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Work, Energy & Power There are many different TYPES of Energy. Energy is expressed in JOULES (J) 4.19 J = 1 calorie Energy can be expressed more specifically by using the term WORK(W) Work = The Scalar Dot Product between Force and Displacement. So that means if you apply a force on an object and it covers a displacement you have supplied ENERGY or done WORK on that object. Scalar Dot Product? W F x Fx cos A product is obviously a result of multiplying 2 numbers. A scalar is a quantity with NO Thie means that F and x MUST be parallel. DIRECTION. So basically To ensure that they are parallel we add the Work is found by multiplying cosine on the end where the cosine is the the Force times the angle between the direction of the force and displacement and result is the direction of the displacement. If the force ENERGY, which has no and displacement are parallel, the angle is direction associated with it. zero, and the cosine is one. Work The VERTICAL component of the force DOES NOT cause the block to move the right. The energy imparted to the box is evident by its motion to the right. Therefore ONLY the HORIZONTAL COMPONENT of the force actually creates energy or WORK. When the FORCE and DISPLACEMENT are in the SAME DIRECTION you get a POSITIVE WORK VALUE. The ANGLE between the force and displacement is ZERO degrees. When the FORCE and DISPLACEMENT are in the OPPOSITE direction, yet still on the same axis, you get a NEGATIVE WORK VALUE. This negative doesn't mean the direction!!!! When the FORCE and DISPLACEMENT are PERPENDICULAR, you get NO WORK!!! The ANGLE between the force and displacement in this case is 90 degrees. The Work Energy Theorem Up to this point we have learned Kinematics and Newton's Laws. Let 's see what happens when we apply BOTH to our new formula for WORK! 1. We will start by applying Newton's second law! 2. Using the v2 equation ! 3. An interesting term appears called KINETIC ENERGY or the ENERGY OF MOTION! The Work Energy Theorem And so what we really have is called the WORK-ENERGY THEOREM. It basically means that if we impart work to an object it will undergo a CHANGE in speed and thus a change in KINETIC ENERGY. Since both WORK and KINETIC ENERGY are expressed in JOULES, they are EQUIVALENT TERMS! " The net WORK done on an object is equal to the change in kinetic energy of the object." Example W=Fxcos A 70 kg base-runner begins to slide into second base when moving at a speed of 4.0 m/s. The coefficient of kinetic friction between his clothes and the earth is 0.70. He slides so that his speed is zero just as he reaches the base (a) How much energy is lost due to friction acting on the runner? (b) How far does he slide? a) W f K F f Fn mg W f 0 1 mvo2 1 (70)( 4) 2 2 2 W f -560 J (0.70)(70)(9.8) = 480.2 N W f F f x cos 560 (480.2) x(cos 180) x 1.17 m Work Done By Friction The frictional force of a surface always acts in the opposite direction of an objects displacement. This means that friction will always do negative work on an object. An object will always do positive work on the surface Work Energy A child pulls a 5kg sled with a rope angled 37 degrees above the horizontal with a force of 10N. The coefficient of friction is 0.1 How much work does he do? Friction? How fast will the sled be moving after moving 4meters? Work Energy Work Energy Work Energy How much work is done by gravity? How much work is done by the normal force? Work as the transfer of energy Just as there is conservation of mass in the universe. There is also a conservation of energy. Energy is neither created or destroyed Energy is transferred from one object to another or changes from one form to another The change in an objects kinetic energy is the result of the net work done on it. Energy Gained is positive work Energy lost is negative work The Scalar Nature of Energy Energy is a scalar quantity. It does not have direction. An object in motion only has positive kinetic energy due to the equation using v2 For work-energy calculations, only the speed of an object can be calculated, not its velocity Work Done by Gravity In this case, because the object is at rest initially, the change in kinetic energy is equal to the final kinetic energy Solve for the final velocity of an object after being dropped from height “h” Work-Energy Kinematics Potential Energy An object with kinetic energy can do work on another object. An object that can fall has the ability to do work once it has fallen. This energy by virtue of its position is its potential energy. Potential Energy Requires a “Reference Level” Potential Energy Due to Gravity