AP PHYSICS B - Amazon S3

1 AP* PHYSICS B Work and Energy Teacher Packet 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 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: 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 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: & Energy Objective To review the student on the concepts, processes and problem solving strategies necessary to successfully answer questions on work and energy. Standards Work and energy are addressed in the topic outline of the College Board AP* PHYSICS Course Description Guide as described below. AP PHYSICS Exam Connections Topics relating to work and energy are tested every year on the multiple choice and in most years on the free response portion of the exam.

2 The list below identifies free response questions that have been previously asked over work and energy, often in conjunction with momentum. These questions are available from the College Board and can be downloaded free of charge from AP Central. Free Response Questions 2005 Question 2 2006 Form B Question 2 2002 Question 1 2005 Form B Question 2 2001 Question 2 2002 Form B Question 1 1999 Question 1 (ex a) I. Newtonian Mechanics C. Work, energy, and power 1. Work and work-energy theorem 2. Conservative forces and potential energy 3. Conservation of energy 4. Power F. Oscillations and Gravitation 1. Simple harmonic motion (dynamics and energy relationships) 2. Mass on a spring 3. Pendulum and other oscillations AP* is a trademark of the College Entrance Examination Board.

3 The College Entrance Examination Board was not involved in the production of this material. Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , 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.

4 Work done by a nonconservative force generally cannot be recovered as usable energy. Key Formulas and Relationships Work: cosW = =Fd Fd unit = Joule = 1 N m Power: WPt= unit = Watt = 1 Joule/second P= FvKinetic Energy: 212Km=v unit = Joule Gravitational Potential Energy: unit = Joule gUmg=hPotential Energy stored in spring: 212sUk=x unit = Joule Conservation of Energy: ''KU K U+= + Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , 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.

5 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 = E). F FyFx d Only the x component of the force does work. 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.

6 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) Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , Energy, & PowerA B 2 1 More work is needed to push an object against friction along path 2 than path 1. Friction is a non-conservative force. F (N) x (m) Work = area under Force vs. Displacement Graph Power is the rate at which work is done and is measured in Watts. 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.

7 Displacement. Work done by a variable force is equal to the area under a graph of force vs. displacement. Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , Energy, & PowerFree Response Question 1 (15 pts) 1. A block of mass m is attached to an ideal spring of spring constant k, the other end of which is fixed. The block is on a level, frictionless surface as shown in the diagram. At time t0, the block is set into simple harmonic motion of period T by an external force pushing it to the right, giving the block initial velocity v0. Express all answers in terms of the given quantities and fundamental constants. m v0 A. Determine the amplitude of the block s motion. (4 points max) Kinitial = Us,max 220m1122mvkx=ax 20maxmvxk= 1 point For applying conservation of energy 1 point For equating the initial kinetic energy of the block with the maximum elastic potential energy 1 point For correctly substituting the definitions of kinetic and elastic potential energy 1 point For the correct answer in terms of the given quantities and fundamental constants B.

8 On the axis below, plot the kinetic energy of the block as a function of time for two periods. Label the vertical axis appropriately. Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , Energy, & Power2T T32T 2T K (J) t (s) (4 points max) sinusoidal graph, positive, with max KE at 0, T/2, T, 3T/2, and 2T 1 point for drawing any sinusoidal graph 1 point for a graph that never shows negative kinetic energy (graph is always positive) 1 point for showing the maximum kinetic energy is 2012mvand the minimum kinetic energy is zero 1 point for correctly showing that the maximum kinetic energy occurs at t = 0, T/2, T, 3T/2, and 2T and that the minimum kinetic energy occurs at t = T/4, 3T/4, 5T/4, and 7T/4. Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , Energy, & PowerC.

9 The block is stopped and a second identical block is glued on top of the first. The How does the amplitude of the motion of the two blocks together compare to reater than _____ Less than _____ Equal _____ ii. Justify your answer. (3 points max) reater than __x blocks are returned to simple harmonic motion with the same initial velocity as before. amplitude found in part a)? G G__ the increased mass increases the kinetic nd sing the equation from part A, as the mass energy when the block is set in motion, meaning the spring will be compressed astretch more uincreases so does the amplitude 20mvmaxxk= 1 point For correctly indicating the point for any reasonable justification amplitude increases when the mass increases 1 Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , Energy, & Poweruestion 2 (20 pts) f mass 650 kg is moving with a velocity of m/s at the top of the.

10 Calculate the maximum velocity of the roller coaster. (4 points max) QA roller coaster car ofirst hill of a roller coaster track as shown in the diagram. The cart rolls without friction down the hill and through a vertical circular loop of radius 12 m. m/s 55 m 12 m30 m A ()()()211mvmgh+=200 msmvvvghmmvmssv=+=+= 1 point for a correct application of point for recognizing that the point for correctly adding the y point for the correct answer icant conservation of energy 1maximum kinetic energy occurs when the roller coaster is at the bottom of the first hill (zero potential energy) 1initial kinetic and potential energto find the total energy 1including correct units and reasonable number of signifdigits Copyright 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: , Energy, & Power he roller coaster travels without friction through the circular loop.