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Work and Energy Remember that a force is a push or a pull. When we push or pull an object through a distance, we do work. Work is a form of energy. All energy is measured in Joules (J). 1 J = 1 Nm = 1 kg m2/s2. But what is energy? Energy: The ability to do work. Work equation W = F d Where W = the work done (in J) F is the force (in N) d is the distance through which the force is exerted (in m) For this equation, the force and the distance moved must lie along the same line. Tug of war example Work equation Often, the work done is lifting an object against the force of gravity. In that case, the force is equal to the weight of the object. If a force is exerted but there is no movement, then there is no work! Work example Sally Student lifts a 2.0 kg book 1.0 meter from the floor. What is the work that Sally has exerted on the book? W = Fd in this case the force is due to the weight of the book (F = mg) W = (2.0 kg) (9.8 m/s2) (1.0 m) W = 20 J Now Sally holds the book over her head. What is the work she is now exerting on the book? W = 0 J (no movement = no work) Work at an angle What if the work and the distance don’t lie along the same line? In this case, we need to use the component of the force that is in the same direction as the distance. W = Fd cos Where is the angle between the direction of the force and the direction of the motion. Note if the force and the distance are perpendicular to each other, W = o J because cos 90º = 0 Work at an angle - example Sid Scorpion pushes a lawn mower with a force of 125N directed at 25.0 º below the horizontal. He pushes the lawn mower 2.00 meters horizontally. How much work has he done? W=Fd cos W = (125 N)(2.00m) cos 25.0 º W = 227 J Power Power is the rate at which work is done. P=W/t Where Wis work (in J) t is time (in s) P is power. Power is measured in Watts (W) – like a light bulb. 1 W = 1 J/s = 1 Nm/s = 1 kg m2/s3 Potential Energy Potential energy is stored energy. It has the same meaning as when your teacher looks at you sadly and says with a sigh, “You have such potential.” She means you could do the work. Just like you, potential energy could do the work under certain circumstances. Potential Energy – derive the equation Demonstration to derive the equation PE = mgh PE is Potential Energy (in Joules) m is mass (in kg) g is 9.8 m/s2 h is height (in m) Potential Energy – example What is the potential energy of a 7.5 kg brick resting on a windowsill 25 meters above the sidewalk? PE = mgh PE = (7.5 kg)(9.8 m/s2)(25 m) PE = 1800 J Kinetic Energy – derive the equation Kinetic energy is the energy of motion. Demonstration to derive the equation KE = ½ mv2 where KE = kinetic energy ( in Joules) m = mass (in kg) v = velocity (in m/s) Kinetic Energy – example What is the kinetic energy of a 5.0 kg bowling ball moving at 12 m/s? KE = ½ mv2 KE = ½ (5.0 kg) (12 m/s)2 KE = 360 J Kinetic Energy – example What is the velocity of the same bowling ball that has a kinetic energy of 450 J? KE = ½ mv2 450 J = ½ (5.0 kg) v2 v = 13 m/s Work - Kinetic Energy Theorem The Work - Kinetic Energy Theorem says that the work that goes into a system becomes the kinetic energy of that system. For example, if I do 150 J of work lifting a bowling ball to the top of a hill, and then released it from rest to roll down the hill, the kinetic energy of the bowling ball would be 150 J at the bottom of the hill. Law of Conservation of Energy Energy can not be created or destroyed. In a closed, isolated system, the total amount of energy must remain the same. However, the energy can change forms. For example, from work to potential energy, to kinetic energy to other forms of energy (sound, heat, light, etc). Law of Conservation of Energy example What is the work required to lift a 1100 kg car 35 meters up to the top of Elitch’s Tower of Terror? W = F d W = (1100 kg) (9.8 m/s2) (35 m) W = 380,000 J Law of Conservation of Energy – example (continued) At the top of Elitch’s Tower of Terror, what is the potential energy of the car? The work has now become the potential energy of the system. The law of conservation of energy says the amount must remain the same. PE = 380,000 J Law of Conservation of Energy – example (continued) Once the car has been released, the total energy becomes part KE and part PE. What is the potential energy of the car halfway down (after falling 17.5 m)? PE = mgh PE = (1100 kg) (9.8 m/s2) (17.5 m) PE = 190,000 J Half the height = half the potential energy. Law of Conservation of Energy – example (continued) What is the kinetic energy of the car halfway down (after falling 17.5 m)? Law of conservation of energy says the total energy must still be 380,000 J. KE + PE = 380,000 J KE + 190,000 J = 380,000 J KE = 190,000 J Law of Conservation of Energy – example (continued) What is the velocity of the car halfway down (after falling 17.5 m)? KE = 190,000 J = ½ mv2 190,000 J = ½ (1100 kg) v2 v = -19 m/s Law of Conservation of Energy – example (continued) What is the velocity of the car just as it reaches the bottom of the Tower of Terror? Now the energy is all kinetic (because h=0). KE = 380,000 J = ½ mv2 380,000 J = ½ (1100 kg) v2 v = -26 m/s Law of Conservation of Energy – example (continued) What is the height of the car when the velocity is - 7.5 m/s? KE + PE= 380,000 J ½ mv2 + mgh = 380,000 J ½ (1100 kg) (7.5 m/s)2 + (1100 kg) (9.8 m/s2) h = 380,000 J h = 32 m Law of Conservation of Energy The trick is to remember that the total amount of energy stays the same throughout the “closed, isolated system” (in this case: the Tower of Terror). Calculate the total energy at the most convenient spot (usually the top since it will all be PE). Law of Conservation of Energy Remember: If a mass has height it has potential energy. If a mass has velocity it has kinetic energy. If a mass starts from rest at the top of a hill, it can never go higher without adding energy. Pendulum examples