the capacitor and the distance between the plates, as shown in the formula E = V/d. The addition of another battery will increase the total voltage applied to the circuit, which, consequently, will increase the electric field. The addition of a resistor in series will increase the resistance and decrease the voltage applied to the capacitor, eliminating A. Adding a resistor in parallel will not change the voltage drop across the capacitor and should not change the electric field, eliminating B. Increasing the distance between the plates, C, would decrease the electric field, not increase it.

8. If the magnetic field a distance r away from a current carrying wire is 10 T, what will be the net magnetic field at r if another wire is placed a distance 2r from the original wire (with r in the middle) and has a current twice as strong flowing in the opposite direction? A. 0 T B. 15 T C. 20 T D. 30 T

D. The safest way to answer this question is to quickly draw a diagram: Notice right away that between the two wires, the direction of the magnetic field is the same: into the page. Therefore, because the vector direction is the same, we can just focus on the magnitudes of the two magnetic fields. We know that B1 = 10 T at a distance r. Consider the relationships in the equation B = uI/2(pi)r. Magnetic field and current are directly proportional, whereas magnetic field and distance are inversely proportional. Therefore, doubling the current will result in double the magnetic field of the first wire, or 20 T. The overall magnitude of the magnetic field is 10 T + 20 T = 30 T.

11. A student is measuring sound frequencies from the side of a road while walking east. For which of the following situations could the student determine that the difference between the perceived frequency and the actual emitted frequency is zero? A. A plane flying directly above him from east to west B. A police car passing the student with its siren on C. A person playing piano in a house on the street D. A dog barking in a car that moves east

D. This question is testing us on our understanding of the Doppler effect. A difference of zero between the perceived and the emitted frequencies implies that the source of the sound is not moving relative to the student. If the car in D is moving at the same speed as the student, then the relative motion between them could be 0. In all of the other cases, the student and the sound source are necessarily moving relative to each other.

Which of the following statements is true about diamagnetic materials? Choose 1 answer: (Choice A) A Diamagnetism is a property that appears in all materials, but in paramagnetic and ferromagnetic substances, the diamagnetic effect is overwhelmed by some other form of magnetism. (Choice B) B Diamagnetic materials such as the transition metal gadolinium are particularly useful as a contrasting agent in diagnostic procedures such as MRI. (Choice C) C Diamagnetic materials form internal, induced magnetic field in the same direction as that of an external magnetic field, while paramagnetic materials form a field opposite that of the external field. (Choice D) D A compound with twelve diamagnetic electrons and one paramagnetic electron is strongly diamagnetic and only weakly paramagnetic.

Diamagnetic materials create an induced magnetic field in a direction opposite to an externally applied magnetic field due to paired electrons. Paramagnetic materials create an induced field in the same direction as the external field due to unpaired electrons. Hint #22 / 4 A compound is either diamagnetic or paramagnetic. A compound with even one paramagnetic electron is paramagnetic. Hint #33 / 4 Gadolinium has an atomic number of 64, and xenon has an atomic number of 54. We would guess that its electronic configuration is [Xe]}6s^24f^8 but in fact, it is [Xe}]4f^7 5d^1 6s^. Regardless, this element is not diamagnetic by any means, but strongly paramagnetic, and we take advantage of such magnetic properties as a MRI contrasting agent. Hint #44 / 4 Diamagnetism is a property of all materials and makes a weak contribution to the material's response to a magnetic field. A substance is called a diamagnet when diamagnetism is the only contribution to the magnetism.

Question 21 The moon's orbit around the Earth is approximately circular. How much work is done on the moon by the force of gravity when the moon completes half an orbit around the Earth? (Note: radius of moon's orbit: 3.85 × 105 m; mass of Earth: 6 × 1024 kg; mass of moon: 7.3 × 1022 kg; moon orbital time: 27 days) A. 0 N B. 0 J C. 1.2 × 10^6 N D. 1.2 × 10^6 J

Difficulty: 1 Easy Reasoning Skill: 1 Knowledge of Scientific Concepts and Principles Concept Category: 4A Kinematics and Force B is correct. For an object moving in a circle, the force is towards the center of the circle, but the velocity vector points at a tangent out from the circle. This makes the angle between the force and velocity vectors 90º. The equation for work is W = Fd cos θ. The cosine of 90º is zero, so the work done on any object moving in a circle by the centripetal force is always zero. A, C: Even if you weren't sure how to solve this question, you can eliminate these choices. The question asks for work, which is measured in joules.

Question 29 The SI unit for power, the watt, is equivalent to one joule/s. This unit can also be written as: A. (kg∙m)/s2. B. (kg∙m2)/s2. C. (kg∙m2)/s3. D. N/m2.

