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SAT2 物理考试内容与考点介绍 Math and physics go hand in hand, right? You might be surprised, then,to learn that you aren’t allowed to use a calculator on SAT II Physics.The math required of you never goes beyond simple arithmetic andmanipulation of equations. You have, on average, 48 seconds to answereach question, and the people at ETS realize that isn’t enough time todelve into problems involving simultaneous equations or complextrigonometry. They’re more interested in testing your grasp of thebasic concepts of physics. If you’ve grasped these concepts, yourweakness in math isn’t going to hurt you. ETS breaks down the concepts you need to know for the test into six categories: Topic Percentage of the Test Mechanics 34–38% Electricity and Magnetism 22–26% Waves 15–19% Heat, Kinetic Theory, and Thermodynamics 8–12% Modern Physics 8–12% Miscellaneous 2–4% While these categories are helpful, they arealso very broad. You may be a whiz with waves but a loser with lenses,and want to know how much of the waves portion of the test will bedevoted to optics. To help you out, we’ve broken the test down evenfurther so that you’ll know exactly where to expect to feel thesqueeze. (These figures are only approximations, and may vary from testto test.) Topic % of the Test Number of Questions Mechanics 34–38% 25–29 Vectors 2% 1–2 Kinematics 6% 4–5 Dynamics 10% 7–8 Work, Energy, and Power 6% 4–5 Special Problems in Mechanics 5% 3–4 Linear Momentum 2% 1–2 Rotational Motion 1% 0–1 Circular Motion and Gravitation 4% 2–4 Thermal Physics 8–12% 6–10 Heat and Temperature 4% 2–4 Kinetic Theory and Ideal Gas Laws 2–3% 1–2 Laws of Thermodynamics 1% 0–2 Heat Engines 2–3% 1–2 Electricity & Magnetism 22–26% 16–20 Electric Fields, Forces, Potential 10% 7–8 Magnetic Fields and Forces 6% 4–5 Electromagnetic Induction 1% 1 Circuits and Circuit Elements 6% 4–5 Waves 15–19% 11–15 Waves 10% 7–8 Optics 7% 5–6 Modern Physics 8–12% 6–9 Special Relativity 1–2% 1–2 Atomic Models 3% 2–3 Quantum Physics 2% 1–2 Nuclear Physics 3% 2–3 Miscellaneous 2–4% 1–3 Graph Analysis 1–2% 0–2 Equation Manipulation 0.5–1% 0–1 Significant Digits and Lab Skills 0.5–1% 0–1 The chapters of this book are organizedaccording to these categories. If a physics topic is not in this book,you don't need to know it. Here's some other helpful information: You need to know: the formulas expressing physical relationships (such as F = ma), how to manipulate equations, how to read a graph You don't need to know: trig identities, calculus, three-dimensional vectors and graphs, physical constants (such as G = 6.67 10–11 N·m2 ⁄ kg2) SAT 物理练习题 1 SAT 物理练习题一 SAT Physics Practice Test One Question 1: An object of mass m moving with a velocity v collides with another object of mass 2m. The two objects stick together and they collide with a third object of mass 3m. After the second collision the three objects move together at the same speed. What is the velocity of the three objects after the second collision? v/12 v/6 v/3 v/2 v Question 2: An electric motor accelerates its rotation with a constant angular acceleration of 2 rad/s2 until it reaches a frequency of f = 10/¶ Hz. If the motor starts from rest, how long does it take to reach frequency f? 6s 10s ¶s 12s 15s Question 3: Two satellites orbit the earth at radii r1 and r1. What is the ratio of the velocities of the two satellites? Question 4: 250J of heat are added to a gas in a cylindrical container and then the gas does 120J of work on the top and bottom walls of the cylinder. What is the change in internal energy for the gas? 0J 120J 130J 250J -120J Question 5: Three point charges of charge +Q are placed as shown above. At what point will a negative charge experience a force toward the bottom of the page? A B C D E Question 6: Resistor R1 = 5Ω and resistor R2 = 10Ω are connected in series to a voltage source E = 60V. What is the ratio between the power dissipation in R2 and the power dissipation in R1? 