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S-29 This cat is not happy. He is in need of a hair dryer. List five sources of energy that might be able to produce electricity for him. Work and Energy AP Physics Chapter 6 Work and Energy 6.1 Work Done by a Constant Force 6.1 Work Done by a Constant Force Work – the product of the magnitude of the displacement times the component of the force parallel to the displacement W Fr (your book replaced r with d) Or (dot product) W Fr cos Work is measure in Joules (Energy) 6-1 6.1 Work Done by a Constant Force If Force an displacement are in the same direction Work is done, velocity increases, energy of the object increases If Force is opposite to displacement, negative work is done, energy decreases 6-1 6.1 Work Done by a Constant Force If there is no motion, or the force is perpendicular to motion, no work is done, there is no change in velocity, there is no change in energy 6-1 6.1 Work Done by a Constant Force As long as Force and displacement are parallel, work is done 6-1 6.1 Work Done by a Constant Force Example: A person pulls a 50 kg crate 40m along a horizontal floor by a constant force of 100N @ 37o. The coefficient of friction is 0.20. What is the work done by each force acting on the crate? N F Free body diagram f W 6-1 6.1 Work Done by a Constant Force By W? N F f W 6-1 6.1 Work Done by a Constant Force Example: A person pulls a 50 kg crate 40m along a horizontal floor by a constant force of 100N @ 37o. The coefficient of friction is 0.20. What is the work done by each force acting on the crate? Work done by F? W Fr cos W (100)(40) cos 37 W 3195 J N F f W 6-1 6.1 Work Done by a Constant Force Example: A person pulls a 50 kg crate 40m along a horizontal floor by a constant force of 100N @ 37o. The coefficient of friction is 0.20. What is the work done by each force acting on the crate? Work done by f? W fr cos f N N F sin mg 0 N (50)(9.8) 100 sin 37 430 f (.2)(430) 86 W (86)(40) cos180 3440 J N F f W 6-1 6.1 Work Done by a Constant Force Example: A person pulls a 50 kg crate 40m along a horizontal floor by a constant force of 100N @ 37o. The coefficient of friction is 0.20. What is the net work done on the object? W WF W f W 3195 (3440) 245 J 6-1 Work and Energy 6.2 Work Done by a Varying Force 6.2 Work Done by a Varying Force Work is the area under a Force vs. displacement graph. If force changes at a constant rate, 1 W 2 ( F F0 )d Otherwise we use calculus to calculate the area x W F ( x)dx x0 6-2 Work and Energy 6.3 Kinetic Energy, & the Work-Energy Principle 6.3 Kinetic Energy, & the Work-Energy Principle W Fx max Energy – the ability to do work 2 2 v v Sufficient for Mechanical Energy 0 2ax 2 2 v v Kinetic Energy (translational) –adue 0 to motion 2x Equation 2 1 K 2 mv v 2 v02 W m x 2x Work-Kinetic Energy W K v 2 v02 W m 2 W 12 mv 2 12 mv02 6-3 S-30 A rocket powered 2000kg truck can go from 0 to 27 m/s in 3.5 s. A. What is the acceleration of the truck? B. What is the displacement of the truck? C. How much work was done on the truck? 6.3 Kinetic Energy, & the Work-Energy Principle Work-Kinetic Energy Theorem (Work-Energy Principle) – the net work done on an object is equal to the change in the object’s kinetic energy Work-Kinetic Energy Physlet 6-3 6.3 Kinetic Energy, & the Work-Energy Principle A 1000 kg car traveling 26.7 m/s can brake to a stop in 20 m. What is the force applied by the brakes? N Free Body Diagram? f mg 6-3 6.3 Kinetic Energy, & the Work-Energy Principle A 1000 kg car traveling 26.7 m/s can brake to a stop in 20 m. What is the force applied by the brakes? N Solve W Fd cos W Fd cos180 Fd W K Fd 12 mv 2 12 mv02 Fd 12 mv 2 0 mv02 (1000)(26.7) 2 F 17800 N 2d 2(20) f mg 6-3 6.3 Kinetic Energy, & the Work-Energy Principle A 1000 kg car traveling 26.7 m/s can brake to a stop in 20 m. If the car is now traveling twice as fast, how far must it travel to stop? N Fd 12 mv02 mv02 (1000)(53.4)2 d 80m 2F 2(17800) f mg 6-3 Work and Energy 6.4 Potential Energy 6.4 Potential Energy Potential Energy – due to position or configuration Gravitational Potential Energy – (Ug) due to position above the earths surface U g mgy 6-4 6.4 Potential Energy Elastic Potential Energy – due to the position of a spring Hooke’s Law Fs kx Determining a Spring Constant Equation for Elastic Potential Energy U s kx 1 2 2 Elastic Potential