Difficulty: 1 Easy Reasoning Skill: 1 Knowledge of Scientific Concepts and Principles Concept Category: 4A Kinematics and Force C is correct. One joule is equivalent to one N∙m, while one newton is the same as one (kg∙m)/s2. In other words, joules can also be described as (kg∙m2)/s2. Since watts are J/s, one watt is one (kg∙m2)/s3. A: These are the units for newtons, not watts. B: These are the units for joules, not watts. D: These are actually the units for pressure, which has an SI unit of the pascal. One pascal is equivalent to one J/m3, which can also be written as it is in choice D.

A 24-kg lawnmower is sitting in a shed. It is then dragged along the ground with a constant force of 120 N. Assuming that no friction is present, how far has it traveled when its velocity reaches 30 m/s? A. 3 m B. 6 m C. 45 m D. 90 m

Difficulty: 1 Easy Reasoning Skill: 4 Data-based and Statistical Reasoning Concept Category: 4A Kinematics and Force D is correct. First, use F = ma to find acceleration. 120 N = (24 kg)(a), giving an acceleration of 5 m/s2. Now, we can plug values in to the formula vf2 = vi2 + 2aΔx to calculate distance. (30 m/s)2 = (0 m/s)2 + 2(5 m/s2)(x) shows that x = 90 m. A: This number results from forgetting to square vf in the formula vf2 = vi2 + 2aΔx. B: This answer results from multiple mistakes: both forgetting to square vf and neglecting the 2 in the 2aΔx term. In other words, it comes from mistakenly using vf = vi2 + aΔx.

A 10-kg sled rests on a 30° ramp with a coefficient of static friction of 0.5. An upward force is applied to the sled, parallel to the slope of the ramp, in incremental values until the sled begins to accelerate up the ramp. Approximately what minimum force is required to perform this action? A. 44 N B. 50 N C. 95 N D. 120 N

Difficulty: 2 Medium Reasoning Skill: 1 Knowledge of Scientific Concepts and Principles Concept Category: 4A Kinematics and Force C is correct. The block will begin to accelerate once all opposing forces have been overcome. Here, these forces are static friction (which opposes motion) and gravity (which opposes upward movement). Since the applied force needs only to minimally surpass equilibrium, we can set our net force equation up as follows: Fnet = Fapplied - (Fg + Fs) = 0 N. This simplifies to Fapplied = Fg + Fs. Now, we need to find the component of the gravitational force that is actually acting on the block, along with the normal force. To do so, we can break our values into components. Gravitational force parallel to the plane is equal to mg sin 30º = (10 kg)(10 m/s2)(0.5) = 50 N. The maximum force exerted by static friction is given by µmg cos 30º, since normal force is equal and opposite to the y-component of the gravitational force. Thus, Fs = (µmg cos 30º) = (0.5)(10 kg)(10 m/s2)(0.866) = 43.3 N. Fapplied is then equivalent to 50 N + 43.3 N, or 93.3 N. Only C is close.

Question 23 A "loop-the-loop" on an amusement park ride has a radius of R, while the cars on the ride travel with a velocity of v. If a man of mass M were able to step on a scale at the instant when he is at the bottom of this loop, how much would he seem to weigh? A. Mg + Mv2/R B. g + v2/R C. Mv2/R D. Mg

Difficulty: 2 Medium Reasoning Skill: 2 Scientific Reasoning and Problem Solving Concept Category: 4A Kinematics and Force A is correct. If the man were not moving in a circular pattern, his weight would simply be Mg. Here, however, he is also subject to centripetal force. Remember that apparent weight can be conceptualized as the normal force exerted on an object. In this case, the normal force is that which points directly upward from the bottom of the loop. This is the combination of centripetal force (Mv2/r) and gravitational force (Mg). B: This is an acceleration (g) but the question asks for a force (weight). C: This choice neglects the effect of gravity on the man's mass. D: This answer forgets to account for centripetal force.

