# Unit 3 Work and Energy Suggested Time: 25 Hours

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1 Unit 3 Work and Energy Suggested Time: 25 Hours PHYSICS 2204 CURRICULUM GUIDE 55

2 DYNAMICS Work and Energy Introduction When two or more objects are considered at once, a system is involved. To make sense of what happens between parts of a system, the concepts of momentum and/or energy are needed. Students have seen many situations where a system of objects is involved. After the students have had a chance to look at the concepts of momentum and energy in familiar contexts, they should apply the concepts to less familiar situations. Students could begin by describing the changes they feel on various playground equipment or amusement park rides and developing an explanation for these changes using the vocabulary and concepts of energy and momentum. Eventually, their understanding of these events will involve the conservation laws, which will allow them to describe, explain, and predict the outcomes of many one-dimensional interactions. Focus and Context All students will be familiar with a playground environment. This context provides a wealth of examples of energy transformation and twobody interactions. Other relevant contexts, such as sport, could be used in individual schools. By reviewing their experiences and collecting data, students can begin inquiring and discussing. By examining playground events, students will discover the need to learn the concepts of momentum and energy. There is increasing social concern about playground safety. Students could be expected to pose questions and identify safety concerns by answering such questions as How high is too high? or What material is appropriate? and to develop a plan to answer their questions. Then they will be able to move from this familiar context to other situations where the concepts can be applied. Science Curriculum Links In intermediate science, students have explored the movement of objects in terms of balanced and unbalanced forces. They have also described quantitatively the relationships among force, area, and pressure. In Physics 3204, students should develop a more precise understanding of momentum and energy and learn to evaluate situations using these concepts. 56 PHYSICS 2204 CURRICULUM GUIDE

3 DYNAMICS Curriculum Outcomes STSE Skills Knowledge Students will be expected to Students will be expected to Students will be expected to Nature of Science and Technology analyze why and how a particular technology was developed and improved over time Relationships Between Science and Technology analyze and describe examples where technologies were developed based on scientific understanding describe and evaluate the design of technological solutions and the way they function using principles of energy and momentum analyze natural and technological systems to interpret and explain their structure and dynamics Social and Environmental Contexts of Science and Technology analyze from a variety of perspectives the risks and benefits to society and the environment of applying scientific knowledge or introducing a particular technology distinguish between questions that can be answered by science and those that cannot and between problems that can be solved by technology and those that cannot Initiating and Planning design an experiment identifying and controlling major variables evaluate and select appropriate instruments for collecting evidence and appropriate processes for problem solving, inquiring, and decision making construct and test a prototype of a device and troubleshoot problems Performing and Recording carry out procedures controlling the major variables and adapting or extending procedures where required use instruments accurately for collecting data Analysing and Interpreting compile and display evidence and information, by hand or computer, in a variety of formats, including diagrams, flow charts, tables, graphs, and scatter plots interpret patterns and trends in data and infer or calculate linear and non-linear relationships among variables compare theoretical and empirical values and account for discrepancies provide a statement that addresses the problem or answers the question investigated in light of the link between data and the conclusion analyze quantitatively the relationships among force, distance, and work analyze quantitatively the relationships among work, time, and power analyze quantitatively the relationships among mass, height, speed, and heat energy using the law of conservation of energy analyze common energy transformation situations using the work-energy theorem describe quantitatively mechanical energy as the sum of kinetic and potential energies determine the percentage efficiency of energy transformations determine which laws of conservation of energy or momentum are best used to solve particular real-life situations involving elastic and inelastic collisions analyze quantitatively problems related to kinematics and dynamics using the mechanical energy concept PHYSICS 2204 CURRICULUM GUIDE 57

