Aim: How is energy Conserved? HW: Problem Set

Energy Conservation: Top Thrill Dragster Name the different energies involved. Justify your reasoning. KE PE Internal Energy (Work done against Friction)

Work Energy Theorem You start out on top of a cliff with 1000J of potential energy. When you hit the ground (having used a parachute, I hope…), you have 400J of kinetic energy. Where did the energy go? Energy was lost due to friction (air resistance in this case)… Theorem: WNC = ΔKE + ΔPE

WNC = (KEB-KEA) + (PEB-PEA) WNC = ΔKE + ΔPE WNC = (KEB-KEA) + (PEB-PEA) WNC: Work done by a non-conservative force (anything except FG for now). Just before touching down… ΔKE = KEF – KEI = 400J – 0 = 400J ΔPE = PEF – PEI = 0 – 1000J = -1000J WNC = 400J + (-1000J) = -600J Lost to friction

Conservative Forces Conservative Forces: depend only on initial and final positions, not the path taken. PE can be defined only for a Conservative Force. Example: gravity, elastic force of spring, charge force Non-Conservative Forces: Work done that depends on the path taken. Examples: Friction See text for more. Wnet is work energy theorem

Conservation of Energy Law Energy can not be created nor destroyed! It can only be converted into different forms! Within a closed, isolated system (where there is no friction), total mechanical energy (KE + PE) is constant. Equation: ME = KE + PE Equation: Einitial = Efinal (ONLY without friction)

A 7 kg bowling ball falls to the floor from a height of 1. 5 meters A 7 kg bowling ball falls to the floor from a height of 1.5 meters. What is its speed just before it hits the floor? PEmax = KEmax 103J = 0.5(7kg)v2 v = 5.4 m/s

Example #1 An aircraft with a mass of 2.0 x 105 kilograms is flying at an altitude of 3.0 x 103 meters. What is its gravitational potential energy? How much work is needed to be done against gravity for the aircraft to reach this altitude? -5.89 x 109 J

How does PE relate to Work?

How does KE relate to Net Work? A 1000 kilogram car changes its speed from 20 meters per second to 10 meters per second within 100 meters of travel. What is the car’s initial KE? 200000 Joules What is the car’s final KE? How much work was done on the car? -150000 Joules With how much force did the car accelerate?

How does KE relate to W?

Writing Activity The following statement was part of an old AP exam, but for the new exam we must be able to define energy carefully with “good physics”. Answer the question, but only after explaining in extreme detail how energy is conserved for the situation.

Consider a 50 kg Tarzan swinging down on a vine from rest Consider a 50 kg Tarzan swinging down on a vine from rest. Tarzan swings to his lowest position which is 2 m below his starting point. Calculate his speed, neglecting air resistance. Ignore the smaller tree and snakes… And Jane 

Treating the Tarzan Earth System Systems can have potential energy due to their interaction. Systems can also have kinetic energy, which is equal to the sum of the kinetic energies of the component parts of the system. Define the lowest position of Tarzan as the zero of gravitational energy for the system. That means the Tarzan-Earth system begins with mgh = 1000 J of gravitational energy, and (because nothing is moving) no kinetic energy, giving 1000 J of system mechanical energy at the start. During the process, no work is done by an object external to the Tarzan-Earth system -- the only other object exerting a force on any part of the system is the rope, and the rope is always pulling perpendicular to Tarzan's velocity, so it does no work. Since the gravitational energy is zero at the bottom point, the entire 1000 J of system mechanical energy must be converted to kinetic energy. Now we use the kinetic energy formula to calculate speed. 1000 J of PEG before…. No work during…. 1000 J KE after

Treating Tarzan as a Single Object Objects can have kinetic energy, but not potential energy. So Tarzan begins with no kinetic energy. During the process, two forces act on Tarzan: the force of the string, and the force of the earth. The string force does no work on Tarzan because it is always perpendicular to Tarzan's velocity. The earth does work on Tarzan equal to Tarzan's weight multiplied by the distance Tarzan travels parallel to the weight, or 1000 J. This is positive work, because the force of gravity is parallel, not antiparallel, to the downward component of Tarzan's displacement. At the bottom, then, we know 1000 J of work has been done on Tarzan; this must change Tarzan's kinetic energy by 1000 J, since we're not treating Tarzan as a system with internal structure. Now we use the kinetic formula to calculate speed. 0 J total energy before…. 1000 J of work done by gravity…. 1000 J KE after.

How can we calculate work from a graph? Force vs Displacement On a force vs displ. Graph Area under line equals work. 10 8 6 4 2 Force (N) 5 10 15 20 Displacement (m)

Calculate work Force vs Displacement 10 8 6 Force (N) 4 2 5 10 15 20 Displacement (m)

Summary How is energy conserved on a roller coaster? Why does a roller coaster never go as high as the first drop? What is the work energy theorem? What is the difference between a conservative and non-conservative force?