Slide 1. Slide 2. Slide 3. Conservation of Mechanical Energy and Efficiency Presentation
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1 Slide 1 Using Newton s 2 nd Law to solve problems can be complicated. Forces are vectors and vectors go in different directions. The math required to get an answer can be very difficult. Slide 2 You would like to find a method that is less complicated. Slide 3 Using vectors makes your calculations harder. As the pendulum swings, the direction of the tension changes. Therefore, the angle θ changes, does the size and direction of the tension. To predict the speed of the pendulum at any point after it is released would require the student to use calculus to help solve the problem.
2 Slide 4 You can use work and energy to simplify your calculation. Work and energy are scalars. Questions involving work and energy are easier to solve because there is no direction that causes problems with the calculations. Slide 5 The law of conservation of energy is a powerful tool you can use. Slide 6 The total amount of energy always remains the same. This is always true. Unfortunately, the almost all energy transformations create heat, and heat is difficult to keep in one place.
3 Slide 7 However, some energies are difficult to measure or contain. An example of this is the conversion of kinetic energy into heat. Slide 8 Potential Energies and Kinetic Energy are much easier to measure. These are known as the Mechanical Energies. Slide 9 E total E total This is the law of conservation of energy expressed as an equation. The prime symbol, which looks like an apostrophe, behind the variable means the final energy. The one without the prime symbol is the initial energy.
4 Slide 10 If there isn t any friction, the sum of gravitational and kinetic energy stay the same. E k E g k m v m v m g h E E g m g h If the friction becomes very small, we can ignore the heat energy and conserve the mechanical energies. Right now, we only have two mechanical energies to worry about, and the total energy is the sum of the gravitational potential energy and kinetic energy. All of the other possible energies will remain constant. Slide 11 Can we make a perpetual motion machine? A perpetual motion machine will continue to move forever without the addition of additional energy. Slide 12 Well, the machine cannot violate the laws of thermodynamics? Not all scientific theories are created the same. Some theories may be modified or changed over time. However, scientists believe that the three laws of thermodynamics will never change.
5 Slide 13 The First Law basically says that energy or matter can neither be created nor destroyed. The first law of thermodynamics is a restatement of the law of conservation of energy. Energy must always come from some other source of energy. Slide 14 The Second Law essentially says that it is impossible to obtain a process where the unique effect is the subtraction of a positive heat from a reservoir and the production of a positive work. The second law of themrodynamics actually says: The entropy of an isolated system consisting of two regions of space, isolated from one another, each in thermodynamic equilibrium in itself, but not in equilibrium with each other, will, when the isolation that separates the two regions is broken, so that the two regions become able to exchange matter or energy, tend to increase over time, approaching a maximum value when the jointly communicating system reaches thermodynamic equilibrium. Entopy is randomness: (thermodynamics) a thermodynamic quantity representing the amount of energy in a system that is no longer available for doing mechanical work; "entropy increases as matter and energy in the universe degrade to an ultimate state of inert
6 uniformity"
7 Slide 15 A steam engine is an example of a Carnot Engine. It uses the hot boiler and the much cooler air around the boiler to create kinetic energy. Slide 16 This is schematic diagram of a Carnot Heat Engine. Q1 is the heat going into the engine from a hot source. Q2 is the heat or energy coming out of the engine to the cooler source. W is the work the engine can do. Q2 is the energy lost to system. Slide 17 The Third Law says that all processes cease as temperature approaches absolute zero. As temperature approaches absolute zero, the entropy of a system approaches a constant minimum. Briefly, this postulates that entropy is temperature dependent and results in the formulation of the idea of absolute zero.
8 Slide 18 How does all of this apply to efficiency? Slide 19 Efficiency is the ratio of the useful work (or useful energy) from a machine compared to the amount of work or energy put into the machine. The laws of thermodynamics basically tell us that we can never find a device that is always 100% efficient. We lose energy to randomness. The random motion of the particles causes heat or thermal energy. E output Slide % E input This is the formula for efficiency. Efficiency is a ratio, but it is normally expressed as a percentage.
9 Slide 21 Efficiency of Some Devices Incandescent lights Fluorescent lamps Combustion Engine Solar Cell Wind turbine Here are some examples of the efficiency of common devices. Notice that the incandescent lights are only about 5 to 10% efficient. Fluorescent lamps are about 28% efficient. The energy lost for devices usually goes into the generation of heat. Slide 22 Efficiency Questions The following are two questions using efficiency of a block and tackle. A block and tackle is a system of pulleys and ropes to apply a force to an object. One of the blocks is a number of pulleys attached together and fixed in one position. The other is block acts as movable pulleys. There is a mechanical advantage based on the number of pulleys used. Slide 23 Find the efficiency of a block and tackle if J of energy are required to raise a 155 kg piano a distance of 6.5 m.
10 Slide 24 Slide 25 Find the height that the piano could be raised if the block and tackle is 90.0% efficient. Slide 26
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