# Using Newton’s 2 nd Law to solve problems can be complicated

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Using Newton’s 2 nd Law to solve problems can be complicated. You would like to find a method that is less complicated. Using vectors makes your calculations harder. You can use work and energy to simplify your calculation. The law of conservation of energy is a powerful tool you can use. - PowerPoint PPT Presentation

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Using Newtons 2nd Law to solve problems can be complicated.

Using Newtons 2nd 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.1You would like to find a method that is less complicated.Using vectors makes your calculations harder.

As the pendulum swings, the direction of the tension changes. Therefore, the angle 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.3You 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.

4The law of conservation of energy is a powerful tool you can use.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.

6However, some energies are difficult to measure or contain. An example of this is the conversion of kinetic energy into heat.

Potential Energies and Kinetic Energy are much easier to measure. These are known as the Mechanical Energies.

Gravitational Potential EnergyThe gravitiational potential energy is the energy of an object due to its position in the gravitational field of the earth. The formula for the gravitational potential energy near the surface of the earth is:

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.10If there isnt any friction, the sum of gravitational and kinetic energy stay the same.

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.

11Can we make a perpetual motion machine?

A perpetual motion machine will continue to move forever without the addition of additional energy.12Well, 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.13The 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.14The 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 uniformity"

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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.

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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.17The 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.

18How does all of this apply to efficiency?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.

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This is the formula for efficiency. Efficiency is a ratio, but it is normally expressed as a percentage.21Here 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.

22Efficiency QuestionsThe 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.

23Find the efficiency of a block and tackle if 11000 J of energy are required to raise a 155 kg piano a distance of 6.5 m.

Find the height that the piano could be raised if the block and tackle is 90.0% efficient.

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