4 Work and Power Outcomes Students will be expected to analyze quantitatively the relationships among force, distance, and work (325-9) list the conditions under which work is done on an object when a force is applied to that object define work in terms of an object s displacement and the force acting on it in the direction of the displacement given two of work, displacement and force, calculate the third term explain how the direction of the applied force affects the work done compare the physics use of the term work with everyday usage apply the concept of work to novel situations involving such variables as mass, force, distance and direction analyze quantitatively the relationships among work, time, and power (325-10) define power calculate one of the following when given the other two: power, work (or a means to determine the work), and time Elaborations Strategies for Learning and Teaching In calculating work, only work done by an applied force will be considered. Teachers should also consider work done by an applied force at an angle to the horizontal surface using: W = F dcos θ. If the object does not move, the force does no work on the object. If the force is perpendicular to the direction of the object s motion, then the force is doing no work. Also note that if an object is already moving a force must be applied to stop the motion. Negative work is done when the applied force and the displacement are in opposite directions. The student will demonstrate an understanding that, for an object moving in a certain direction, it is the component of the applied force in that direction that determines the work done. When an object is lifted and we only know its mass, the student should be able to determine the force (the weight) from F g = mg and then proceed to calculate work. In one step: W = F g x d = mgd. Note: Power for lifting an object at constant speed can also be expressed as P = mgv since: W mgd P = = t t d = v t P = mgv 58 PHYSICS 2204 CURRICULUM GUIDE

5 Work and Power Suggested Assessment Strategies Journal Referring to the data collected, students could describe how force, distance, and work are related. They should give an analysis with an explanation of their understanding of the situation. (325-9) Paper and Pencil As a written record of the dynamics cart exploration, students could submit work sheets which include neat sketches, data, and calculations for each of the three situations from their lab activity. (325-10) A locomotive exerts a constant forward force of 5.4 x 10 4 N while pulling a train at a constant speed of 25 m/s for 1.0 h. How much work does the locomotive do? What average power did the locomotive generate while pulling the train? (325-10) Performance Students could compare their power output by completing Lab 9.3, Physics: C and C, p 380. Resources main.htm Physics: C and C, p 325 Physics: C and C, pp Physics: C and C, p 325 Physics: C and C, p 325 Physics: C and C, p 331 Physics: C and C, pp PHYSICS 2204 CURRICULUM GUIDE 59

6 Potential and Kinetic Energy Outcomes Students will be expected to Elaborations Strategies for Learning and Teaching analyze quantitatively the relationships among mass, height, gravitation field strength, gravitational potential energy, and kinetic energy (326-1) define gravitational potential energy in terms of its height, mass, and the force of gravity relate energy transformations to work done solve numerical problems related to gravitational potential energy define an object s kinetic energy in terms of its mass and its speed solve numerical problems related to kinetic energy Students should demonstrate an understanding that gravitational potential energy of an object relative to a certain reference level is the same as the work required to lift the object vertically to its present position. (Conversely, gravitational potential energy can be defined as the work that the force of gravity can do on the object, if allowed to fall to the reference level). Given, for example, a 10 kg box sitting on the floor, the student can calculate the work required to lift it 1.5 m to a tabletop and state that the gravitational potential energy of the box on the tabletop, with respect to the floor, is the same value as the work required to lift it against gravity. 60 PHYSICS 2204 CURRICULUM GUIDE

7 Potential and Kinetic Energy Suggested Assessment Strategies Resources Performance Students could design an experiment and using computer interface technology complete the experiment to verify the law of conservation of mechanical energy. (i.e., swinging pendulum, falling objects) (326-1) Physics: C and C, pp Physics: C and C, pp Physics: C and C, pp Physics: C and C, p 332 Physics: C and C, p 333 PHYSICS 2204 CURRICULUM GUIDE 61

8 Hooke s Law and Simple Harmonic Motion Outcomes Students will be expected to analyze quantitatively the relationships among force, distance, and spring constant (326-1) explain how a stretched spring can possess elastic potential energy define the spring constant k state Hooke s Law given two of: force, distance, and k, determine the third quantity write an expression for potential energy stored in a spring given two of: potential energy, k, and x, determine the third quantity explain qualitatively the relationship between displacement, velocity, time, and acceleration for simple harmonic motion (SHM) (327-2) explain quantitatively the relationship between potential and kinetic energies of a mass in SHM (327-4) - define SHM - calculate speed and acceleration of a mass on a spring Elaborations Strategies for Learning and Teaching Students should investigate the force/stretch relationship for springs (Hooke s Law) and related energy changes when a mass oscillates at the end of a spring. Using a spring placed horizontally and a spring scale, students could investigate how much force is required to stretch the spring to various distances. A graph of force versus distance leads to recognition of work done as the spring is stretched. The spring might be hung vertically with a mass attached which holds the spring stretched to something less than half the elastic limit of the spring. X 0 X rest X max At the rest position, X rest, the change in length of the spring is equal to the height of the mass above the bottom-most point, X max, if the mass had been dropped from a height where the spring is completely unstretched, X 0. (X max - X rest = X rest - X 0 ) If the mass is released at this highest point, it will oscillate up and down for some time before coming to rest at the middle position. Students should determine velocities at various positions. This is an ideal time to use a position sensor and computer software to generate a complete set of kinematics data. This can lead students to such questions as the following: What effect would changing the mass have? How does the kinetic energy change during an oscillation? What happens if a spring with a different force constant is used? Students will not be responsible for damping or pendulums. Also simple harmonic motion is to be applied to vertical situations only. 62 PHYSICS 2204 CURRICULUM GUIDE

