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P PHYSICS B 004 SCORING GUIDELINES (Form B) General Notes about 004 P Physics Scoring Guidelines. The solutions contain the most common method(s) of solving the free-response questions, and the allocation for these solutions. Other methods of solution also receive appropriate credit for correct work.. Generally, double penalty for errors is avoided. For example, if an incorrect answer to part (a) is correctly substituted into an otherwise correct solution to part (b), full credit will usually be awarded. One exception to this may be cases when the numerical answer to a later part should be easily recognized as wrong, e.g. a speed faster than the speed of light in vacuum. 3. Implicit statements of concepts normally receive credit. For example, if use of the equation expressing a particular concept is worth one point, and a student s solution contains the application of that equation to the problem but the student does not write the basic equation, the point is still awarded. 4. The scoring guidelines typically show numerical results using the value 0 m s is of course also acceptable. g = 9.8 m s, but use of 5. Numerical answers that differ from the published answer due to differences in rounding throughout the question typically receive full credit. The exception is usually when rounding makes a difference in obtaining a reasonable answer. For example, suppose a solution requires subtracting two numbers that should have five significant figures and that differ starting with the fourth digit (e.g. 0.95 and 0.78). Rounding to three digits will lose the accuracy required to determine the difference in the numbers, and some credit may be lost. Copyright 004 by College Entrance Examination Board. ll rights reserved.
P PHYSICS B 004 SCORING GUIDELINES (Form B) Question 5 points total Distribution (a) 4 points For any indication of conservation of energy For a correct conservation equation for this situation mu0 + mgh0 = mu + mgh u u 0 g h 0 ( h ) = + - For the correct substitutions ( ) u =.5 m s + ( 9.8 m s )(.0 m -.9 m) u 4.( m s) = (or 4.3( m s ) using For the correct answer g = 0 m s ) u =.0 m s (or. m s if u was not rounded or if g = 0 m s was used) (b) points For each correctly drawn and labeled force One point earned for correct forces was deducted for having any extraneous forces. pt each (c) For indicating that the sum of the forces equals the centripetal force mu  F = r For having the correct relative signs in the application of the above equation mu mg - N = r For solving for the normal force, substituting, and solving correctly mu N = mg - r ( 0.50 kg) 4.( m s) N = ( 0.50 kg)( 9.8 m s ) - 0.95 m N =.7 N ( ) Copyright 004 by College Entrance Examination Board. ll rights reserved. 3
P PHYSICS B 004 SCORING GUIDELINES (Form B) (d) Question (continued) Distribution For any indication that the work done must equal the kinetic energy at point in the absence of friction W =- mu friction For correct substitution W friction =- ( 0.50 kg )( 4. ( m s ) ) For the correct answer, including the negative sign W =-. J friction (e) Method : For indicating that one should decrease the radius of the curve of the second hill mu The cart will lose contact when mg - 0. Decreasing the radius of the curve r will cause the second term to increase and thus meet the condition. mu For referring to the equation N = mg - r For indicating that the cart will loose contact when N 0 Method : For indicating that one should make the initial hill higher or the second hill lower mu The cart will loose contact when mg - 0. Increasing the difference in r heights will cause the speed at to increase, and thus the second term will increase and the condition will be met. mu For referring to the equation N = mg - and indicating that the cart will r loose contact when N 0 For indicating that the speed at will increase () () () Copyright 004 by College Entrance Examination Board. ll rights reserved. 4
P PHYSICS B 004 SCORING GUIDELINES (Form B) Question 5 points total Distribution (a) 4 points For calculating the length of time takes to reach the constant speed u ) u c = at t = u a c ( ) ( ) t that the diving bell is accelerating (i.e. the time it c t =.0 m s 0.0 m s = 0 s For calculating the distance the bell descends while accelerating d = at d ( )( ) = 0.0 m s 0 s = 0 m The bell therefore descends a distance d = 80 m - 0 m = 60 m at the constant speed. For calculating the time to descend this 60 m d = u t c t = d u c ( ) ( ) t = 60 m.0 m s = 30 s For calculating the total time ttot = t + t = 0 s + 30 s t = 50 s tot (b) For a correct expression for the weight of the water above the cross-sectional area w = rvg = rhg For correct substitution w = ( 05 kg m 3 )( 9.0 m )( 80 m )( 9.8 m s ) For the correct answer, including units 6 6 w = 7. 0 N (or 7.4 0 N using g = 0 m s ) Full credit could also be earned for determining the pressure due to the water alone, and using F = P to determine the weight maximum of points could be earned for only determining the mass of the water, or for calculating the absolute pressure and using F = P. Copyright 004 by College Entrance Examination Board. ll rights reserved. 5
P PHYSICS B 004 SCORING GUIDELINES (Form B) (c) Question (continued) Distribution For indicating that the pressure at a depth h has a term r gh, or using P = w and the value of the weight from part (b) For indicating that the atmospheric pressure must be added (in correct SI units otherwise the r gh term must be converted to atmospheres for full credit) P = ( w ) + Patm ( ) 6 5 P = 7. 0 N 9.0 m +.0 0 N m For the correct answer, including units P = 9.0 0 N m 5 5 (or 9. 0 N m using g = 0 m s ) (d) For a correct expression for the force on an area F = P hatch For a correct expression for the area of the hatch hatch hatch = pr Since there is one atmosphere pressure inside the diving bell, the net pressure corresponding to the minimum applied force is that from the water only. Fmin = rghhatch Substituting: 3 ( )( )( )( p ( ) ) Fmin = 05 kg m 9.8 m s 80 m 0.5 m For the correct answer 5 F min =.6 0 N Since the question could have been interpreted as asking for the minimum total force required, full credit was awarded for including atmospheric pressure. (e) points For a correct modification that would reduce the force necessary to open the hatch For a correct justification Examples: Increase the pressure inside the diving bell. The internal pressure would then compensate for atmospheric pressure plus some of the pressure of the water, reducing the force needed. Reduce the size of the hatch. Pressure times a smaller area yields a smaller force. Use a tool that gives a mechanical advantage, such as a lever. Such a tool is designed so that one exerts a smaller force over a larger distance than one would without it. Copyright 004 by College Entrance Examination Board. ll rights reserved. 6
