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Problem B-1 Problem B-2 Problem B-3 Problem B-4 Problem B-5 Problem B AP Physics B END Problem B-7 Grade Distributions

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2009 Grade Distributions ,702 Exams Mean Grade = AP Physics B Menu

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In an experiment, students are to calculate the spring constant k of a vertical spring in a small jumping toy that initially rests on a table. When the spring in the toy is compressed a distance x from its uncompressed length L 0 and the toy is released, the top of the toy rises to a maximum height h above the point of maximum compression. The students repeat the experiment several times, measuring h with objects of various masses taped to the top of the toy so that the combined mass of the toy and added objects is m. The bottom of the toy and the spring each have negligible mass compared to the top of the toy and the objects taped to it. Physics B-1 (15 points) 2009 AP-B Exam

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(a) 3 points Derive an expression for the height h in terms of m, x, k, and fundamental constants. Physics B-1 (15 points) 1 pt. Conservation of Energy 1 pt. Correct Energy Expression 1 pt. Solving for h 2009 AP-B Exam

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With the spring compressed a distance x = m in each trial, the students obtained the following data for different values of m. (b) i. 2 points What quantities should be graphed so that the slope of a best-fit straight line through the data points can be used to calculate the spring constant k ? Physics B-1 (15 points) 2 pt. Expression 2009 AP-B Exam

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With the spring compressed a distance x = m in each trial, the students obtained the following data for different values of m. (b) ii. 2 points Fill in one or both of the blank columns in the table with calculated values of your quantities, including units. 1/m (kg -1 ) /h (m -1 ) Physics B-1 (15 points) 1 pt. Filling table with correct values. 1 pt. Correct Units AP-B Exam

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(c) 4 points On the axes below, plot your data and draw a best-fit straight line. Label the axes and indicate the scale. h(m) /m (kg 1 ) Physics B-1 (15 points) 1 pt. Correctly plotting Points. 1 pt. Best Fit Straight Line. 1 pt. Correctly Scaling Axis. 1 pt. Correctly Labeling Axis AP-B Exam

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(d) 2 points Using your best-fit line, calculate the numerical value of the spring constant h 1/m 1 m Physics B-1 (15 points) 1 pt. Calculating the Slope 1 pt. Correct Value for Spring Constant 2009 AP-B Exam

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(e) 2 points Describe a procedure for measuring the height h in the experiment, given that the toy is only momentarily at that maximum height Use a timer to measure the time the toy is in the air. Calculate the maximum height reached using this time. Physics B-1 (15 points) 2 pt. Correct, Complete Procedure 2009 AP-B Exam Menu

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Two small objects, labeled 1 and 2 in the diagram above, are suspended in equilibrium from strings of length L. Each object has mass m and charge +Q. Assume that the strings have negligible mass and are insulating and electrically neutral. Express all algebraic answers in terms of m, L, Q, , and fundamental constants. Physics B-2 (10 points) 2009 AP-B Exam

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(a) 3 points On the following diagram, sketch lines to illustrate a 2-dimensional view of the net electric field due to the two objects in the region enclosed by the dashed lines. Physics B-2 (10 points) 1 pt. Field direction away from charges. 1 pt. Correct Curvature of Field Lines 1 pt. Zero field at point A 2009 AP-B Exam

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(b) 2 points Derive an expression for the electric potential at point A, shown in the diagram at the top of the page, which is midway between the charged objects. Physics B-2 (10 points) 1 pt. Showing Field Contributions. 1 pt. Correct Expression Using Given Quantities 2009 AP-B Exam r

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(c) 2 points On the following diagram of object 1, draw and label vectors to represent the forces on the object. T mg FEFE Physics B-2 (10 points) 1 pt. Correct Arrows. 1 pt. Correct Labeling of vectors AP-B Exam

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(d) 3 points Using the conditions of equilibrium, write—but do not solve—two equations that could, together, be solved for and the tension T in the left-hand string. T mg FEFE Physics B-2 (10 points) 1 pt. T X = F E. 1 pt. T Y = mg. 1 pt. Stating the Two Equations Using Given Quantities 2009 AP-B Exam r Menu

