VIEWS: 12 PAGES: 52 POSTED ON: 5/13/2010
Work, Power & Energy Basic Terminology and Concepts Review Newtons Laws Used to analyze motion of an object Net force on a mass acceleration Acceleration change in velocity over time Used to predict final state of an object's motion What are other ways to look at motion? Motion Based on Work and Energy Objective: Understand and calculate the effect of work on the energy of an object (or system of objects) Predict the resulting velocity and/or height of the object from energy information Basic Terminology Work Total mechanical energy Potential energy Kinetic energy Power Work A force acting upon an object to cause a displacement For a WORK to be done: 1. Displacement MUST happen 2. Force MUST cause the displacement 3. Force and displacement must be parallel What are some examples of work? Examples a horse pulling a plow through the fields a father pushing a grocery cart down the aisle of a grocery store a freshman lifting a backpack full of books (would a junior do work like this?) a weightlifter lifting a barbell above her head a shot-putter launching the shot, etc. climbing a flight of stairs Work Work or NOT? A teacher applies a force to a wall and becomes exhausted. A book falls off a table and free falls to the ground. A rocket accelerates through space. Answers No. The wall is not displaced. Yes! The is a downward force (gravity) which acts on the book to displace it. Yes. The expelled gas is the force which accelerates the rocket through space. What about this one? Be careful! A waiter carries a tray full of meals above his head by one arm across the room. Consider the following: In which direction is the force exerted on the tray? Which direction does the tray move? Are those directions parallel? Answer: We need to be specific because there are two forces. The normal force is exerted vertically on the tray. The tray moves horizontally. Since those are not in the same direction, there is no work done on the tray by the normal force. There is a horizontal frictional force in the same direction as the horizontal displacement. Therefore, friction does work on the tray! A Force Does NO WORK When It Is Perpendicular to the Displacement Force at an Angle The tension in the chain pulls upward and rightward. Fido moves rightward. Only the horizontal part (component) of the tension does work on Fido. The ANGLE determines the component of the force which actually causes a displacement. We won’t do this mathematically. Which angle is used? The angle between the force vector and the displacement vector. NOT the angle of ascent in this case Direction of pull = Displacement direction Describing Work Mathematically Work = Force x Displacment W = F*d Force and displacement are rightward. WORK IS DONE!!! Force left, displacement right. NEGATIVE WORK IS DONE!!! Force up, displacement left. NO WORK!!! When angle = 0 or 180°, WORK IS DONE! Perpendicular force REMEMBER! A vertical force CANNOT cause horizontal displacement! When angle = 90°, NO WORK IS DONE!!! Work and Gravity Work = Force * displacement When something freefalls, the force it exerts is m*g (mass * acceleration due to gravity). g = -9.8 m/s2. Displacement of object is height (h). Work = m*g*h Units of Work (and Energy) The joule (J) 1 joule = 1 newton*meter 1 J = 1 N*m Each set of units is equivalent to a force unit times a displacement unit. Summary Work is a force acting upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Force Displacement Angle between the force and the displacement. If angle is 90°, NO WORK IS DONE!!! Power When you exert a force over a distance, that is called work. But… work takes time! Does the amount of work change if you do it over an hour vs. in 5 minutes? Power Calculation Power is the rate at which work is done Power = Work / time P=W/t Units of Power Units of Power = Units of Work / Units of Time = joules / second 1 joule / second = 1 watt Units of Power: watts (W) Joules/sec = Watts! Machines Machines change the magnitude and/or direction of forces. “multiplying the force” can also multiply the distance NOTHING WORKS FOR FREE!!! Work is CONSERVED work input = work output (F*d)input = (F*d)output So if we can’t get any free work out of the deal, why bother? Machines Machines can make work easier Less input force & more input distance More output force & less output distance Examples: using a jack to lift a car Machines can increase speed More input force & less input distance Less output force & more output distance Examples: bicycle gears Mechanical Advantage Mechanical Advantage: how much a machine multiplies force or distance output force input distance mech. adv. input force output distance Mechanical Advantage Calculate the Equation: mechanical advantage input distance of a ramp that is 5.0 m mech. adv. output distance long and 1.5 m high. Given: Plug & Chug: input distance = 5.0 m 5m output distance = 1.5 m mech.adv. 3.3 1.5 m Unknown: mechanical advantage Simple Machines Simple Machine How Does It Examples Work? Lever Pulley Wheel & Axle Inclined Plane Wedge Screw Work and Energy What is the relationship? Objectives Explain the relationship between energy and work Define potential energy and kinetic energy Calculate kinetic energy and gravitational potential energy Distinguish between mechanical and non- mechanical energy Identify non-mechanical forms of energy What is Energy? Energy: the ability to do work Units: joules, J (same as work) Why? Definition of work: Transfer or transformation of energy Transfer is often from one system to another It takes ENERGY