9 Hooke s Law and Simple Harmonic Motion Suggested Assessment Strategies Resources Paper and Pencil Given that a 5.00 x 10 2 g mass is attached to a vertical spring of force constant 40.0 N/m, students could answer the follow questions: How far below the bottom of the empty spring will the rest position of the mass be? If the mass is lifted about halfway, what period of oscillation will result? Determine the gravitational potential energy, the spring potential energy, and the kinetic energy at the centre of oscillation if the mass is released from the empty spring position. (327-2, 327-4) web site (Energy Conservation Simulation) Physics: C and C, pp Physics: C and C, pp 180 and 339 Physics: C and C, pp 180 and 339 Physics: C and C, pp Physics: C and C, pp Physics: C and C, p 341 Physics: C and C, p 358 Physics: C and C, p 359 Physics: C and C, p 357 Physics: C and C, p 358 PHYSICS 2204 CURRICULUM GUIDE 63

10 Conservation of Energy Outcomes Students will be expected to analyze common energy transformation situations using the closed system workenergy theorem (326-7) state the work-energy theorem as it applies to an object experiencing a force on a horizontal frictionless surface Elaborations Strategies for Learning and Teaching After students are familiar with the basic concepts, teachers can introduce the algebraic deduction below. Work is the name given to the product of force and displacement. Since more work is done if a larger force acts, OR if the same force acts through a larger distance, the F d product is a cause. What is the effect? 2 2 For Kinematics; v2 = v1 + 2a d 2 2 Rearranging; v v = 2a d 2 1 F But F = ma, a = m F 2 2 Therefore 2 d = v2 v1 m mv2 mv1 F d = KE = m Dimensionally, work = Nm i, Energy = kgi s 2 2 m m Nm i = kgi im = kgi s 2 s 2 given the expression for work-energy theorem, calculate the value of any variable, given the value of the other variables, or information from which they may be found describe the relationship between the concepts of work and energy carry out an investigation of the work-energy theorem For convenience, both are called joules, which is the unit for all forms of energy. The Laboratory outcomes (212-3, 212-8, 213-2, 213-3, 214-3, 214-5, ) and are addressed by completing Work Energy Theorem CORE LAB #5. Students should also solve algebraic problems involving energy transformations. Some examples of these types of problems include: 1. A car of mass 1000 kg accelerates from 0.0 m/s to 4.0 m/s. How much work is done by the engine? 2. If the car in problem #1 travelled 10.0 m, what was the average force exerted on the car as a result of the actions of the engine? 3. A 50.0 g arrow is pulled back a distance of 80 cm in a bow. When the string is released, it exerts an average force of 60 N on the arrow. With what speed does the arrow leave the bow? 64 PHYSICS 2204 CURRICULUM GUIDE

11 Conservation of Energy Suggested Assessment Strategies Resources Presentation Based on their investigations of toys and other transformation situations, students could develop a poster or other visual display that illustrates the work-energy theorem. (326-7) Paper and Pencil Students could solve problems such as: A golf ball of mass 50.0 g is hit by a golf club at a speed of 35 m/s. If the effective mass of the club head is 0.32 kg and the collision is totally elastic, what velocity will the ball have just after the impact? (326-7) Students could solve problems such as: A 2.4 kg dynamics cart moving at 1.5 m/s undergoes an in-line elastic collision with another stationary cart of the same mass. What will the velocity of the stationary cart be after impact? (326-7) Physics: C and C, p 334 Core Lab #5: Work Energy Theorem Physics: C and C, p 378 Physics: C and C, pp Physics: C and C, p 334 Physics: C and C, p 378 PHYSICS 2204 CURRICULUM GUIDE 65