1 2 3 4 5 Question 7: Resistor R1 = 4Ω and resistor R2 = 6Ω are connected in series. If the tolerance of R1 is 1% and the tolerance of R2 is 2%, what is the tolerance of the equivalent resistor R? .8% 1% 1.6% 2% 3% Question 1 solution: According to the law of conservation of momentum, mv = (m + 2m)v1 and, (m + 2m)v1 = (m + 2m + 3m)v2, where v1 and v2 are the speed after the first and after the second collision. In conclusion, mv = 6mv2 and v2 = v/6. Question 2 solution: t = ω / ε = 2πf / ε where ω is the angular speed and ε is the angular acceleration. t = 2π(10/π) / 2 t = 10s. Question 3 solution: We equate the formulas for gravitational force and centripetal force: mv2/r = GmM/r2 r = radius of the orbit; m = mass of satellite; M = mass of planet; v = speed of satellite; v12 = GM/r1 v22 = GM/r2 Question 4 solution: According to the First Law of Thermodynamics, the change in internal energy is equal to the change in heat plus the work done on the system. ΔU = ΔQ + ΔW = 250J - 120J = 130J. Question 5 solution: A and D are the only points that have the horizontal component of the force equal to zero. A negative charge experiences a force toward the bottom of the page in point A and towards the top of the page in point B. (a) is the correct answer. Question 6 solution: P2 = R2I2 P1 = R1I2 We divide the 2 equations and, P2/P1 = R2/R1 P2/P1 = 100/50 P2/P1 = 2 Question 7 solution: R1(1 + t1) + R2(1 + t2) = R(1 + t), We also know that R1 + R2 = R. We substract the second equation from the first equation: R1t1 + R2t2 = Rt, t = (R1t1 + R2t2)/R t = (4·1% + 6·2%)/10 t = 1.6% is the tolerance of the series resistor combination. SAT 物理练习题 2 SAT 物理练习题二 SAT Physics Practice Test Two Question 1: Five particles charged with the same charge +q move with the same speed v in a magnetic field B, as shown above. Which particle experiences the highest magnetic force? A B C D E Question 2: Two wires of circular cross-sectional areas have resistances R1 and R2. If ρ1 = 2ρ2, l1 = 2l2 and r1 = 2r2, what is the ratio R1/R2? ρ1, ρ2 are the resistivities of the two wires, l1, l2 are the lengths of the two wires, r1, r2 are the radii of the two wires. 1 1/2 1/4 2 4 Question 3: Two wires carry identical currents I, as shown above. At which point is the magnetic field the strongest? A B C D E Question 4: Two metallic bars slide along metallic rails at speeds v1 = .1m/s and v2 = .2m/s as shown above. The bar and the rails are situated in a magnetic field of 4T. What is the induced voltage in the bar and rails? 20mV 30mV 40mV 120mV 150mV Question 5: A police car with its siren on travels at a speed v1 toward a person. The frequency of the siren is f1 and the person hears the sound at a frequency f2. If vs is the speed of sound, v1 = vsf2/f1 vs(1 - f2/f1) vs(f1/f2 - 1) vs(1 - f1/f2) vs(f2/f1 - 1) Question 6: Violet light has a wavelength of 400nm. What is its frequency, if the speed of light is 3·108? 5·1014 7.5·1014 1015 2·1015 5·1015 Question 7: The activity of a radioactive sample at time t = 0s is A0 and the activity of the same radioactive sample at time t1 is A1. What is the decay constant of the sample? [ln(A1/A0)]/t1 [ln(A0/A1)]/t1 [ln(A1 - A2)]/t1 [ln(A1/A0)]t1 e(A1/A0)t1 SAT2 物理练习题参考答案与解析参见下一页 Question 1: Five particles charged with the same charge +q move with the same speed v in a magnetic field B, as shown above. Which particle experiences the highest magnetic force? Solution: The magnetic force experienced by a moving particle is given by the formula F = q(v x B). We can maximize F by ensuring that the speed and the magnetic field are perpendicular to one another. Particule A is the correct answer. Question 2: Two wires of circular cross-sectional areas have resistances R1 and R2. If ρ1 = 2ρ2, l1 = 2l2 and r1 = 2r2, what is the ratio R1/R2? ρ1, ρ2 are the resistivities of the two wires, l1, l2 are the lengths of the two wires, r1, r2 are the radii of the of the cross-sectional areas of the two wires. Solution: R1 = ρl11/A1 = ρ1l1/(¶r12) R2 = ρ2l2/(¶r22) = (ρ1/2)(l1/2)/(¶r12/4) = ρ1l1/(¶r12) R1/R2 = 1. Question 3: Two wires carry identical currents I, as shown above. At which point is the magnetic field the strongest? Solution: Points D and B are situated at equal distance from the two wires and the magnetic field is 0 at these points. As the magnetic fields created by the two currents have opposite directions at points A, C and E, the strongest magnetic field will be at point A, because the component generated by the "horizontal" current is much lower than the one created by the "vertical" one. Question 4: Two metallic bars slide along metallic rails at speeds v1 = .1m/s and v2 = .2m/s as shown above. The bar and the rails are situated in