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Work, Power,Efficiency, Energy MHR Chapters 6, 7 Specific Curriculum Outcomes analyse quantitatively the relationships among force, distance, and work (325-9) analyse quantitatively the relationships among work, time, and power (325-10) design and carry out an experiment to determine the efficiency of various machines (212-3,213-2,213-3,214-7) Transformation, Total Energy, and Conservation analyse quantitatively the relationships among mass, speed, and thermal energy, using the law of conservation of energy (326-1 ) describe quantitatively mechanical energy as the sum of kinetic and potential energies (326-5) o compare empirical and theoretical values of total energy and account for discrepancies (214- 7) o analyse quantitatively problems related to kinematics and dynamics using the mechanical energy concept (326-6) o analyse common energy transformation situations using the closed system work-energy theorem (326- 7) o analyse and describe examples where technological solutions were developed based on scientific understanding ( 116-4) o determine the percentage efficiency of energy transformation (326-8) o design an experiment, select and use appropriate tools, carry out procedures, compile and organize data, and interpret patterns in the data to answer a question posed regarding the conservation of energy (212-3, 212-8, 213-2, 214-3, 214-11, 326-4) o distinguish between problems that can be solved by the application of physics-related technologies and those that cannot (118-8) o determine which laws of conservation, momentum, and energy are best used to analyse and solve particular real-life problems in elastic and inelastic interactions (326-4) Technological Implications analyse and describe examples where energy- and momentum-related technologies were developed and improved over time (115-5, 116-4) describe and evaluate the design of technological solutions and the way they function using principles of energy and momentum (116-6) explain the importance of using appropriate language and conventions when describing events related to momentum and energy (114-9) Key terms Work Energy Power Efficiency Conservation of energy Kinetic energy Gravitational Potential Energy Elastic Potential Energy Total Mechanical Energy Introduction Energy-related concepts are essential in science. Some different forms of energy are: Kinetic, Gravitational Potential, Elastic Potential, Chemical Potential, Thermal, Nuclear, Biochemical, Electrical etc Introduction Every living and dynamic process in nature involves conversion of energy from one form to another e.g. photosynthesis, combusting gasoline and other fossil fuels, using electricity. In Science 10 you learned about the energy of the Sun driving weather patterns on the Earth and providing energy input for ecosystems. Work and Energy Defined Work is one way to transfer energy between different objects e.g. a rope is used to pull a crate, a baseball is thrown by a pitcher. In Physics, work is done when a force acts on an object as the object moves from one place to another. The meaning differs from the everyday use of the word. Work can be positive or negative. Positive work results in an increase in kinetic energy. Formulas W=F·d·cosθ or W=Fdcosθ In words, work is defined as the dot product of force and displacement. This is the first time you are multiplying vectors in this class. The dot product is one way to multipy two vectors. The product, however, is not a vector; it is a scalar. The direction of the work will always be in the direction of the displacement so it will not change. Work and Energy If work is the product of force and displacement,the units for work are Newtons ·metres 1 N·m Ξ 1 Joule (Ξ means defined as) If you examine the formula W=Fdcosθ Fcosθ is also the x component of the force, so if the displacement is along the x, then work can also be found by multiplying the x-component of the force and the displacement Work and Energy Energy is defined as the ability to do work so the units for energy are also Joules and energy is also a scalar. Kinetic energy is defined as the energy of motion whereas gravitational potential energy is defined as the stored energy an object has because work was done on the object against the gravitational field. Energy Ek = ½ mv2 where Ek is kinetic energy (aka KE) in Joules, m = mass in kg and v = velocity in m/s Ep = mgh where Ep is gravitational potential energy (aka GPE) , m = mass in kg, and h is height (or vertical displacement) in m Stored energy in a Spring If you have every stretched a spring or rubber band and released it, you would have observed that the work you did in stretching the spring or rubber band is stored in the spring/band and can be released. Another example of this is the spring above a garage door. When these doors are installed, some of the strings are “torqued” so that they hold about 200-300 pounds of force. It is this stored energy that essentially lifts the garage door. The drive mechanism does provide some of the lift. Stored energy in a Spring The work done in stretching or compressing a spring is stored in the spring as elastic potential energy. Ee = ½ kx2 where Ee is elastic potential energy in Joules, k is the spring or force constant in N/m and x is the amount of stretch or compression in m Power Power is defined as the time rate of doing work or the time rate of energy transfer. The unit of power is the Watt. A 13 W compact fluorescent bulb changes 13 joules of electrical energy into mainly light and some heat every second. 1 Watt Ξ 1 Joule/s 1 W Ξ 1 J/s Work Kinetic Energy Theorem Experimental evidence and everyday experience suggests that when the work done on an object increases its motion, then the kinetic energy of the object increases. This is known as the Work-Kinetic Energy Theorem. Symbolically: W = ΔEk = Ek final – Ek initial Example 1 Sebastien does work on a curling 3.0 kg curling stone by exerting a force of 35 N over a displacement of 2.0 m. A) How much work is done on the stone? B) Assuming the stone started from rest and neglecting friction, what was the final velocity of the stone upon release? Solution to Example 1 W = Fdcosθ = (35 N)(2.0 m) cos 0° W = 70. J W = Ek final – Ek initial 70. J = ½ mv2 = ½ (3.0 kg) v2 v = √(70. J/1.5 kg) = 2.16 m/s v = 2.2 m/s (in the direction of motion) Work and Gravitational Potential Energy Gravitational potential energy is measured in relation to a reference (or zero) level. A convenient choice of reference level is the surface of the Earth. If work is done in lifting a book from a desk to a book shelf, then there is an increase in gravitational potential energy of the book at the book shelf level relative to the desk as work has been done against the gravitational field. We say that the work done becomes “stored” gravitational potential energy. Symbolically this is W = ∆Eg = Eg final – Eg initial Work and Gravitational PE W = Eg final – Eg initial W = mg∆h Example 2: A grade 11 physics student of mass 50.0 kg walks up the stairs at CHS and undergoes a change in vertical displacement of 10.0 m. How much work was done by the student? Solution to Example 2 W = mg∆h W = (50.0 kg)(9.81 m/s²)(10.0 m) W = 4905 J → 4.90 x 10³ J (3 sig figs) Note that this is also 4.90 kJ Work Energy Theorem If doing work on an object increases different forms of energy such as kinetic and gravitational potential, then we can generalize the work kinetic energy theorem to the following: W = ∆E Example 3 Jess pushes her 10. kg trunk up a 2.0 m high ramp starting from rest. At the top of the ramp, the trunk is moving at 3.0 m/s. Neglecting friction, how much work was done on the trunk? W = ∆E = ∆Ek + ∆Eg W = (½mvf2 - ½mvi²) + (mg∆h) W = (45 J – 0 J) + (196.2 J) =241.2 J W = 240 J (2 sig fig)

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Newton's Laws, Component Method, Relative Velocity, Lab 5, Angular Momentum, Projectile Motion, lab reports, Fall Semester, Physics Formulas, Any Questions

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posted: | 4/7/2010 |

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