Question 22 A prosthetics researcher is conducting tests on a 40-cm-long prosthetic forearm, which is positioned according to the simplified diagram below. He exerts an upward force of 5 N on the forearm 30 cm to the right of the point of rotation (the elbow joint). Image If the forearm has a weight of 15 N that is uniformly distributed, which of the forces listed below will allow the system to exist in rotational equilibrium? A. A 15-N upward force exerted 30 cm to the right of the point of rotation B. A 20-N upward force exerted 7.5 cm to the right of the point of rotation C. A 5-N downward force exerted 30 cm to the right of the point of rotation D. A 20-N downward force exerted 7.5 cm to the right of the point of rotation

Difficulty: 2 Medium Reasoning Skill: 2 Scientific Reasoning and Problem Solving Concept Category: 4A Kinematics and Force B is correct. When dealing with multiple torques, it's helpful to separate them based on whether they rotate the system clockwise or counterclockwise. To exist in rotational equilibrium, the system must have no net torque, meaning that the counterclockwise and clockwise torques must be equal. The only counterclockwise torque shown is due to the upward 5-N force. Remember, torque = F r sin θ, where r represents the distance between the point of application of force and the fulcrum, or rotation point; θ represents the angle at which the force is applied. Here, then, torquecounterclockwise = (5 N)(0.3 m)(sin 90°) = (1.5 Nm)(1) = 1.5 Nm. It may not immediately appear that any clockwise torques are present, but remember, this prosthetic forearm has a weight of 15 N! When positioned as shown in the diagram, this weight will "want" to pull it downward, making it a clockwise torque. Since the forearm has a uniformly-distributed mass, we can position this torque at its center of mass, exactly in the center of the forearm (20 cm to the right of the rotation point). Torqueclockwise = (15 N)(0.2 m)(sin 90°) = (3 Nm)(1) = 3 Nm. Now, we can see that we have a net torque of 3 Nm clockwise - 1.5 Nm counterclockwise = 1.5 Nm clockwise, or "down." We thus need a counterclockwise, or "upward," force of 1.5 Nm to bring the system to equilibrium. This eliminates options C and D immediately. For choice B, (20 N)(0.075 m)(sin 90°) = 1.5 Nm, giving us the proper magnitude of force required to bring our net force to zero. A: The "upward" part of this answer choice is correct, but (15 N)(0.3 m)(sin 90°) = 4.5 Nm, not 1.5 Nm. C: This choice may be tempting, as it is the exact opposite of the force shown in the diagram! However, it fails to account for the effect of the forearm's weight, which will produce a torque that must be considered as well. D: This answer includes the correct magnitude of force, but the wrong direction.

Four blocks of mass M are connected by a massless cord. If the cord is pulled from the left with a force of 15 N, causing all of the blocks to accelerate, what net force will be experienced by the block that is second from the right? A. 3.75 N B. 7.5 N C. 15 N D. 60 N

Difficulty: 2 Medium Reasoning Skill: 4 Data-based and Statistical Reasoning Concept Category: 4A Kinematics and Force A is correct. A 15-N force is being exerted on a system with a total mass of 4M. We can therefore plug in to Newton's equation for net force to yield 15 N = 4Ma. Next, solving for acceleration gives us a = (15 N) / (4M). Since all of the blocks are connected, they will accelerate at the same rate. Substituting an acceleration of (15 N) / (4M) and a mass of M (since we are now considering only one of the blocks) gives F = M[(15 N) / 4M] = 15/4. 15/4 N is equal to 3.75 N. C: 15 N is the net force on the entire system, not a single block. D: This value is larger than the applied force, which would require an impossible efficiency of 400%.

Question 24 A ball attached to a string on a tabletop is swung in a circle with a velocity of v. The string is threaded through a small hole in the table such that it can be pulled on to be shortened. If the string is loosened and allowed to extend to three times its original length, how will the ball's velocity change? A. The velocity of the ball will remain constant. B. The velocity of the ball will decrease to one-third of its previous value. C. The velocity of the ball will increase by a factor of 1.7. D. The velocity of the ball will increase by a factor of 3.

Difficulty: 2 Medium Reasoning Skill: 4 Data-based and Statistical Reasoning Concept Category: 4A Kinematics and Force B is correct. The initial and final values for the ball's angular momentum should be identical. Angular momentum, or L, is given by the quantity mvR. From this expression, we see that v (velocity) must decrease by a factor of three to compensate for the increase in R (the length of the string).

A 12-kg bag of clothes is lifted until it has 360 J of potential energy. Approximately how long will it take to hit the ground if dropped? A. 0.3 s B. 0.6 s C. 0.8 s D. 6 s

Difficulty: 3 Hard Reasoning Skill: 4 Data-based and Statistical Reasoning Concept Category: 4A Kinematics and Force C is correct. Using PE = mgh and the potential energy given, we can first find the height of the bag. 360 J = (12 kg)(10 m/s2)(h) shows that the elevation must be 3 m. From there, we simply need to use d = v0t + ½at2 to find time, remembering that v0 is zero. 3 m = ½(10 m/s2)t2, and t2 = 0.6 s. You don't need to actually calculate the square root of 0.6 — you simply need to know that when you take the square root of a decimal, it becomes a slightly larger decimal. The only answer choice that fits is C.