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A metal rod of mass 0.22 kg lies across two parallel conducting rails that are a distance of 0.52 m apart on a tabletop, as shown in the top view above. A 3.0 resistor is connected across the left ends of the rails. The rod and rails have negligible resistance but significant friction with a coefficient of kinetic friction of There is a magnetic field of 0.80 T perpendicular to the plane of the tabletop. A string pulls the metal rod to the right with a constant speed of 1.8 m/s. Physics B-3 (15 points) 2009 AP-B Exam

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(a) 3 points Calculate the magnitude of the current induced in the loop formed by the rod, the rails, and the resistor. Physics B-3 (15 points) 1 pt. Ohm’s Law 1 pt. Motional EMF1 pt. Correct answer 2009 AP-B Exam

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(b) 4 points Calculate the magnitude of the force required to pull the rod to the right with constant speed. Physics B-3 (15 points) 1 pt. Force of Friction 1 pt. Correct Magnetic Force 1 pt. Adding the Two Forces 1 pt. Correct answer 2009 AP-B Exam

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(c) 3 points Calculate the energy dissipated in the resistor in 2.0 s. Physics B-3 (15 points) 1 pt. Power-Energy Relationship 1 pt. Electric Power (I 2 R) 1 pt. Correct Substitution 2009 AP-B Exam

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(d) 2 points Calculate the work done by the string pulling the rod in 2.0 s. Physics B-3 (15 points) 1 pt. Correct Expression for Distance 1 pt. Correct Substitution for Force 2009 AP-B Exam

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(e) 2 points Compare your answers to parts (c) and (d). Provide a physical explanation for why they are equal or unequal. Answer (c) does not include work done by friction. Work done by friction dissipates energy. Physics B-3 (15 points) 1 pt. Work Done by Friction not Included 1 pt. Friction Dissipates Energy 2009 AP-B Exam Menu

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The cylinder contains 2.2 kg of water vapor initially at a volume of 2.0 m 3 and an absolute pressure of 3.0 x 10 5 Pa. This state is represented by point A in the PV diagram below. The molar mass of water is 18 g, and the water vapor can be treated as an ideal gas. Physics B-4 (10 points) 2009 AP-B Exam

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(a) 3 points Calculate the temperature of the water vapor at point A. Physics B-4 (10 points) 1 pt. Ideal Gas Law 1 pt. Correct Number of Moles 1 pt. Correct Substitution 2009 AP-B Exam

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(b) 1 point Calculate the temperature of the water vapor at point C. Physics B-4 (10 points) 1 pt. Correct Answer and Units 2009 AP-B Exam The absolute pressure of the water vapor is increased at constant volume to 4.0 x 10 5 Pa at point B, and then the volume of the water vapor is increased at constant pressure to 2.5 m 3 at point C, as shown in the PV diagram.

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(c) 3 points Does the internal energy of the water vapor for the process A→B→C increase, decrease, or remain the same? ____Increase ____Decrease ____Remain the same Justify your answer Internal energy is proportional to temperature. Physics B-4 (10 points) 1 pt. Selecting Increase 2 pt. Correct Justification 2009 AP-B Exam

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(d) 3 points Calculate the work done on the water vapor for the process A→B→C. The area under the curve represents the work done on the water. Physics B-4 (10 points) 1 pt. Work Equals Area Under Curve 1 pt. Correct Numerical Answer and Units 1 pt. Negative Sign on Answer 2009 AP-B Exam Menu

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Three objects of identical mass attached to strings are suspended in a large tank of liquid, as shown above. Physics B-5 (10 points) 2009 AP-B Exam

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(a) 3 points Must all three strings have the same tension? ____ Yes ____ No Justify your answer. The tension in each string depends on the weight and buoyant force on each object. The buoyant force on a submerged object depends on the object’s volume. Physics B-5 (10 points) 1 pt. Selecting No 2 pt. Correct Justification 2009 AP-B Exam

