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What is Energy? The ability to do work –The ability to create a change Energy comes in many forms –Mechanical Potential Kinetic –Electrical –Thermal –Nuclear –Chemical It can be transformed from one form to another Like work, it is measured in Joules

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Mechanical Energy Deals with the energy an object has because of either it’s motion (kinetic energy), and/or the outside forces acting on the object trying to make it move (potential energy) A car moving at 50 mph can do a lot of damage to a pedestrian if they hit--this is because of the car’s motion. On the other hand, a 16 pound bowling ball being held 10 ft above a person’s head (but not moving) can be dangerous, because the force due to gravity pulls down on the ball. The ball has the potential to fall on the person’s head. The ball is not falling, BUT IT COULD because of the force of gravity.

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Potential Energy Energy that is not being applied to the object’s motion, BUT IT COULD BE LATER ON. It is the work done by something, other than you (such as gravity), naturally on its own. –Gravity causing things to fall –Attraction/repulsion of electrical charges –Expansion/contraction of a spring Potential energy depends on the position and condition of the object (the forces that act on it). Think of a stretched rubber band on a slingshot. It has potential energy due to its position. If the rubber band is released, it is capable of doing work. Some call potential energy “stored energy” but that term is very misleading (the energy does not come from the object).

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Gravitational Potential Energy Potential Energy due to gravity (E pg ). –Gravity is always trying to do work on objects by pulling them down to the ground. E pg of an object is equal to the work done by gravity to make an object fall. Work = Force*distance Work gravity = Force gravity * distance dropped = ma g (-h) Since ag = -9.8 m/s/s we use g. (g = 9.8 m/s/s) E pg = mgh Gravitational potential energy = /F g / * height

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Calculating E pg Calculate the change in potential energy of 8 million kilograms of water dropping 50 m over Niagara Falls. Know: m= 8 million kg h = 50 m g = 9.8 m/s 2 E Pg = mgh =(8,000,000 kg)(9.8 m/s 2 )(50 m) = 3,920,000,000 J or 3.92 x10 9 J

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Elastic Potential Energy Since a compressed spring wants to expand, and is willing to do work on any object in the way of its expansion, we call the work done by a spring the elastic potential energy (E pel ). This is also true for a stretched spring. It wants to contract back to its original length, and will pull anything attached to it. Some people call the elastic potential energy of a spring the potential energy of a spring (E ps ). elastic potential energy (E pel ) is a more general name. (E ps ) = work of a spring = (1/2)k( x) 2

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Kinetic Energy Energy of motion –It is the energy an object has BECAUSE it is moving. It IS NOT, IN ANY WAY, BY NO MEANS the energy an object uses to keep moving. (REMEMBER INERTIA). Depends on the mass and velocity of the object. Kinetic energy = (½)(mass)(velocity) 2 E k = (½)mv 2 Notice an object’s velocity has a greater impact on its kinetic energy than it’s mass.

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Work - Energy Theorem The work done on an object is defined as the change in that object’s energy. Work = Change in E p + Change in E k W = E p + E k

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Work - Energy Theorem A moving object is capable of doing work. –It can lose some of it’s kinetic energy (slow down) and create a change on another object in the process. –Car hitting an object –A bat hitting a ball –Electrical charges moving through a wire –Hot steam moving the turbines of an electrical generator An object can also convert it’s potential energy into kinetic energy so that it can do work. Work Potential Energy Kinetic Energy

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Net Work This is the overall work done on an object The net work is done by the net force acting on an object The net work always equals the change in kinetic energy F net// d = (1/2) mv f 2 - (1/2) mv i 2 Objects in equilibrium never have any net work done on them F net = 0 N Objects that move with a constant speed, never have any net work done on them.

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A quick comparison Objects A and B are initially sliding on smooth ice and come to a rough surface. Object A slides a distance of D as it comes to a stop. How far (in terms of D) will object B have to slide to also come to a stop? (The coefficient of kinetic friction is the same for both boxes.) mAmA mBmB VAVA V B = 2V A mAmA Rest D Since object B has twice the velocity of A it has 4X the E K. This means friction must do 4X the work on B than on A. And since the masses of A and B are the same, they both have the same frictional force. So object B must slide 4X farther than object A to do all that work. This is why you should never speed when driving.