A slingshot propels a rubber ball horizontally from a 30 m platform at 15 m/s. Approximately how far from the base of the platform will the ball land? A. 14 m B. 21 m C. 30 m D. 38 m

Difficulty: 3 Hard Reasoning Skill: 4 Data-based and Statistical Reasoning Concept Category: 4A Kinematics and Force D is correct. Let's start by listing our known values. The height of the platform, or vertical distance, is 30 m. The initial velocity is 15 m/s, but remember that this is entirely horizontal! The initial vertical velocity is 0 m/s and the gravitational acceleration can be estimated at 10 m/s2. First, use vertical components and the equation Δx = v0t + ½at2 to find time. 30 m = ½(10 m/s2)(t2) means that t2 = 6, so t ≈ 2.5 (you should know that the square root of 4 is 2 and the square root of 9 is 3; so the square root of 6, which is between 4 and 9 should be between 2 and 3; just estimate that as 2.5). Next, use horizontal components to find range, which is equal to the product of initial horizontal velocity and time. Range = (15 m/s)(2.5 s) = 37.5 m. That's closest to choice D.

A weight is suspended from the ceiling by two massless ropes. (rope 1 at 30 degrees and rope 2 at 60 degrees) If the force exerted by tension on Rope 1 is 15 N, what force is felt by Rope 2? A. 6.5 N B. 17.5 N C. 20.2 N D. 25.5 N

Difficulty: 3 Hard Reasoning Skill: 4 Data-based and Statistical Reasoning Concept Category: 4A Kinematics and Force D is correct. Since the object is not moving (static equilibrium), the horizontal components of the tension force must be equal and opposite. Rope 1 has a tension of 15 N, giving it a horizontal component of (15 N)(cos 30) or around 13 N. Next, we can solve for the force along the second rope by setting 13 N equal to F2cos60. Solving for force gives us F2 = 13 / (cos 60), or 26 N. This value is closest to choice D.

Question 34 A cylinder fitted with a piston exists in a high-pressure chamber (3 atm) with an initial volume of 1 L. If a sufficient quantity of a hydrocarbon material is combusted inside the cylinder to produce 1 kJ of energy, and if the volume of the chamber then increases to 1.5 L, what percent of the fuel's energy was lost to friction and heat? A. 15% B. 30% C. 85% D. 100%

Difficulty: 3 Hard Reasoning Skill: 4 Data-based and Statistical Reasoning Concept Category: 5E Kinetics and Bioenergetics C is correct. The energy used for expansion must come from the energy of combustion, minus the amount lost to friction. Since work = PΔV, we know that the expansion required (3 atm)(0.5 L), or 1.5 L∙atm. Using the conversion factor 1 L∙atm = 101.325 J, we see that 1.5 L∙atm is approximately 150 J. As the fuel was theoretically capable of producing a 1000-J energy output, the amount lost to the environment must be 1 - (150/1000), or about 85%. A: This is the percent devoted to useful work, not the percent lost to the outside environment. D: This value is impossible, since if all the energy were lost to friction, no volume change would be observed.

2. Compare the relationship b/w electrical potential energy and Coulomb's law to the relationship b/w gravitational potential energy and the universal law of gravitation.

Electrical potential energy is Coulomb's law multiplied by distance, whereas gravitational potential energy is the universal law of gravitation multiplied by distance.

1. What is the difference between electrical potential and voltage?

Electrical potential is the ratio of the electrical potential energy to the magnitude of the charge itself. Voltage, or potential difference, is a measure of the change in electrical potential between two points, which provides an indication of the tendency toward movement in one direction or another.

3. For each of the following combinations of velocity and magnetic field directions, determine the direction of the magnetic force on the given particle: v B Particle Up the page Left Electron Into the page Out of the page Proton Right Into the page Proton Out of the page Left Electron Down the page Right Neutron

F Into page None (sin 180 = 0) Up the page Up the page None (q = 0)

4. True or false: To determine the volume of an object by fluid displacement it must have a specific gravity greater than 1.

False. A fluid with a low specific gravity can be used instead of water to determine volumes of objects that would otherwise float in water.

3. True or False: Sound waves are a prime example of transverse waves.

False. Sound waves are the most common example of longitudinal waves on the MCAT.

2. True or False: A voltmeter and an ammeter should not be placed in the same circuit.

False. Voltmeters and ammeters are designed to have minimum impact on a circuit, thus they can be used together.

