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# Energy methods and static mechanics

## Gears in Automobiles

Gears are used in automobiles to move from the engine crankshaft to the driving wheel axle. They relay the motion from one end to the other. The gears of the automobile sector are used to slow down or speed up the motion of the cars. The mechanism entails the movement of moments and forces from one point to the other, as well as being accelerated and attenuated. Consider the gears below which shift the forces from the crankshaft to the axle of the driving wheels of the vehicle. The attenuation and amplification of the force transmitted from the crankshaft to the wheels are given by the radius ratio of the wheels, (Pratap & Ruina, 2001, p. 183).

## The balanced moments about An in diagram (d) gives

Taking moments about B in the second free body diagram gives

Simplifying the two equations together gives

If the is the input, the force is attenuated and the force is amplified if is the input. This system is useful in designing the gearbox of the vehicle in automobile engineering.

## Energy Methods

### Energy Flow in Diesel Engines

The combustion of fuel in the diesel engine converts the energy stored in the chemical bonds of the fuel into mechanical work and heat. The principle of conservation of energy as defined by the first law of thermodynamics says that when all the energy stored in the fuel is released during combustion in the cylinders of the engine, it does not disappear. The total amount of heat energy remains the same and, therefore, accountability for all the energy. For the diesel engine diagram below, the energy is converted to either heat (thermal energy) or work (mechanical energy) (Tatar & Oktay, 2011, p 315-332)

For example, for every 100 units of diesel burned in the engine, a total of 100 units of energy are produced in form of thermal energy and mechanical energy. The diagram below shows where the converted energy goes and this example, the engine is assumed to be operating in "steady state."

Therefore, the chemical energy stored in the fuel is converted to mechanical and thermal energy. The sum of thermal energy and mechanical energy is equal to the energy stored in the fuel, which is the first law of thermodynamics.

### The Second Law of Thermodynamics

The second law of thermodynamics applies to both the heat engine and the internal combustion engines that are used in motorcycles, cars, ships, etc. The combustion of fuel within the engine produces heat. Part of the generated heat inside the engine is used to do work of moving the piston in the cylinder of the engine, (Chris, 2016, n.a). The reciprocating action of the piston is turned into the rotating motion of the crankshaft. The rotating motion is then transmitted to the wheels through a system of gears. The other part of the generated heat is released into the atmosphere in the form of exhaust gases. For this case, the engine that generates the heat is called the source while the atmosphere to which the heat is released is the sink. According to the second law of thermodynamics, the higher the temperature, the difference between the source and the sink, the greater the efficiency of the combustion engine, (Chris, 2016, n.a).

The second law of thermodynamics can be applied to all engine cycles. Consider the Otto cycle.

From the above expressions, the diesel engine has high compression ratios thus the engine has higher efficiency.

## References

Tatar, E., and Oktay, M. (2011). The effectiveness of problem-based learning on teaching the first law of thermodynamics. Research in Science & Technological Education, 29(3), 315-332.

Pratap, R, and Ruina, A. (2001). Introduction to Statics and Dynamics. Oxford University Press. pg 183.

Chris Woodford. (2016). Heat Engines. Retrieved from http://www.explainthatstuff.com/engines.html