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Another comparison Objects A and B are initially sliding on smooth ice and come a rough surface. Object A slides a distance of D as it comes to a stop. How far (in terms of D) will object B have to slide to also come to a stop? (The coefficient of kinetic friction is the same for both boxes.) mAmA m B = 2m A VAVA V B = V A mAmA Rest D Since object B has 2X the mass of object A, it has 2X the E K of A. This means friction must do 2X the work on B than on A. Because Object B has 2X the mass of object A it also has 2X the frictional force of object A. So object B slides the same distance as object A.

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Conservative forces. Some forces (such as gravity and electrical forces) convert the work needed to overcome them, into potential energy. This means that the energy you used to move an object can be given back later on. For example, you do 30 joules of work to lift a block (you had to fight gravity to lift it). The block now has 30 joules of gravitational potential energy that can be used later on. Gravity is called a CONSERVATIVE FORCE. These forces conserve the amount of mechanical energy in a system. They convert E K into E P and vice versa. Conservation means to save. The total energy in a conservative system is a constant.

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Non-conservative forces Other forces, such as friction, convert the work done on an object into heat. Heat is a form of energy, but not one we can ever use again. Thus some say that the energy is “lost”. You push a block across a rough floor. Once it stops moving, it does not return on its own to the starting point. Non-conservative forces often create heat--they do not keep the amount of mechanical energy of a system constant. Work = Change in E p + Change in E k + Heat (if any) W = E p + E k + Q (if any)

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Law of Conservation of Energy It states: Energy cannot be created nor destroyed. It is transformed from one form into another, but the total amount of energy never changes. Example - when gasoline combines with oxygen in a car’s engine, the chemical E p of the fuel is converted to molecular E k, and thermal energy. Some of this energy is transferred to the piston and some of this energy causes the motion of the car. The rest of the energy escapes (“is lost”) the system of the engine (as heat) and enters the environment. “Lost energy” is not energy that is destroyed, it is simply energy we cannot use.

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Application of the Conservation of Energy If there are only conservative forces acting on a system then we can say: –The starting total mechanical energy = the final mechanical energy E Ti = E Tf E pi + E ki = E pf + E kf The conservation of energy simplifies many complex problems into one easy process.

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Sample problem 1 A block is released from rest at the top of a smooth incline and slides to the bottom. What is the block’s final speed when it reaches the bottom? 5 m

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0 m E pgi = mass(9.8m/s/s)(5m) E pgf = mass(9.8m/s/s)(0m) E ki = (1/2)mass(0 m/s) 2 E kf = (1/2)mass(V f ) 2 E Ti = mass(9.8m/s/s)(5m)E Tf = (1/2)mass(V f ) 2 mass(9.8m/s/s)(5m) = (1/2)mass(V f ) 2 2(9.8m/s/s)(5m) = V f VfVf

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EpEp EKEK EpEp EKEK EpEp EKEK The total energy at one point is the same for all points for a conservative system Start Middle End

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Sample problem 2 A ball held from a height of 5 meters is dropped. What is the speed of the ball when it hits the ground? 5 m

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0 m E pgi = mass(9.8m/s/s)(5m) E pgf = mass(9.8m/s/s)(0m) E ki = (1/2)mass(0 m/s) 2 E kf = (1/2)mass(V f ) 2 E Ti = mass(9.8m/s/s)(5m)E Tf = (1/2)mass(V f ) 2 mass(9.8m/s/s)(5m) = (1/2)mass(V f ) 2 2(9.8m/s/s)(5m) = V f VfVf

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Independence of Path When a system is conservative, the path the object takes to go from point A to point B has no impact (is independent of) … The work needed to go there The change in E p The change in E k

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Work and Energy. Work… …is the product of the magnitude of displacement times the component of force parallel to the displacement. W = F ‖ d Units: N.

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