4. True or False: The sum of the voltage sources in a circuit is equal to the sum of the voltage drops in that circuit.

False. While the voltage sources and voltage drops are equal in any closed loop, that is not necessarily true for the entire circuit. For example, a 9 V battery that powers 10 light bulbs in parallel has a 9 V voltage source and a 9 V drop across each light bulb - a total of 90 V of drop across all the light bulbs combined.

1. How does gauge pressure relate to the pressure exerted by a column of fluid?

Gauge pressure is equal to the pressure exerted by a column of fluid plus the ambient pressure above the fluid, minus atmospheric pressure. When atmospheric pressure is the only pressure above the fluid column, then gauge pressure equals the fluid pressure.

2. What would the meniscus of a liquid that experiences equal cohesive and adhesive forces look like?

If adhesive and cohesive forces are equal, then no meniscus would form and the liquid surface would be flat.

2. If two waves are out of phase at any interval besides 180 degrees, how does the amplitude of the resultant wave compare to the amplitudes of the two interfering waves?

If two waves are perfectly in phase, the amplitude of the resulting wave is equal to the sum of the amplitudes of the interfering waves. If two waves are perfectly out of phase, the ampltiude of the resulting wave is the difference of the amplitudes of the interfering waves. Therefore, if the two waves are anywhere between these two extremes, the amplitude of the resulting wave will be somewhere between the sum and difference of the amplitudes of the interfering waves.

3. How does electrical potential energy change between two particles as the distance between them increases?

It increases if the particles are opposite charged, and decreases if they are the same charge.

Which of the following describes the most realistic shape of middle-sized raindrops as they fall through the Earth's atmosphere? A "hamburger bun"-like due to air pressure B teardrop-shaped due to gravitational forces C spherical due to surface tension D circular due to air resistance forces

In deciding on the shape of the raindrop, there are two forces at play here: the surface tension holding the droplet together and the air pressure pushing from below against the bottom surface of the droplet. Hint #22 / 5 Spherical is the most ideal shape achieved by surface tension to minimize surface area, but that shape is maintained for only small droplets. Hint #33 / 5 While teardrop-shaped is the shape promoted by popular culture and used in weather forecasts, small raindrops will be spherical due to surface tension. Hint #44 / 5 Circular is a 2-dimensional shape and would make the raindrop a flat disc. Hint #55 / 5 Flattened on the bottom and with a curved dome on top, the medium-sized raindrop takes on a hamburger bun shape due to the pressure pushing up against the bottom distorting its shape.

3. How does flow in the venae cavae relate to flow in the main pulmonary?

In theory, there should be equal flow in the venae cavae and the main pulmonary trunk. The flow in the venae cavae is slightly less than in the pulmonary trunk because some of the blood entering the right side of the heart is from cardiac (coronary) circulation, not systemic circulation.

1. What do each of the following types of meters measure? Where are they placed in circuits? What are their ideal resistances? Ammeter Voltmeter Ohmmeter

Meter Type Measures... Placement Ideal Resistance Ammeter Current In series with a point of interest 0 Voltmeter Voltage Parallel with circuit element of interest Infinite Ohmmeter Resistance Two points in series with circuit element of interest 0

Which of the following scenarios most accurately represents Pascal's law? Choose 1 answer: A. When a pregnant mother is riding in a car that crashes, the fluid surrounding the fetus will help to dissipate any force from the crash. B. The volume displaced by piston 1 is equal to the volume displaced by piston 2 in a hydraulic lift. C. When you push down on the stopper of a big water jug with 10 N, the same force of 10 N is transmitted undiminished to the larger bottom surface of the jug. D. A person pushes the brake with a small area with a small force over a short distance to produce an equivalent force to stop the car.

Pascal's Law states that pressure is transmitted undiminished to every portion of the fluid and to the walls of the container. Hint #22 / 4 This allows us to write the equation P_1 1 ​ start subscript, 1, end subscript = P_2 2 ​ start subscript, 2, end subscript, and then F_1 1 ​ start subscript, 1, end subscript/A_1 1 ​ start subscript, 1, end subscript = F_2 2 ​ start subscript, 2, end subscript/A_2 2 ​ start subscript, 2, end subscript, as well as F_1 1 ​ start subscript, 1, end subscriptd_1 1 ​ start subscript, 1, end subscript = F_2 2 ​ start subscript, 2, end subscriptd_2 2 ​ start subscript, 2, end subscript. Hint #33 / 4 As a result, we can explorate that a small force applied on a small area over a long distance will produce a large force applied on a large area over a short distance. Hint #44 / 4 We also can deduce that W1/V1 = W2/V2. Since work is the same on both sides, the volume displaced by one side will be equal to the volume displaced on the other side in a hydraulic lift.

