AP* Physics B: Newton s Laws YOU MAY USE YOUR CALCULATOR
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1 AP* Physics B: Newton s Laws Name: Period: YOU MAY USE YOUR CALCULATOR CLEARLY SHOW THE METHOD YOU USED AND STEPS INVOLVED IN ARRIVING AT YOUR ANSWERS. It is to your advantage to do this, because you may earn partial credit if you do and you will receive little or no credit if you do not. Attention should be paid to significant figures. Be sure to write all your answers to the questions in the space provided. 1. (15 points) A child pulls a 15 kg sled containing a 5.0 kg dog along a straight path on a horizontal surface. He exerts a force of 55 N on the sled at an angle of 20 above the horizontal, as shown in the figure above. The coefficient of friction between the sled and the surface is (a) On the dot below that represents the sled-dog system, draw and label a free-body diagram for the system as it is pulled along the surface. (b) Calculate the normal force of the surface on the system. (1) Test Questions are Copyright by College Entrance Examination Board, Princeton, NJ. All rights reserved. For face-to-face teaching purposes, classroom teachers are permitted to reproduce the questions. Web or Mass distribution prohibited. (2) AP is a registered trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of and does not endorse this product. Permission is granted for individual classroom teachers to reproduce the activity sheets and illustrations for their own classroom use. Any other type of reproduction of these materials is strictly prohibited.
2 AP* Physics B: Newton s Laws Name: Period: (c) Calculate the acceleration of the system. (d) Calculate the work done by the child's pulling force as the system moves a distance of 7.0 m. (e) At some later time, the dog rolls off the side of the sled. The child continues to pull with the same force. On the axes below, sketch a graph of speed v versus time t for the sled. Include both the sled's travel with and without the dog on the sled. Clearly indicate with the symbol t r the time at which the dog rolls off.
3 2007 Q1 (15 points) AP* Newton s Laws Free Response Questions page 8 An empty sled of mass 25 kg slides down a muddy hill with a constant speed of 2.4 m/s. The slope of the hill is inclined at an angle of 15 with the horizontal as shown in the figure above. (a) Calculate the time it takes the sled to go 21 m down the slope. (b) On the dot below that represents the sled, draw and label a free-body diagram for the sled as it slides down the slope.
4 AP* Newton s Laws Free Response Questions page 9 (c) Calculate the frictional force on the sled as it slides down the slope. (d) Calculate the coefficient of friction between the sled and the muddy surface of the slope. (e) The sled reaches the bottom of the slope and continues on the horizontal ground. Assume the same coefficient of friction. i. In terms of velocity and acceleration, describe the motion of the sled as it travels on the horizontal ground.
5 AP* Newton s Laws Free Response Questions page 10 ii. On the axes below, sketch a graph of speed u versus time t for the sled. Include both the sled s travel down the slope and across the horizontal ground. Clearly indicate with the symbol t l the time at which the sled leaves the slope.
6 AP* Newton s Laws Free Response Questions KEY 1981 Q1 (1) AP is a registered trademark of the College Board. The College Board was not involved in the production of and does not endorse this product. (2) Test Questions are Copyright by College Entrance Examination Board, Princeton, NJ. All rights reserved. For face-to-face teaching purposes, classroom teachers are permitted to reproduce the questions. Web or Mass distribution prohibited. 1
7 AP PHYSICS B 2007 SCORING GUIDELINES Question 1 15 points total Distribution of points (a) 2 points For using a correct equation relating distance, speed, and time x = u Dt x D t = u 21 m D t = 2.4 m s For the correct answer D t = 8.75 s Note: Only was awarded for the correct answer with no supporting work. (b) 3 points For each correct force that is correctly labeled, is attached to the dot, and has an arrowhead pointing in the correct direction, was awarded. For each incorrect vector, a point was deducted, with the minimum possible score being 0. 3 points (c) 3 points For recognizing that the sum of the forces upon the sled is zero  F = 0 Writing the equation for the forces acting along the slope,  F = mgsin15 - f = 0, where f represents the force of friction For equating the force of kinetic friction with the component of weight that acts down the slope f = mgsin15 f = 2 ( )( ) 25 kg 9.8 m s sin15 For the correct answer 2 f = 63.4 N (64.7 N if g = 10 m s is used) Note: Only was awarded for the correct answer with no supporting work The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for students and parents). 3 8
8 AP PHYSICS B 2007 SCORING GUIDELINES (d) 3 points Question 1 (continued) Distribution of points For equating the force of kinetic friction to the product of the coefficient of friction and the normal force f = mn  F = mgcos15 - N = 0 For equating the normal force to the component of the sled s weight that is normal to the slope N = mgcos15 f mgsin15 m = = = tan15 N mgcos15 For the correct answer or for an answer consistent with the friction force obtained in (c) m = 0.27 Note: Only was awarded for the correct answer with no supporting work. (e) (i) 2 points For implicitly or explicitly stating that the velocity of the sled decreases For explicitly stating that the acceleration of the sled is constant (ii) 2 points For sketching a horizontal non-zero line For sketching a line of constant negative slope that begins at the right-hand end of the previously drawn horizontal line and also indicating the time t on the graph Note: The second point was awarded only if the first point was awarded The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for students and parents). 4 9
You may use g = 10 m/s 2, sin 60 = 0.87, and cos 60 = 0.50.
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