P PHYSICS B 004 SCORING GUIDELINES (Form B) Question 3 5 points total Distribution (a) 4 points There must be a node at the liquid surface and an antinode near the top of the tube, so the length of consecutive resonances differ by a half wavelength. For equating the difference in air column lengths to the difference in the number of wavelengths l L - L = ( ) l = L - L For correct substitution and answer l = ( 0.80 m - 0.5 m) l =. m maximum of was awarded for using only one of the air column lengths to calculate a wavelength maximum of points was awarded for equating the difference in air column lengths to one or one-quarter wavelength (b) points For using the relationship between wavelength, speed, and frequency f = uair l For correct substitutions (using l from part (a)) and a corresponding correct answer f = ( 343 m s) (. m) f = 3 Hz (c) For indicating the need to use the values of the wave properties appropriate for water lwater = uwater fwater For indicating that the frequency in water is the same as in air For correct substitution and answer ( 490 m s) l water = 3 Hz l = 4.8 m water Copyright 004 by College Entrance Examination Board. ll rights reserved. 7
P PHYSICS B 004 SCORING GUIDELINES (Form B) (d) Question 3 (continued) Distribution L3 is approximately wavelengths, which is one-half wavelength longer than L 4 For any indication that L3 equals L + l or L + l points. m L 3 = 0.80 m + For the correct answer (using whatever wavelength was determined previously) L 3 =.35 m maximum of points were awarded for using L3 = 5l or L3 = L + l One point was awarded for a good drawing of the standing wave in the air column with no calculation. (e) For indicating that the calculation of frequency was too low For a correct justification For example: s temperature increases, the speed of sound in air increases, so the speed used in part (b) was too low. Since f = uair l, that lower speed of sound yielded a frequency that was too low. points Copyright 004 by College Entrance Examination Board. ll rights reserved. 8
P PHYSICS B 004 SCORING GUIDELINES (Form B) Question 4 5 points total Distribution (a) 4 points For a correct expression for the magnitude of the emf per turn in the coil f e = D OR e = B u Dt DB w ( B - 0) B w e = = OR e = Dt Dt Dt For correct substitutions in either equation (both yield the same value) ( 0.5 m)( 0.5 m)( 0.0 T) e = 0.50 s For correct calculation e = 0.05 V per turn For recognizing that with 0 turns the total emf in the coil is 0 times the emf per turn e = 0( 0.05 V per turn) = 0.30 V tot (b) points For correct expression for Ohm s law, substitution from part (a), and magnitude V = IR V 0.30 V I = 0.06 R = 5.0 W = For correct direction, i.e., counterclockwise (c) For a correct expression for the power dissipated in the coil P = IV OR P = I R OR P = V R For correct substitution of answers from (a) and/or (b) into one of these expressions (Must recognize that V = e tot ) For example, P = ( 0.06 )( 0.30 V) For correct calculation including correct units P = 0.08 W Copyright 004 by College Entrance Examination Board. ll rights reserved. 9
P PHYSICS B 004 SCORING GUIDELINES (Form B) (d) Question 4 (continued) Distribution The force on the right side is zero, and forces on the top and bottom sides cancel, so the net force is that on the left side. For the correct expression for the force on a straight wire (force per turn in this situation) in a magnetic field F = BI sin q OR F = BI (recognizing that the wire is perpendicular to the field) For correct substitutions F = ( 0.0 T)( 0.60 )( 0.5 m) F = 0.008 N For recognizing that with 0 turns the total force on the left side of the coil is 0 times the force per turn F = 0.036 N tot lternate Solution For using one of the equations P = Fusin q OR W P = t = P F usinq Pt F = d For correct substitutions (both approaches yield same value) ( 0.08 W)( 0.50 s) F tot = 0.5 m For correct answer F = 0.036 N tot Fd t lternate points (e) For recognition that doubling the number of turns doubles the total emf, which would tend to increase the current For recognition that doubling the number of turns doubles the total resistance, which would tend to decrease the current For putting these together to show that the current is unchanged e f ei ei I f = = = = Ii R R R f i i Note: The third point was awarded for an indication that the current is unchanged, even if the justification was wrong. Copyright 004 by College Entrance Examination Board. ll rights reserved. 0
P PHYSICS B 004 SCORING GUIDELINES (Form B) Question 5 0 points total Distribution (a) points For recognizing that P = PB t point : PV = nrt V t point B: P = nrt Dividing these equations and solving for T : PV T = V T P T = T For the correct answer T = T (b) points nswer can be obtained by either comparing points B & C or points & C using the ideal gas law at each point For recognizing that T T OR T C = B C T = point Comparing points B & C Comparing points C & V T t point B: P = nr t point : PV = nrt V V t point C: P = nrt t point C: P = nrt Dividing the equations and solving for : Dividing the equations and solving for P : V P V P P T nr = PV nrt V P P = P = P P = For the correct answer For the correct answer P = P P = P Copyright 004 by College Entrance Examination Board. ll rights reserved.