12 Conservation of Energy (continued) Outcomes Students will be expected to describe quantitatively mechanical energy as the sum of kinetic and potential energies (326-5) analyze quantitatively the relationship between kinetic and potential energy, using the law of conservation of energy (326-1) state the law of conservation of energy state the law of conservation of energy as it applies to mechanical energy solve problems using the law of conservation of energy, including changes in gravitational potential energy and kinetic energy solve problems using the law of conservation of energy, including changes in elastic potential energy investigate the relationship between E p and E k (212-3) evaluate and select appropriate instruments for collecting evidence and appropriate processes for problem solving, inquiring, and decision making (212-8) carry out procedures controlling the major variables and adapting or extending procedures where required (213-2) use instruments effectively and accurately for collecting data (213-3) Elaborations Strategies for Learning and Teaching The Laboratory outcomes (212-3, 212-8, 213-2, 213-3, 214-3, 214-5, 214-7, ) and are addressed by completing Conservation of Energy CORE LAB #6. The students should be able to state that for a particular object, the sum of the E p and E k is a constant term. That is, (E p + E k ) at one time is equal to (E p + E k ) at any other time. One way to express this is: E + E = E + E p1 k1 p2 k2 For an object falling or rising vertically, we therefore have, at the extremes of the motion (top and bottom): E + E = E + E ptop ktop pbottom kbottom E ptop + 0= 0+ E E = E ptop kbottom kbottom 66 PHYSICS 2204 CURRICULUM GUIDE

13 Conservation of Energy (continued) Suggested Assessment Strategies Resources Paper and Pencil After referring to the diagram below, students could answer the following questions: How much gravitational potential energy does the roller coaster car have at position A if the loaded mass is 1100 kg? What is the maximum kinetic energy the car could have at B? What speed would it have at B? What speed would the car have at position D? (326-1) A 20 m B 10 m D C 15 m Kristen is playing on a swing. At her highest swing, the seat is 3.2 m above the rest position. Students could determine what speed does she have as she passes through the lowest position? (326-6) A pole vaulter wants to clear the bar at a height of 7.0 m above the mat. Students could determine what vertical speed must he/she have to just clear the bar? What role does the pole play in the pole vault? (326-6) Given that a 65 kg boy runs at a constant speed of 6.0 m/s. He jumps on a stationary 35 kg freight dolly so that his feet stay in one position and the combined mass (boy + dolly) moves off at a new speed. Assume that the dolly wheels are frictionless. Students could answer the following: What final velocity will the combined mass have? What impulse acted on the dolly? on the boy? Was energy conserved in this interaction? If the best estimate of the time of interaction is 0.20 seconds, what force acted on the dolly? What acceleration did the boy experience? (326-1, 326-5, 214-7, 326-6) Students could determine what is meant by each of the following: W = E Physics: C and C, pp Core Lab #6: Conservation of Energy Physics: C and C, p OR Computer Interface Alternative: main.htm Physics: C and C, p 342 Physics: C and C, p 343 Physics: C and C, pp Physics: C and C, pp Physics: C and C, pp E k = mv 2 2 E g = mgh E e = 1 2 kx2 (326-6) PHYSICS 2204 CURRICULUM GUIDE 67

14 Conservation of Energy (continued) Outcomes Students will be expected to compile and display evidence and information, by hand or computer, in a variety of formats, including diagrams, flow charts, tables, graphs, and scatter plots (214-3) interpret patterns and trends in data, and infer or calculate linear and nonlinear relationships among variables (214-5) provide a statement that addresses the problem or answers the question investigated in light of the link between data and the conclusion (214-11) determine the percent efficiency of energy transformation including the comparision of empirical and theoretical values of total energy, accounting for discrepancies (214-7, 326-8) explain the role of friction in the loss of mechanical energy from a system compute the percent efficiency of a system where energy is lost due to friction determine whether the law of conservation of momentum, or, the law of conservation of energy is best to analyze and solve particular real-life problems in elastic and inelastic interactions (326-4) analyze quantitatively problems related to kinematics and dynamics using the mechanical energy concept (326-6) Elaborations Strategies for Learning and Teaching The student will express ideas such as: friction will cause agitation of the molecules of the surfaces that are in contact. This will be manifested in the production of heat and possibly, but not likely, light (sparks). Sound is almost sure to be produced because the vibration of the molecules in the materials will likely cause the neighboring air molecules to vibrate as well. All of this means that if an object is being pushed along a rough surface, it will not gain as much kinetic energy as it would on a frictionless surface. A student might suggest the law of conservation of energy has been disproven. The response to this is that, indeed, when friction is present, mechanical energy is not conserved. However, total energy is conserved. Teachers should expose students to solving problems from both a momentum and energy perspective. Students have developed confidence in kinematics tools for solving motion problems in a straight line. In achieving this outcome, students should come to appreciate energy solutions for vertical motions. 68 PHYSICS 2204 CURRICULUM GUIDE

