Advanced Placement. PHYSICS B Work, Energy, & Power

Transcription

1 Advanced Placement PHYSICS B Work, Energy, & Power Student

2 Work, Energy, & Power What I Absolutely Have to Know to Survive the AP* Exam Work is the defined quantity from which the entire theory of energy begins. It is the scalar product of the force acting on an object and the displacement through which it acts. Power is the rate at which work is done. Objects are said to have energy if they have the ability to do work, either due to the fact that they are moving (kinetic energy) or due to their position in a force field (potential energy). Conservative forces are forces that do work that is path independent. Conserved quantities are quantities that do not change with time. If the mechanical energy of a system is conserved, then the sum of the system s kinetic and potential energies at any given time will always add to the same number. Work done by a nonconservative force generally cannot be recovered as usable energy. Key Formulas and Relationships Work: W = F d = Fd cosθ unit = Joule = 1 N m W Power: P = t P = F v unit = Watt = 1 Joule/second 1 2 Kinetic Energy: K = mv 2 unit = Joule Gravitational Potential Energy: = mgh unit = Joule Ug 1 Potential Energy stored in spring: Us 2 ' ' Conservation of Energy: K + U = K + U 2 = kx unit = Joule AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of this material. Copyright 2013 National Math + Science Initiative, Inc., Dallas, TX. All rights reserved.

3 Work, Energy, & Power Important Concepts Work is done by a force parallel to the displacement of the object: perpendicular forces (centripetal forces for example) do no work. If the force is at an angle to the displacement, you must resolve it into components. Work is a scalar quantity but can be negative Work-Energy Theorem: Work causes a change in energy: it is the method by which energy is transferred (W = ΔE). F F y Only the x component of the force does work. θ F x Work is positive when the force and displacement are in the same direction (object gains energy): work is negative when the force and displacement are in opposite directions (object looses energy.) Energy is defined as the ability to do work. It is also a scalar and cannot be negative. Kinetic energy energy through motion. Potential energy energy through position (position in a gravitational or electric field or position next to a stretched or compressed spring). Conservative force a force where the work done in moving an object between two positions is the same regardless of the path taken o Three conservative forces you should know: Gravitational, Elastic (springs), Electric o Example: the work done against gravity in lifting a box on top of a shelf is the same regardless of whether you lift it straight up or push it up a ramp. When only conservative forces act on an object, then the total energy (kinetic plus potential energy) remains constant. Non-conservative force a force where the work done in moving an object between two points does depend on the path taken o Examples: friction, drag o Work done by a non-conservative force is equal to the change in energy of the object (remember the work-energy theorem) d Copyright 2013 National Math + Science Initiative, Inc., Dallas, TX. All rights reserved.

4 Work, Energy, & Power 1 B More work is needed to push an object against friction along path 2 than path 1. Friction is a non-conservative force. A 2 Power is the rate at which work is done and is measured in Watts. Work done by a variable force is equal to the area under a graph of force vs. displacement. F (N) Work = area under Force vs. Displacement Graph x (m) Copyright 2013 National Math + Science Initiative, Inc., Dallas, TX. All rights reserved.

5 2004 AP PHYSICS B FREE-RESPONSE QUESTIONS PHYSICS B SECTION II Time 90 minutes 6 Questions Directions: Answer all six questions, which are weighted according to the points indicated. The suggested time is about 17 minutes for answering each of questions 1-4, and about 11 minutes for answering each of questions 5-6. The parts within a question may not have equal weight. Show all your work in the pink booklet in the spaces provided after each part, NOT in this green insert. 1. (15 points) A roller coaster ride at an amusement park lifts a car of mass 700 kg to point A at a height of 90 m above the lowest point on the track, as shown above. The car starts from rest at point A, rolls with negligible friction down the incline and follows the track around a loop of radius 20 m. Point B, the highest point on the loop, is at a height of 50 m above the lowest point on the track. (a) i. Indicate on the figure the point P at which the maximum speed of the car is attained. ii. Calculate the value u max of this maximum speed. (b) Calculate the speed u B of the car at point B. (c) i. On the figure of the car below, draw and label vectors to represent the forces acting on the car when it is upside down at point B. ii. Calculate the magnitude of all the forces identified in (c)i. (d) Now suppose that friction is not negligible. How could the loop be modified to maintain the same speed at the top of the loop as found in (b)? Justify your answer. Copyright 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). 5 Page 10 GO ON TO THE NEXT PAGE.

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7 (b) 2005 AP PHYSICS B FREE-RESPONSE QUESTIONS i. Calculate the average acceleration for the time period t = 8 s to t = 10 s. ii. On the box below that represents the elevator, draw a vector to represent the direction of this average acceleration. (c) Suppose that there is a passenger of mass 70 kg in the elevator. Calculate the apparent weight of the passenger at time t = 4 s. 2. (10 points) A simple pendulum consists of a bob of mass 1.8 kg attached to a string of length 2.3 m. The pendulum is held at an angle of 30 o from the vertical by a light horizontal string attached to a wall, as shown above. (a) On the figure below, draw a free-body diagram showing and labeling the forces on the bob in the position shown above. (b) Calculate the tension in the horizontal string. (c) The horizontal string is now cut close to the bob, and the pendulum swings down. Calculate the speed of the bob at its lowest position. Copyright 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). 6 Page 12 GO ON TO THE NEXT PAGE.