P PHYSICS B 004 SCORING GUIDELINES (Form B) (c) points Question 5 (continued) Distribution For correct equation for work done on the gas (regardless of sign) OR for recognition that work is the area under the line B on the graph. (No work is done from B to C because the change in volume is zero.) W =- P DV V W P Ê ˆ =- Á -V Ë For the correct answer including correct sign PV W = (d) 4 points Heat was added to the gas in processes BC and C, but not in B. For two or three correct indications of whether or not heat was added to the gas in each process (The absence of a check mark was taken as in indication that heat was not added.) For a reasonable justification for process B. This point was awarded only if this process was indicated correctly (i.e., not checked) Example: The volume decreases so the work done on the gas is positive. The temperature decreases so the change in internal energy is negative. Therefore Q = DU -W is negative. Heat is expelled from the gas. (Note: nswer must mention work for credit.) For a reasonable justification for process BC. This point was awarded only if this process was indicated correctly (i.e., checked) Example: There is no change in volume so no work is done. The temperature increases so the internal energy increases. Therefore Q = DU -W is positive. (This point also awarded for only referring to increasing temperature or for referring to increasing speed of the molecules.) For a reasonable justification for process C. This point was awarded only if this process was indicated correctly (i.e., checked). Example: There is no change in temperature or internal energy. The volume increases so work is done by the gas. Heat needs to be added to the gas to do this work. Copyright 004 by College Entrance Examination Board. ll rights reserved.
P PHYSICS B 004 SCORING GUIDELINES (Form B) Question 6 0 points total Distribution (a) For a smooth curve passing through or very close to all plotted points Partial credit points could be awarded for curves of lesser quality. For example: Showing all the data points connected by straight-line segments earned points. Curves that generally fit the data points at small angles, but are concave upward for the whole range earned or points depending on how badly the curve misses the points at higher angles. single straight best fit line or really bad curve earned. curve that was monotonically decreasing earned no points. Copyright 004 by College Entrance Examination Board. ll rights reserved. 3
P PHYSICS B 004 SCORING GUIDELINES (Form B) (b) Question 6 (continued) Distribution For reading the wavelength shift from the graph From the graph shown, the wavelength shift at 0 is 8. 000 0 m. The photon loses energy, which means the wavelength increases. For adding (not subtracting) the wavelength shift to the original wavelength l s -4-7 =.400 0 m + 8.000 0 m For correct answer l s -6-4 = 40.8 0 m =.4 0 m -7 (c) points For using the de Broglie equation to calculate momentum (even if a value from (b) that was actually Dl was substituted) l = h p OR p = h l p s s p s = h l s s ( 6.63 0-34 J i s 4 ) (.408 0 - m ) = For consistent answer including correct units p s -0 = 4.7 0 kgi m s Note: The answer point could also be awarded if the value of ls = li -Dl instead of the correct relationship. was used (d) points For use of conservation of energy DEnuc =- DEphoton hc DEphoton D( hf ) D( l = = ) OR ( ) hc DEphoton = D pc = D( ) Êhc hc ˆ Ê ˆ DEnuc =-Á - = hc - Ë ls l i Á Ëli l s (.99 0-5 DE J m nuc = Ê ˆ ) Á - Ë.400 0-4 m.408 0-4 m For the correct answer DE nuc -4 = 8.08 0 J (or 50 kev) Note: The answer point was awarded for correct use of whatever ls was obtained from part (b), but not for using the value of Dl. l Copyright 004 by College Entrance Examination Board. ll rights reserved. 4