Energy k=spring constant 6-4 Work and Energy 6.5 Conservative and Nonconservative Forces 6.5 Conservative and Nonconservative Forces Conservative Forces – independent of pathway (gravity) Energy can be returned (conserved) Nonconservative Forces – depends on pathways (friction) Energy can not be returned Physlet 6-5 S-31 A unfortunate 45 kg child never learned to slide on anything but his face. If his face and the dirt have a coefficient =0.4, and he is running at 11 m/s when he starts his slide how much work is done by friction by the time he comes to a stop? Work and Energy 6.6 Mechanical Energy and its Conservation 6.6 Mechanical Energy and its Conservation If no energy is lost to nonconservative forces E E0 We can expand that to include the types of energy we have K U g U s K 0 U g0 U s0 Principle of Conservation of Mechanical Energy-energy just switches forms 6-6 6.6 Mechanical Energy and its Conservation If energy is lost to nonconservative forces E E0 WNC For example if the energy was lost to friction K U g U s K 0 U g0 U s0 fr 6-6 Work and Energy 6.7 Problem Solving Using Conservation of ME 6.7 Problem Solving Using Conservation of ME 1. List the types of energy before the reaction 2. List the types of energy after the reaction 3. Consider any non conservative forces 6-7 S-32 The 75 kg Henry (French) jumps off a cliff that is 102 m high. Assuming that the bungee has a resting length of 40 m, follows Hooke’s Law, and stops the guy 3 m before he hits the surface, what is the elastic constant of the bungee cord? Work and Energy 6.8 Other Forms of Energy 6.8 Other Forms of Energy 1. 2. 3. 4. Electric Nuclear Thermal Chemical 6-8 6.8 Other Forms of Energy Law of Conservation of Energy – The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another. 6-8 Work and Energy 6.10 Power 6.10 Power Power – the rate at which work is done W P t Measured in watts Often convenient to write in terms of force W Fr P Fv t t 6-9 S-33 The worlds strongest woman lifts 186 kg upward a distance of 0.75 m. Assuming that the mass accelerated upward from rest the whole distance in 0.44s, A. What is the work done by the dainty lady? B. How much power did she generate? S-34 Mike is not a very impressive driver. He drives his 1500 kg minivan into the living room of his mom’s house. If the van was traveling at 20 m/s and came to a stop in 2 m, what is the average force on Mike and the van? S-35 I can use the conservation of energy to calculate changes in position or speed Tarzan (and his very 50’s family) are out swinging on their vine. The vine is 45 m long and makes and angle of 10o to the vertical. If Tarzan (m=105 kg) runs at 15 m/s and jumps on the vine, what will be the vertical angle at the highest point the vine reaches? S-36 I can use the conservation of energy to calculate changes in position or speed Sven likes to ride his pogo stick really high. If he has a mass of 115 kg, and manages to reach a maximum height of 13 m when the spring is compressed 0.4 m, what is the constant of the spring? S-37 I can use the conservation of energy to calculate changes in position or speed The worlds biggest swing drops 19 stories (57 m). If our 150 kg chubby champion ran at 11 m/s to jump off the cliff, and the rope was 89 m long, what is his velocity at the bottom? Treat this as a pendulum S-38 I can use the conservation of energy to calculate changes in position or speed Big Mouse Trap! S-39 Don’t mess with this dog. If he has a mass of 25 kg (all muscle) and hits the 5 kg pendulum going 7.2 m/s, what will be the maximum vertical angle the rope makes. The string is 8 m long. S-40 I can relate transformations between kinetic and potential energy Using your brilliant knowledge of energy, why has the style of the high jumping changed over the years from A. Scissor B. Straddle C. Flop S-41 A 112 kg weasel running at 32 m/s trips and rolls into a ball. He rolls up a 45m long frictionless hill that makes an angle of 22o to the horizontal. At the top of the hill, falls off a cliff that is 120 below his starting point. He falls on a spring that compresses 1.5 m before shooting him back into the air. He passes his girlfriend who is sitting in a tree that is 81 m tall. What is his velocity as he passes his girlfriend? S-42 This is a ridiculously huge rabbit May your brain be as large while you take your test!