Work, Energy, Power Lecture Slides-1.pdf

Outline Work and Energy Work-Kinetic Energy Theorem Gravitational and Elastic Potential Energies Law of Conservation of Energy Power  Work, W It is a scalar quantity done by force parallel to the displacement covered by the object Wor...

Outline Work and Energy Work-Kinetic Energy Theorem Gravitational and Elastic Potential Energies Law of Conservation of Energy Power  Work, W It is a scalar quantity done by force parallel to the displacement covered by the object Work done by constant force: 𝐖 = 𝐅𝐝 𝐜𝐨𝐬 𝛉 = 𝐅⃗ * 𝐝⃗ where: F = constant force in newton (N) d = displacement in meter (m) θ = angle between F and d SI unit is joule (J): 1 J = 1 N·m 𝐖𝐓 = 𝐅𝐧𝐞𝐭,𝐱 ∆𝐱  Work done by a varying force Work done by a variable force: 𝑊 = lim & 𝐹" ∆𝑥# = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝐹" − 𝑣𝑒𝑟𝑠𝑢𝑠 − 𝑥 𝑐𝑢𝑟𝑣𝑒 ∆"! # This limit is the integral of 𝐹' over x. It follows that the work done by a variable force 𝐹' acting on a particle as it moves from 𝑥( to 𝑥) is: '" '" 𝑊 = 3 𝐹' 𝑑𝑥 = 3 𝐹⃑ * 𝑑 𝑥⃑ '! '! = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝐹' − 𝑣𝑒𝑟𝑠𝑢𝑠 − 𝑥 𝑐𝑢𝑟𝑣𝑒  Work done by a varying force A force 𝐹! varies with x as shown in figure below. Find the work done by the force on a particle as it moves from x = 0 m to x = 6 m.  Examples The figure below shows different forces acting on different objects. Calculate the work done in each case.  Examples The figure below shows different forces acting on different objects. Calculate the work done in each case.  Energy It is a scalar quantity, a conserved extensive property of a physical system, which cannot by observed directly but can be calculated from its state. It is the capacity to change the state of a system. SI unit: joule (J): 1 J = 1 N·m Gaussian unit: erg: 1 erg = 1 dyne·cm Other units: electron-volt (eV): 1 eV = 1.6 x 10-19 J calorie (cal): 1 cal = 4.186 J (Mechanical equivalent of heat) *1 cal = the heat required to raise the temperature of 1 g of water by 1°C Food calorie (Cal): 1 Cal = 1000 cal = 1 kcal = 4186 J *1 Cal = the heat required to raise the temperature of 1 kg of water by 1°C  Kinetic Energy, K It is energy associated with the motion of an object. Some forms of kinetic energy: 1 Motion: K "#$%& = 𝑚𝑣 ' Radiant Sound Thermal Wave 2  Work-KE Theorem A constant net force changes the velocity of an object and does work on that object. v1 v2 F F m m d 𝟏 𝟏 𝑾𝐧𝐞𝐭 = 𝒎𝒗𝟐 − 𝒎𝒗𝟐𝟏 = 𝑲𝟐 − 𝑲𝟏 = ∆𝐊 𝟐 𝟐 𝟐  Example #1 A 260-g beach volleyball is spiked so that it acquires a speed of 25 m/s. (a) What is its kinetic energy? (b) What was the net work done on the ball to make it reach its speed, if it started from rest?  Example #2 How much net work is required to accelerate a 1000-kg car from 15 m/s to 60 m/s?  Power, P The power P supplied by a force is the rate at which the force does work. Recall: 𝑑𝑊 = 𝐹⃑ & 𝑑𝑥⃑ = 𝐹⃑ & 𝑣𝑑𝑡 ⃑ The power delivered to the particle: 𝑑𝑊 𝑃= = 𝐹⃑ & 𝑣⃑ 𝑑𝑡 SI unit: watt (J): 1 W = 1 J/s Other unit: horsepower (hp): 1 hp = 746 W = 550 ft *lb/s  Example #3 A 5-kg box is being lifted upward at a constant velocity of 2 m/s by a force equal to the weight of the box. (a) What is the power input of the force?(b) How much work is done by the force in 4s?  Example #3 A 5-kg box is being lifted upward at a constant velocity of 2 m/s by a force equal to the weight of the box. (a) What is the power input of the force?(b) How much work is done by the force in 4s?  Example #4 A sky diver falls through the air toward the ground at a constant speed of 120 mph, her terminal velocity, before opening her parachute. (a) If her mass is 55-kg, calculate the magnitude of the power due the drag force. (b) After she opens her parachute, her speed slows to 15 mph. What is the magnitude of the power due to the drag force now?  Example #4 A sky diver falls through the air toward the ground at a constant speed of 120 mph, her terminal velocity, before opening her parachute. (a) If her mass is 55-kg, calculate the magnitude of the power due the drag force. (b) After she opens her parachute, her speed slows to 15 mph. What is the magnitude of the power due to the drag force now?  Potential Energy, U It is energy associated with the configuration of a system, due to arrangements of its parts, its composition, location, and structure Some forms of potential energy: 1 ' Gravitational: U = 𝑚𝑔𝑦 chemical elastic: 𝑈() = 𝑘𝑥 electrical nuclear 2  Two Types of Forces Conservative Forces Dissipative Forces The total work it does on a particle is zero Forces that only do negative work when the particle moves around any closed path, returning to its initial position Negative Work done → heat Forces that do both positive and negative Examples: work Friction Negative Work done → ∆U Viscosity Air drag Examples: Gravitational force Elastic force (e.g. spring) Electrical force Gravitational Potential Energy 𝑊! = 𝐹𝑑 cos 𝜃 = 𝑚𝑔 𝑑 cos 90° − 𝛼 For infinitesimal displacement: 𝑊! = −𝑚𝑔ℎ = −𝑚𝑔 𝑦" − 𝑦# 𝑑𝑈 = − 𝐹⃑ 4 𝑑 𝑠⃑ 𝑊! = − 𝑚𝑔𝑦" − 𝑚𝑔𝑦# 𝑑𝑈 = − −mg𝚥̂ 4