to do WORK!!! Work – Energy Example Rubber band or slingshot or bow You stretch the rubber band. Energy is transferred from you to the band. Do you do work on the rubber band? You release the rubber band. Energy is transferred from the rubber band to the projectile. Amount of energy transferred is measured by “work” done on the projectile. Transfer of Energy (bow & arrow): Work on bow Energy in bow Work on arrow Potential Energy How does the rubber band get energy? Where is the energy in the stretched rubber band? Where is the energy upon release? Potential Energy Def: stored energy; energy of position Results from the relative position of objects in the system. rubber band: distance between the two ends Stored energy occurs if something is stretched or compressed (elastic) clock spring bungee cord Gravitational Potential Energy Gravitational potential energy: PE that an object has by virtue of its HEIGHT above the ground GPE = mass x freefall acceleration x height GPE = mgh = (Fd) mg = weight of the object in Newtons (F) h = distance above ground (d) GPE stored = Work done to lift object GPE Example - Solved A 65 kg rock climber Equation: ascends a cliff. What is PE = mgh the climber’s gravitational potential Plug & Chug: energy at a point 35 m PE = (65 kg)(9.8 m/s2)(35 m) above the base of the cliff? Answer: Given: GPE = 22000 J m = 65 kg h = 35 m Unknown: GPE = ? J GPE Example - Unsolved What is the gravitational Equation: potential energy of a 2.5 GPE = mgh kg monkey hanging from a branch 7 m above the jungle floor? Plug & Chug: GPE = (2.5 kg)(9.8 m/s2)(7m) Given: Answer: m = 2.5 kg GPE = 171.5 J h=7m Unknown: GPE = ? J Kinetic Energy Def: the energy of a moving object due to its motion Moving objects will exert a force upon impact (collision) with another object. KE = ½ (mass) (velocity)2 KE = ½ (mv2) The Impact of Velocity Which variable has a greater impact on kinetic energy: mass or velocity? Velocity! It’s SQUARED! Velocity as a factor: Something as small as an apple: At a speed of 2 m/s = 0.2 J At a speed of 8 m/s = 3.2 J (4 x velocity = 16x energy) KE Example - Solved What is the kinetic Equation: energy of a 44 kg KE = ½ mv2 cheetah running at 31 m/s? Plug & Chug: Given: KE = ½ (44 kg)(31 m/s)2 m = 44 kg v = 31 m/s Answer: KE = 21000 J Unknown: KE = ? J KE Example - Unsolved What is the kinetic Equation: energy of a 900 kg KE = ½ mv2 car moving at 25 km/h (7 m/s)? Plug & Chug: Given: KE = ½ (900 kg)(7 m/s)2 m = 900 kg Answer: v = 7 m/s KE = 22050 J Unknown: KE = ? J Conservation of Energy Objectives Identify and describe transformations of energy Explain the law of conservation of energy Where does energy go when it “disappears”? Analyze the efficiency of machines Other Forms of Energy Mechanical Energy – the total energy associated with motion Total Mechanical Energy = Potential Energy + Kinetic Energy Examples: roller coasters, waterfalls Other Forms of Energy Heat Energy – average kinetic energy of atoms & molecules The faster they move, the hotter they get! Ex. Boiling water Other Forms of Energy Chemical Energy – potential energy stored in atomic bonds When the bonds are broken, energy is released Ex. Combustion (burning), digestion, exercise Other Forms of Energy Electromagnetic Energy – kinetic energy of moving charges Energy is used to power electrical appliances. Ex. Electric motors, light, x-rays, radio waves, lightning Other Forms of Energy Nuclear Energy – potential energy in the nucleus of an atom Stored by forces holding subatomic particles together Ex. Nuclear fusion (sun), Nuclear fission (reactors, bombs) Conservation of Energy The Law of Conservation of Energy Energy cannot be created nor destroyed, but can be converted from one form to another or transferred from one object to another Total Energy of a SYSTEM must be CONSTANT! Conservation of Energy Total Mechanical Energy = Kinetic + Potential TME = KE + PE TME must stay the same! If a system loses KE, it must be converted to PE In reality… some is converted to heat We will USUALLY consider frictionless systems only PE & KE Energy Conversions in a Roller Coaster Energy changes form many times. Energy from the initial “conveyor” Work stored: Grav. Potential Energy Some PE is converted to KE as it goes down Some KE is converted to PE as it goes up Where does the coaster have max. PE? Where does the coaster have min. PE? Where does the coaster have max. KE? Where does the coaster have min. KE? Where could energy be “lost”? Friction, vibrations, air resistance Conservation of Energy: Example Problem You have a mass of 20 Equations: kg and are sitting on TMEi = TMEf your sled at the top of a PEi + KEi = PEf + KEf 40 m high frictionless hill. What is your velocity at the bottom of PE = mgh the hill? KE = ½ mv2 Given: m = 20 kg hi = 40 m vi = 0 m/s Unknown: vf = ? Efficiency Does work input always equal energy output? NO! Energy may be “lost” to friction. No machine is perfect! Efficiency: a quantity, usually expressed as a percentage, that measures the ratio of useful work output to work input efficiency = useful work output / work input Efficiency A sailor uses a rope and an Equation: old squeaky pulley to raise a Efficiency = useful work output / sail that weighs 140 N. He work input finds that he must do 180 J of work on the rope in order to Plug & Chug: raise the sail by 1 m (doing 140 J of work on the sail). What is the efficiency of the Efficiency = 140 J / 180 J = 0.78 pulley? Given: Efficiency = 0.78 x 100% = 78% Work input = 180 J Useful work output = 140 Answer: J Efficiency = 78% Unknown: Efficiency = ? %