3. What variables does flow rate depend on?

Radius of the tube, pressure gradient, viscosity, and length of tube.

1. How is sound produced and transmitted?

Sound is produced by mechanical vibrations. These are usually generated by solid objects like bells or vocal cords, but occasionally can be generated by fluids. Sound is propagated as longitudinal waves in matter, so it cannot propagate in a vacuum.

4. What physical qualities contribute to the capacitance of a capacitor?

Surface area, distance, and dielectric constant all contribute to the capacitance of a capacitor.

According to the Lorentz force law, a particle carrying a charge of 1 C and passing through a magnetic field of 1 Tesla at a speed of 1 meter per second perpendicular to said field experiences a force with magnitude 1-newton. Which of the following expressions represents the Tesla in SI base units? Choose 1 answer: A N*s/(C*m) B kg/(A*s^2) C N/(A*m) D Wb/m^2 ​

The SI base units are the following: meter for length, kilogram for mass, second for time, ampere for electric current, kelvin \ for temperature, candela for luminous intensity, and mole for the amount of substance. Hint #22 / 4 All answer choices are correct expressions of the Tesla, but only one has the Tesla in base units. Tesla is often defined as one Weber per square meters. Hint #33 / 4 C⋅m/ N⋅s ​ fraction emphasizes that the magnetic field comes from moving charges. The unit for electric field is N/C and what separates the electric and magnetic field m/s. kg/A*s^2 is the correct answer.

1. Assuming the plates are attached by a conducting material, how does a capacitor behave after the voltage source has been removed from a circuit?

The capacitor discharges, providing a current in the opposite direction of the initial current.

1. Under what conditions could the continuity equation be applied to human circulation?

The continuity equation cannot be applied to human circulation. The presence of pulses, the elasticity of the vessels, and the nature of the pressure gradient preclude this type of analysis. Poiseuille's law should instead be used for isolated segments.

2. How do the following concepts relate to one another: Venturi effect, Bernoulli's equation, and continuity equation? What relationship does each describe?

The continuity equation describes the relationship of flow and cross-sectional area in a tube, while Bernoulli's equation describes the relationship between height, pressure, and flow. The Venturi effect is the direct relationship between cross-sectional area and pressure, and results from the combined relationships of the Bernoulli and continuity equations.

3. A block is fully submerged three inches below the surface of a fluid, but is not experiencing any acceleration. What can be said about displaced volume of fluid and buoyant force?

The displaced volume is equal to the volume of the block. The buoyant force is equal to the weight of the block, and is equal to the weight of the displaced fluid. By extension, the block and fluid in which it is immersed must have the same density.

1. What is the electric field midway between two negative charges in isolation?

The electric field would be 0 because the two charges are the same. In this case, the fields exerted by each charge at the midpoint will cancel out and there will be no electric field.

1. When placed one meter apart from each other, which will experience a greater acceleration: one coulomb of electrons or one coulomb of protons?

The electrons will experience the greater acceleration because they are subject to the same force as the protons but have a significantly smaller mass.

Suppose two parallel plates are inserted into a solution, and the current that passes between them for a known potential difference is used to measure the electrolytic resistivity of the solution. How would this resistivity change if the area of both of the two plates was doubled, at a fixed separation distance? Choose 1 answer: A It would remain the same B It would be halved C It would quadruple D It would double

The measured resistance is given by the relation R = (rho)L/A where roh is the resistivity. If the plate area were doubled, the resistance measured would decrease by a factor of 2. The resistivity is found by dividing the resistance by the area and separation of the plates, and so this factor of two would cancel out. Resistivity is an intrinsic property of a medium, and so it remains the same when the area of the plates is changed.

The resistivity of a solution can be measured by inserting two leads connected to a battery into it, and then measuring the current that passes through the solution. If the shape and separation of the electrodes is unknown, which of the following measurements must be done in order to determine the resistivity of an unknown solution? Choose 1 answer: A The depth of the electrodes beneath the surface B Determining the material that the electrodes are made from C Inserting an additional resistor of known resistance into the circuit, and measuring any changes D First measuring the resistance of a solution of known resistivity

The measured resistance is given by the relation R = pL/A where p is the resistivity. If a solution with known resistivity p(known) is inserted into the device, the ratio L/A is given by R(known)/p(known) This can then be used to infer the resistivity p(unknown), of an unknown solution, p(unknown) = R(unknown)/L/A. ​ ​

3. What is the net charge of an object with one coulomb of electrons and 3 moles of neutrons?

The net charge will be -1 C; neutrons do not contribute charge.