a magnetic field of 4T. What is the induced voltage in the bar and rails? Solution: e = -dΦ/dt = -B·dA/dt dA/dt = l(dx/dt) = l(v1 + v2) The induced voltage in the bar is B·l·(v1 + v2) = 120mV. Question 5: A police car with its siren on travels at a speed v1 toward a person. The frequency of the siren is f1 and the person hears the sound at a frequency f2. If vs is the speed of sound, v1 = Solution: The frequency heard by the person is given by the formula: f2 = [vs/(vs - v1)]f1 f2vs - f2v1 = f1vs v1 = vs(f1/f2 - 1) Question 6: Violet light has a wavelength of 400nm. What is its frequency, if the speed of light is 3·108? Solution: f = c/λ = 3·108/400·10-9 = 7.514Hz. Question 7: The activity of a radioactive sample at time t = 0s is A0 and the activity of the same radioactive sample at time t1 is A1. What is the decay constant of the sample? Solution: A1 = A0eλt1 A1/A0 = eλt1 λ = [ln(A1/A0)]/t1 SAT 物理练习题 3 SAT 物理练习题三 SAT Physics Practice Test Three Question 1: What is the magnitude of the vector 3A - B in the figure above? A.3 B.4 C.5 D.2 E.6 Question 2: The graph above shows the acceleration of a particle. At t = 0s, the speed of the particle is 1m/s. What is the speed of the particle at t = 4s? 11 m/s 9 m/s 19 m/s 13 m/s 10 m/s Question 3: Forces F1 and F2 in the figure above act on a block of mass m = 10kg that moves on a frictionless surface. What is the acceleration of the block? 1 m/s 1.5 m/s 2 m/s 2.5 m/s 3 m/s Question 4: A block of mass m is moving down an inclined plane with a decreasing speed. The coefficient of friction between the block and the plane is μ. Which of the following statements is true? sin(α) < μ sin(α) > μ cos(α) < μ cos(α) > μ tan(α) < μ Question 5: When a car's kinetic energy increases 9 times, what happens with its speed? increases 9 times increases 3 times decreases 9 times decreases 3 times remains constant Question 6: An object of mass 4kg is attached to a spring. The equilibrium position of the object is .4m from the point where the spring exerts no force on the object. What is the spring constant, k? 10 N/m 80 N/m 100 N/m 150 N/m 200 N/m Question 7: An object of mass 10kg sitting on a frictionless horizontal plane is moved from a stationary state by the force shown above. What is the velocity of the object at time t = 5s? 2.5 m/s 3 m/s 4 m/s 5 m/s 6 m/s SAT2 物理练习题参考答案与解析参见下一页 Question 1: What is the magnitude of the vector 3A - B in the figure above? Solution: The magnitude of the vector 3A is 3 and the magnitude of vector B is 4. The angle between vectors 3A and B is 90o. According to the Pythagorean theorem, the magnitude of 3A - B is 5. o Question 2: The graph above shows the acceleration of a particle. At t = 0s, the speed of the particle is 1m/s. What is the speed of the particle at t = 4s? Solution: At t = 2s, the speed of the particle is v2s = v0s + 2m/s2·2s = 5m/s. At t = 4s, the speed of the particle is v4s = v2s + 3m/s2·2s = 11m/s. o Question 3: Forces F1 and F2 in the figure above act on a block of mass m = 10kg that moves on a frictionless surface. What is the acceleration of the block? Solution: F1cos(60o) + F2cos(60o) = m·a 20·1/2 + 30·1/2 = 10·a 25 = 10·a a = 2.5m/s2 o Question 4: A block of mass m is moving down an inclined plane with a decreasing speed. The coefficient of friction between the block and the plane is μ. Which of the following statements is true? Solution: mg sin(α) - � mg cos(α) = a The speed is decreasing so a < 0. This means that mg sin(α) - � mg cos(α) < 0 mg sin(α) < � mg cos(α) tan(α) < � o Question 5: When a car's kinetic energy increases 9 times, what hapens with its speed? Solution: The car's initial kinetic energy is E i = mvi2/2 and the final kinetic energy is E f = mvf2/2. Ef/Ei = (vf/vi)2 (vf/vi)2 = 9 vf/vi = 3 o Question 6: An object of mass 4kg is attached to a spring. The equilibrium position of the object is .4m from the point where the spring exerts no force on the object. What is the spring constant, k? Solution: F = kx mg = kx k = mg/x k = 40N/.4m k = 100N/m o Question 7: An object of mass 10kg sitting on a frictionless horizontal plane is moved from a stationary state by the force shown above. what is the velocity of the object at time t = 5s? Solution: The area under a force versus time graph gives us the impulse given to the object. p = 10/2 + 30 + 10/2 = 40 kg m/s v = p/m v = 4 m/s