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Object A has a volume of 1.0 x 10 5 m 3 and a density of 1300 kg m 3. The tension in the string to which object A is attached is N. (b) 3 points Calculate the buoyant force on object A. mg T B Physics B-5 (10 points) 1 pt. Expression of Equilibrium 1 pt. Using Density and Volume 1 pt. Correct Answer 2009 AP-B Exam

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(c) 2 points Calculate the density of the liquid. Object A has a volume of 1.0 x 10 5 m 3 and a density of 1300 kg m 3. The tension in the string to which object A is attached is N. Physics B-5 (10 points) 1 pt. Correct Substitution 1 pt. Correct Answer 2009 AP-B Exam B

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(d) 2 points Some of the liquid is now drained from the tank until only half of the volume of object A is submerged. Would the tension in the string to which object A is attached increase, decrease, or remain the same? ____ Increase ____ Decrease ____ Remain the same Justify your answer. Less liquid is displaced therefore the buoyant force is less Physics B-5 (10 points) 1 pt. Selecting Increase 1 pt. Correct Justification 2009 AP-B Exam Menu

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In a classroom demonstration, a beam of coherent light of wavelength 550 nm is incident perpendicularly onto a pair of slits. Each slit has a width w of 1.2 x 10 6 m, and the distance d between the centers of the slits is 1.8 x 10 6 m. The class observes light and dark fringes on a screen that is a distance L of 2.2 m from the slits. Physics B-6 (10 points) 2009 AP-B Exam

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(a) 2 points Calculate the frequency of the light. Physics B-6 (10 points) 1 pt. Speed-Frequency-Wavelength 1 pt. Correct answer 2009 AP-B Exam

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(b) 3 ponts Calculate the distance between two adjacent dark fringes on the screen. Physics B-6 (10 points) 1 pt. Interference position 1 pt. Interference Separation 1 pt. Correct Substitution 2009 AP-B Exam = 550 nm L = 2.2 m d = 1.8 x 10 6 m

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The entire apparatus is now immersed in a transparent fluid having index of refraction 1.4. (c) 2 points What is the frequency of the light in the transparent fluid? Physics B-6 (10 points) 2 pt. Frequency Does Not Change 2009 AP-B Exam

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(d) 3 points Does the distance between the dark fringes increase, decrease, or remain the same? _____ Increase _____ Decrease _____ Remain the same Explain your reasoning. x is proportional to the wavelength nad the wavelength decreases in the fluid. Physics B-6 (10 points) 1 pt. Selecting Decrease 2 pt. Correct Reasoning 2009 AP-B Exam Menu

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A photon of wavelength 250 nm ejects an electron from a metal. The ejected electron has a de Broglie wavelength of 0.85 nm. (a) 3 points Calculate the kinetic energy of the electron. Physics B-7 (10 points) 1 pt. Correct Substitution of wavelength for Velocity 1 pt. Correct Substitution of Planck’s Constant 1 pt. Correct Substitution of Electron Mass 2009 AP-B Exam

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(b) 3 points Assuming that the kinetic energy found in (a) is the maximum kinetic energy that it could have, calculate the work function of the metal. A photon of wavelength 250 nm ejects an electron from a metal. The ejected electron has a de Broglie wavelength of 0.85 nm. Physics B-7 (10 points) 1 pt. Photoelectric Effect 1 pt. Correct Substitution of Photon Wavelength 1 pt. Correct Substitution of (hc) 1 pt. Correct Units in Parts (a) and (b) 2009 AP-B Exam

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(c) 3 points The incident photon was created when an atom underwent an electronic transition. On the energy level diagram of the atom below, the transition labeled X corresponds to a photon wavelength of 400 nm. Indicate which transition could be the source of the original 250 nm photon by circling the correct letter. Justify your answer. Emission of the original photon means the atom goes to a lower energy level. Energy is inversely proportional to wavelength. Physics B-7 (10 points) 1 pt. Selecting Correct Transition 2 pt. Correct Justification 2009 AP-B Exam Menu

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