Physics 2204: Unit 3 Unit 3: Work, Power & Energy What is Work? Work: applying a force to cause or stop movement • the force, or some component of the force, must be parallel to the displacement • if the force acts to cause an increase in displacement, it is positive work • if the force acts to stop the object, we say the work is negative 1 Physics 2204: Unit 3 • The equation for work is: W = F|| x d • which makes the units N m, however this is replaced with joules (J) • F|| can be replaced with Fcosθ if we are using the angle at the base of the force • This makes the equation: W = Fcosθ x d or W = Fdcosθ Ex) A girl pedals her bike with an average force of 150 N over a distance of 2.5 m. How much work does she do? Ex 2) If she falls off the bike and the ground does 41 J of work on her by applying 55 N of friction to her, how far does she slide? 2 Physics 2204: Unit 3 Ex 3) How much work does it take to lift a 20 lb (9.1 kg) weight 0.5 m? Ex 4) The handle of a lawnmower is angled at 50.0º as shown. My yard is 12 m long. If I apply an average force of 35 N on the lawnmower, how much work is it to mow a single strip? 3 Physics 2204: Unit 3 Power • the ability to do work • having a high power rating means more work can be done in less time P = W / t where W is work in Joules and t is time in seconds • therefore the unit for power is J / s but we commonly use watts (W) • in everyday life we often use horsepower (hp) where 1 horsepower = 745.699872 watts (this conversion will not be tested) Ex) How much work can a 2014 Ford F­150 do in 15 seconds? (306 000 W) Ex 2) A truck winch has a power of 1200 W. If it takes 60 s to drag a car 1.5 m, how much force does the winch provide? 1200 W ~ 1.6 hp 4 Physics 2204: Unit 3 Ex 3) A crane has a power rating of 194 000 W. How long will it take to raise a 250 kg crate a height of 18 m? 234 (ft / min) = 1.18872 m / s 5 Physics 2204: Unit 3 Practice 1) An engine does 14000 J of work on a car over a period of 4.5 seconds. What is the power of the engine? 2) How long would it take a 150 W motor to do 350 J of work? 3) How much power is required to move a car 150 m in 60 s if a force of 1500 N is applied over the entire distance? 4) A 85 kg person climbs 6.5 m up a vertical ladder in 20.0 s. How much power is involved? 6 Physics 2204: Unit 3 Energy • closely related to work (often used interchangeably, but not always correctly) • when work is done on an object its energy changes • positive work increases energy while negative work decreases energy Work ­ Energy Theorem W = ΔE • since there are no additional factors, the unit for energy is also joules (J) Ex) A coyote wearing a rocket is running. While running is has 125 J of energy. The rocket is then turned on, delivering a power of 1200 W for a total of 20.0 s. What is the final energy of the coyote? Think about it. What does a car's engine do to change the energy of the car? • two main forms of energy 1. Potential (stored) 2. Kinetic (active) 7 Physics 2204: Unit 3 8 Physics 2204: Unit 3 Kinetic Energy • related to mass and velocity linear curved (quadratic) E α m E α v2 • the equation for kinetic energy is 2 Ek = 1/2 m v Ex) A 25 kg dog runs at 4.5 m/s. What is its kinetic energy? Ex 2) A 0.03 kg bullet has a kinetic energy of 130 J. What is the velocity of the bullet? Ex 3) A 250 kg car increases its speed from 12 m/s to 18 m/s. How much work has the engine done on the car? 9 Physics 2204: Unit 3 Gravitational Potential Energy • gravitational potential energy (Eg) is the stored energy in an object that is currently above the ground, or some other baseline • since we know work changes the energy of an object, we will consider the work involved in lifting different objects Which requires more work (and therefore increases the energy more)? More importantly, why does it require more work? 1) Lifting a feather or lifting a rock? 2) Lifting a barbell to chest height or over your head? 3) Picking up a 20 kg mass on Earth or on the moon? • considering these three factors, it should be clear that the equation for gravitational potential energy is Eg = mgh 10 Physics 2204: Unit 3 Energy of a Falling Ball 1) A 0.01 kg ball is dropped from a height of 1.0 m. Using kinematics, determine the final velocity of the ball as it hits the ground. 2) Before the ball is dropped it has only gravitational potential energy. How much energy does it have at the top? 3) As it strikes the ground, the ball has only kinetic energy. How much energy does it have just before impact? 11 Physics 2204: Unit 3 Practice 1) A 5.0 kg statue is on top of a 2.8 high shelf. What is its potential energy? 2) What height would a 1.0 kg kitten have to be held to have a potential energy of 25 J? 3) What speed would a 180 kg car need to travel to have 3500 J of kinetic energy? 4) What is the kinetic energy of a 2.5 x 10­4 kg bee travelling at 3.5 m/s? 12 Physics 2204: Unit 3 5) What is the gravitational energy of a 55 kg physics teacher on a 1200 m tall tower? 6) A 0.25 kg ball has 12 J of potential energy. How high is it above the ground? 7) A 5.0 kg dog is 1.2 m above the surface of a strange planet. If it has 28.0 J of energy, what is the gravitational constant of that planet? 13 Physics 2204: Unit 3 Hooke's Law • Hooke noticed that while different springs stretch differently with given forces, the relationship between the force applied and the amount of stretch was linear (up to a point) • "hard" springs had a greater slope while "soft" springs had a lower slope • the equation for spring force (or elastic force) is Fs = ­k x where F is force (N) k is spring constant (N/m) x is amount of stretch or compression (m) • spring constant is specific to each particular spring • stretch (x) is measured relative to the rest position / equilibrium point and is often recorded in cm 14 Physics 2204: Unit 3 Practice 1) A spring with a spring constant of 12 N/m was stretched by 25 cm. How much force was applied? 2) 1.5 N of force is applied to compress a spring (k = 5.0 N/m) How much does it compress? 3) A 0.15 kg mass is hung from a spring. If it stretches 12 cm, what is the spring constant? 15 Physics 2204: Unit 3 Elastic / Spring Energy • when we apply a force to a spring or elastic, we move it a distance and therefore do work on it • this implies that stretching a spring or elastic increases its energy • the harder the spring the more work required to give it energy E α k • the greater the stretch, the greater the energy however this is not linear • it takes four times the work (and therefore give four times the energy gain) to double the stretch E α x2 • the full equation is 2 Es = 1/2 k x 16 Physics 2204: Unit 3 Practice 1) A spring with a spring constant of 12 N/m was stretched by 25 cm. How much energy is stored in it? 2) 1.5 N of force is applied to compress a spring (k = 5.0 N/m) What is its elastic energy? 3) A 0.15 kg mass is hung from a spring. If it stretches 12 cm, how much energy does it store? 17 Physics 2204: Unit 3 Total Energy • the total energy of a system is the sum of its potential and kinetic energy at any given point Etotal = Eg + Es + Ek • the first task is to determine the type, or types, of energy involved then calculate them separately and add them together What types of energy are present? 1) 2) 18 Physics 2204: Unit 3 3) 4) 19 Physics 2204: Unit 3 Ex) A 0.05 kg arrow is travelling at 8.5 m/s a height of 2.0 m above the ground. What is the total energy of the arrow? Ex 2) A 25 kg child runs at 3.8 m/s and is about the jump on a crazy carpet. If the crazy carpet in at the top of a 6.5 m high hill, what is the total energy of the child? Ex 3) A 52 kg person jumps onto a trampoline with a spring constant of 250 N/m.