4. How does applying a force at the natural frequency of a system change the system?

The object will resonate because the force frequency equals the natural (resonant) frequency. The amplitude of the oscillation will increase.

5. To which side of a hydraulic lift would the operator usually apply a force - the side with the larger cross-sectional area, or the side with the smaller cross-sectional area? Why?

The operator usually applies a force to the side with the smaller cross-sectional area. Because pressure is the same on both sides of the lift, a smaller force can be applied on the smaller surface area to generate the desired pressure.

2. Which likely has a higher conductivity: 1 M glucose or 0.25 M NaCl? Why?

The sodium chloride solution likely has a higher conductivity because it is a salt and will increase the ion content of water. Glucose does not dissociate, and therefore it has a near-zero impact on conductivity.

2. What is the voltage between two points on an equipotential line? Will this voltage cause a charge to move along the line?

There is no voltage between two points on an equipotential line, so there will be no acceleration along the line. However, there is a potential difference between different sets of equipotential lines, which can cause particles to move and accelerate.

2. During exhalation, how does the total resistance of the encountered airways change as air leaves the alveoli to escape the nose and mouth?

Total resistance increases as the air exits the body despite the increase in diameter of the airways. This is because there are fewer airways in parallel with each other.

3. If two objects are traveling toward each other, how does the apparent frequency differ from the original frequency? What if two objects are traveling away from each other? What if one object is following the other? Toward each other:

Toward each other: The apparent frequency is higher than the original frequency (f' = f(v + vD)/(v - vS). Away from each other: The apparent frequency is lower than the original frequency (f' = f(v- vD)/(v + vS). One object follows the other: The apparent frequency could be higher, lower, or equal to the original frequency depending on the relative speeds of the detector and the source (f' = ff(v+ vD)/(v + vS) or f' = f(v - vD)/(v - vS).

4. True or false: Density is a scalar quantity.

True. Density is directionless, and is thus a scalar quantity.

3. True or False: The units of electrical potential energy and electrical potential are different.

True. Electrical potential energy is measured in joules, while electrical potential and potential difference (voltage) are measured in volts.

4. True or False: The internal resistance of a battery will lower the amount of current it can provide.

True. The internal resistance will lower the available voltage for the circuit. Lowering the available voltage will also lower current for any given resistance.

3. True or False: In a circuit, the number of electrons entering a point and leaving that point are the same.

True. This is a restatement of Kirchhoff's junction rule.

4. What phenomena can be detected or treated using ultrasound?

Ultrasound can be used for prenatal screening or to diagnoses gallstones, breast and thyroid masses, and blood clots. It can be used for needle guidance in a biopsy, for dental cleaning, and for treating deep tissue injury, kidney stones, certain small tumors, cataracts, among many other applications.

1. Define the following terms: Wave speed Frequency Angular frequency Period Equilibrium position Amplitude Traveling wave Standing wave

Wave speed: The rate at which a wave transmits the energy or matter it is carrying. The product of wavelength and frequency. Frequency: a measure of how often a waveform passes a given point in space. It is measured in Hz. Angular frequency: the same as frequency, but is measured in radians per second. Period: the time necessary to complete a wave cycle. Equilibrium position: the point with zero displacement in an oscillating wave. Amplitude: the maximal displacement of a wave from the equilibrium position. Traveling wave: have nodes and antinodes that move with wave propagation. Standing wave: have defined nodes and antinodes that do not move with wave propagation.

2. Which would experience a larger magnetic field: an object placed five meters to the left of a current carrying wire, or an object palced at the center of a circle with a radius of five meters. (Note: Assume the current is constant; u0 = 4 x 10-7 T*m/A)

We need not determine the actual values of the magnetic fields in these two cases and can compare the two equations instead. The magnetic field created by the current-carrying wire is given by B = uI/2(pi)r; the magnetic field created by the loop of wire is given by B = uI/2r. u, I, and r are the same in both equations. Therefore, the magnetic field at the center of the loop must be large because the denominator in the equation does not include pi.

2. What is the relationship between weight and density?

Weight is density times volume and acceleration due to gravity.

