» Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic, potential or the combination. » » ME total = PE + KE

» Some forces will change the total mechanical energy of the object. » And some forces will NOT change the total mechanical energy of an object, but instead can only transform the energy of an object from potential energy to kinetic energy (or vice versa). » Our tennis ball lab demonstrated this principle...

» The diagram below demonstrates a ski jump of Li Ping Phar (esteemed Chinese ski jumper) as she glides down the hill and makes one of her record-setting jumps.

» The total mechanical energy of Li Ping Phar is ME total = PE + KE = 50,000 J » Notice that ME total = constant throughout her motion.

» There are conditions under which the ME total will be a constant value and conditions under which it will be a changing value. » We can categorize forces based upon whether or not their presence is capable of changing an object's total mechanical energy.

» Internal forces = Conservative Forces » Gravity » electrical forces » magnetic forces » spring forces » When an internal force is applied, the ME total of that object remains constant, but the object's energy changes form. » ME f = ME 0 »

» For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy is transformed into kinetic energy. » The sum of the kinetic and potential energies remains constant. » This is referred to as energy conservation. » Because internal forces do not change ME total, they are called conservative forces. They conserve mechanical energy.

» External forces = Non-conservative Forces (forces due to contact b/w objects) include » applied force » normal force » tension force » friction force » air resistance force. » When an external force is applied, the ME total is changed.

» If the work is positive work, then the object will gain energy. » If the work is negative work, then the object will lose energy. » » The gain or loss in energy can be in the form of potential energy, kinetic energy, or both. »

» The work that is done, W = ΔME total = ME f – ME 0 » Because external forces are capable of changing the total mechanical energy of an object, they are referred to as non- conservative forces.

» ME total = PE + KE i.e., the total mechanical energy at any moment » W external = ME final - ME 0 i.e., the total WORK done by external non-conservative forces » W external = [KE final + PE final ] - [KE 0 + PE 0 ] » » This is often re-written as "the initial energy + the work done = final energy". » ME 0 + W external = ME final

» EX: A weightlifter applies an upwards force of 1000 N to a barbell to displace it upwards a given distance = 0.25 m at a constant speed. The barbell begins with 1500 Joules of potential energy because it is resting on a rack above the gym floor, approximately at chest-level of the weightlifter. » How much work does the weightlifter apply? » Fdcos θ= = 250 J » How much energy does the barbell have once he has lifted the barbell? » 1500 J+ 250 J = 1750 J. »

» In what form (PE or KE or both) is the final energy? » The barbell began with potential energy. KE was added to the bar by lifting it (external force) and then this was changed into PE. The final energy is all PE.

» EX: Now consider a car that is skidding from a high speed to a lower speed. » The force of friction between the tires and the road exerts a leftward force = 8000 N. » The car moves rightward 30 m. » The car begins with Joules of energy. » How much work does the Friction Force do? » (Fdcosθ = cos(180) = JFdcos »

» How much energy does the car finish with? » 320,000 + (-240,000) = 80,000. » The car finishes with 80, 000 Joules of mechanical energy. » In what form (PE or KE or both) is the final energy? » The car began with KE. KE was removed from the car by friction (external force). There was no change in height so no change in PE. The car is still in motion at the end of the scenario; all ME is KE. »

» In both examples, an external force does work upon an object over a given distance to change the total mechanical energy of the object. » If the external force (nonconservative force) does positive work, then the object gains mechanical energy. The amount of energy gained is equal to the work done on the object. ».

» If the external force (nonconservative force) does negative work, then the object loses mechanical energy. The amount of mechanical energy lost is equal to the work done on the object. » The work-energy relationship can be combined with the expressions for potential and kinetic energy to solve complex problems. » W= ∆ME = FdcosƟ

» P. 187 Focus #13 » P. 190 #37-45odd; 51-57odd » For #37, you will need to use kinematics to find v 2 » For #45, you will need to start with kinematics to find v at the bottom of the slide, and to find h (the height of the bottom of the slide from the water).