15 Conservation of Energy (continued) Suggested Assessment Strategies Resources Paper and Pencil When analyzing a problem, students could consider how they decide whether to use kinematics, momentum, or energy concepts to solve for unknowns? (326-6) Students could solve problems such as: An average force of 8.0 N is applied to a 1.2 kg dynamics cart that is initially at rest. If the force is maintained for a distance of 0.80 m, what velocity will the cart attain? If the force is maintained over a distance of 1.6 m, what velocity is reached? What is the ratio of the two velocities? Explain in terms of work and energy why this is so. Compared to the first trial, what could be changed to give the cart twice the velocity? (326-6) Students could write a scientific abstract about their experiment design, results, and interpretations. (212-8, 214-3, 214-5, ) Presentation In groups of three to four, students could demonstrate and discuss their experiment on the machine they chose. They must decide on their presentation format. An explanation of the data, procedure, and the efficiency of the machine should be included. (212-3, 213-2, 213-3, 214-7) Students could present a song, poem, speech, or short story to their classmates that involves the following terms: work, kinetic energy, gravitational potential energy, elastic potential energy, and efficiency. The presentation should show a clear understanding of the relationships between the terms momentum and energy. (326-1, 326-6) Performance Students could design and conduct an experiment to demonstrate an energy transformation and account for discrepancies. For example, they could release a block at the top of a ramp, and, using available technology, determine the velocity at several points, including the bottom. They could compare theoretical kinetic energy values to the actual values and account for any differences. (326-1, 326-5, 214-7, 326-6) Students could conduct their lab on transformation, total energy, and conservation, and write a lab report on the experiment. They should include the data collected, analysis, information, conclusion(s), and a graph. (212-3, 212-8, 213-2, 214-3, 214-5, ) Physics: C and C, pp Physics: C and C, p 377 Physics: C and C, pp PHYSICS 2204 CURRICULUM GUIDE 69

16 Conservation of Energy (continued) Outcomes Students will be expected to analyze and describe examples where energy related technologies were developed and improved over time (115-5, 116-4) analyze and describe examples where technological solutions were developed based on scientific understanding (116-4) describe and evaluate the design of technological solutions and the way they function using energy principles (116-6) analyze natural and technological systems to interpret and explain their structure (116-7) analyze the risks and benefits to society and the environment when applying scientific knowledge or introducing a particular technology (118-2) distinguish between problems that can be solved by the application of physics related technologies and those that cannot (118-8) construct and test a prototype of a device and troubleshoot problems (212-14) Elaborations Strategies for Learning and Teaching The CORE STSE component of this unit incorporates a broad range of Physics 2204 outcomes. More specifically it targets (in whole or in part) 115-5, 116-4, 116-6, 116-7, 118-2, 118-8, , 326-1, 326-5, The STSE component, The Physics of Bungee Jumping, can be found in Appendix A. Note: Students are not responsible for the derivations found in this module. The intent is for students to recognize the relationships between the three types of energy involved in bungee jumping. 70 PHYSICS 2204 CURRICULUM GUIDE

17 Conservation of Energy (continued) Suggested Assessment Strategies Resources Journal Students could write a note explaining momentum, energy, and their transformations so a grade 8 student could understand them. (326-1) Core STSE #3: The Physics of Bungee Jumping, Appendix A PHYSICS 2204 CURRICULUM GUIDE 71

18 Outcomes Elaborations Strategies for Learning and Teaching Students will be expected to 72 PHYSICS 2204 CURRICULUM GUIDE

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