Four capacitors of 10 pF are connected in parallel with two of the capacitors having a Mylar dielectric (κ = 3) of thickness L inserted and two capacitors only separated by air at a distance L. A voltage potential of 40 V is applied across the circuit and subsequently disconnected. The Mylar dielectrics are then removed and charges are allowed to equilibrate in the system. What is the energy stored on each capacitor? Choose 1 answer: A 64000 pJ B 32000 pJ C 3200 pJ D 6400 pJ

When four capacitors are connected in parallel, they all experience the same voltage 40V. We are interested in U, which is given by 0.5*Q^2/C. So what is Q? For the capacitors without the Mylar, it would be Q = CV or 400 pFV (or pC, since a coulomb = FV). For the capacitors with the Mylar, it would be Q = 3*CV or 1200 pC. When the voltage potential and the Mylar dielectrics are removed, the charge in the circuit will redistribute equally to all of the different capacitors. Initially, we have 2*400 + 2*1200, so a total of 3200 pC in charge distributed among 4 capacitors. When charges are allowed to freely equilibrate, we have 800 pC on each capacitor. We can use this to find the energy stored on each capacitor. Use U=0.5*Q^2/C and we have 32000 pJ (a joule is equivalent to coulomb squared divided by farad).

2. How does a dielectric material impact capacitance? Voltage? Charge?

• Capacitance: Will always increase capacitance • Voltage: Decreases voltage in an isolated capacitor; if it is in a circuit, its voltage is constant because it is dictated by the voltage source. • Charge: Increases charge in a capacitor in a circuit; if a capacitor is isolated, the stored charge will remain constant because there is no additional source of charge.

1. Contrast cohesion and adhesion

• Cohesion: Cohesion is the attractive force experienced by molecules of a fluid for one another. • Adhesion: Adhesion is the attractive force experienced by molecules of a fluid for a different material (usually a solid).

2. Categorize the following materials as either conductors or insulators: blood, hair, copper, glass, iron, sulfuric acid, distilled water

• Conductors: Blood, copper, iron, sulfuric acid • Insulators: Hair, glass, distilled water

1. Define the following terms and provide their SI units:

• Current: The movement of positive charge through a conductive material over time and is given in amperes (C/s). • Voltage: A potential difference between two points and is given in volts. • Electromotive force (emf): Refers to the potential difference of the voltage source for a circuit, usually a battery, and is given in volts. • Conductivity: The inverse of resistance and is a measure of permissiveness to current flow; it is measured in siemens (S)

1. Define the following terms: Dynamic pressure: Static pressure: Pitot tube: Viscosity: Laminar flow: Turbulence:

• Dynamic pressure: The pressure associated with flow, and is represented by 1/2roh*v^2. • Static pressure: The pressure associated with position; static pressure is scarified for dynamic pressure during flow. • Pitot tube: A device that measures static pressure during flow to calculate speed. • Viscosity: A measure of the resistance of a liquid to flow. • Laminar flow: Flow in which there are no eddies and in which streamlines are roughly parallel to each other. • Turbulence: The presence of backflow or current eddies.

1. Define the following terms: Equipotential lines: Electric dipole

• Equipotential lines: the sets of points within space at which the potential difference between any two points is zero. This is best visualized as concentric spheres surrounding a source charge. • Electric dipole: the separation of charge within a molecule such that there is a permanent or temporary region of equal and opposite charges at a particular distance.

2. What direction does a negative electrostatic force point? What direction does a positive electrostatic force point?

• Negative electrostatic force: For a pair of charges, a negative electrostatic force points from one charge to the other (attractive) • Positive electrostatic charge: A positive electrostatic force points from one charge away from the other (repulsive).

1. What are the requirements to have a nonzero electric field? A nonzero magnetic field? A nonzero magnetic force?

• Nonzero electric field: One needs charge. • Nonzero magnetic field: One needs a charge that must also be moving. • Nonzero magnetic force: One needs an external electric field acting on a charge moving any direction except parallel or antiparallel to the external field.

2. What four physical quantities determine the resistance of a resistor?

• Resistivity • Length • Cross-sectional area • Temperature

3. What is the SI unit for pressure? What are other common units of pressure?

• SI unit: Pascal • Torr, mmHg, and atm

1. How does adding or removing a resistor change the total resistance of a circuit with resistors in series? In parallel?

• Series: Adding a resistor in series increases the total resistance of a circuit; removing one in series decreases the total resistance in the circuit. • Parallel: These relationships are reversed in parallel: adding a resistor decreases resistance while removing one increases it.

3. How does adding or removing a capacitor change the total capacitance of a circuit with capacitors in series? In parallel?

• Series: Adding capacitors decreases the total capacitance of the circuit; removing increases the total capacitance in the circuit. • Parallel: These relationships are reversed for parallel: Adding capacitors increases total capacitance while removing decreases it.

4. How do distance and charge related to electrostatic force and electric field?

• • Electrostatic force: Electrostatic force is inversely related to the square of the distance and directly related to each charge. • Electric field: Electric field is unrelated to test charge but is still related to distance by an inverse square relationship. Note that it is the source charge that creates the electric field - not the test charge - so we cannot use the equation E = Fe/q to determine a relationship.