Introduction to Mechanical Science

1. An internal combustion engine is an object which converts the chemical energy of the fuel into mechanical kinetic energy. Internal combustion engines have complex thermal cycles which convert this energy. Initially the fuel is burned which converts the chemical energy into thermal energy. The increase of thermal energy is equivalent to an increase in kinetic energy of the fuel and air mix particles. The thermal energy is used to move mechanical parts in the engine producing a useful work output, i.e. converting it to mechanical kinetic energy.
The most common internal combustion engine is seen in automobiles. The gasoline internal combustion engine works on the Otto Cycle which has four separate steps or strokes. First, during the intake stroke an air fuel mix is drawn into the cylinder. Next is the compression stroke where the fuel/air mixture is compressed and lit. The combustion stroke occurs as the fuel combusts and expands converting the chemical energy into thermal energy. This release of thermal energy in the expansion causes the piston to expand. The piston then returns to its compressed position exhausting the burned fuel/air mix. This process is then repeated (Logan 1999). The efficiency of converting chemical energy into work moving the pistons is called the thermal efficiency and for a standard petrol engines is around 38% (Hinrichs and Kleinbach 2002). This cycle can be seen in Figure 1.
The efficiency is low for various reasons. Energy is lost due to friction from the movement of the piston in its casing. In the engine there is only one working stroke where energy is produced. The other three strokes act to drawn in, compress and exhaust the mixture. The compression stroke alone requires considerable energy. Each of these stages requires energy from the fuel. This energy is lost as heat and sound energy from the casing of the engine and from the exhaust gases. Another major source of energy loss is the combustion stroke. When the fuel/air is lit the chemical energy is released as thermal energy (kinetic energy of the particles) which causes the gas to expand and thus work on the piston as kinetic energy. The temperature of the gas will not return to its initial temperature at the start of the stroke and so energy will be lost as heat through the engine and in the exhaust gases.
In a car these pistons provide rotational kinetic energy which can be used to drive the wheels. On contact with a frictional surface this kinetic energy will drive the car. Energy once again will be lost in the transmission of this power from the energy to the wheels. This is called mechanical efficiency and is the region of 50%. As the vehicle is in motion losses occur from rolling resistance and air drag. When the car is at a constant velocity all of the energy is lost as heat or sound from friction from the air and ground and the car will not accelerate further. Energy is also used in a car to run electrical accessories. The energy from the engine is transferred into electrical energy and used to power radios (sound energy), satellite navigation, power steering, traction control, air conditioning, electrical windows etc. Figure 2 shows how energy produced by the engine is distributed.
Internal combustion engines are seen in a whole range of transportation. Older and smaller planes use a gasoline based engine to provide kinetic energy for a propeller to propel the plane. Today planes usually run on gas turbine engines which are continuous internal combustion engines. Lorries and ships often run on diesel which is another form of internal combustion engine but acts on a different cycle to the 4 stroke gasoline engine. Lawnmowers and motorcycles use a two stroke gasoline engine. All these engines work on the same principle, converting the chemical energy of the fuel into thermal engine which then does mechanical work.
The internal combustion engine can be used in a combined heat and power system for home and large commercial building. The rotational kinetic energy of the pistons can be used to drive a generator to produce electricity. A generator converts mechanical energy into electrical energy using electro-magnetic induction. The internal combustion energy wastes a lot of energy in the form of heat. In a combined heat and power plant this excess heat can be used to heat water for heating and other home or business use. This system provides a use for the waste energy produced by the internal combustion engine and increases the efficiency of the unit from around 30-40% to well over 80% (EPA 2007).
2. When a ball is suspended in the air it has gravitational potential energy. This quantity is given by the product of the ball’s mass, the acceleration due to gravity and the height of the ball from the surface it is suspended above. As the ball is released and begins to fall this energy is transferred to kinetic energy. As the ball falls more potential energy is converted to kinetic energy and the ball’s velocity increases. When the ball has fallen to the surface all the potential energy has become transformed. Some energy is lost from air resistance and is dissipated as heat. If the height is great enough, terminal velocity can be reached where all of the potential energy is being converted to heat energy due to air friction. At this point the ball cannot accelerate further. When the ball hits the surface a force is exerted on it which changes its direction. Since neither the ball nor the surface are perfectly elastic, energy is lost in deforming the ball and the ground and is released as heat and sound. As the ball and ground are compressed the kinetic energy is converted to elastic potential energy. As the ball and ground expand again this energy is released as kinetic energy, which causes the ball to return upwards. As the ball rises the kinetic energy is transferred into potential energy. When all the kinetic energy turns to potential energy the ball stops moving, it has reached the maximum height for the bounce. Due to losses from air resistance and during contact with the ground this height is less than the initial height. The ball then begins downwards and the potential energy is once again converted to kinetic, repeating the cycle. With each successive bounce the maximum height of the ball decreases until eventually the ball no longer has enough energy to bounce and rests on the surface.
3. As a ball, m1 is travelling over a surface it has kinetic energy and a momentum given by the product of its mass and velocity. In a perfectly elastic collision when ball m1 strikes a stationary ball, m2 energy and momentum must be conserved. This collision however will be non-elastic and energy and momentum will be lost at contact in the form of heat and sound. In what proportions the mass and energy are transferred to each ball at contact depends upon their relative masses. Assuming similar masses, if the moving ball, m1 hits the other squarely then all of the energy and momentum will be transferred to the stationary ball, m2. Ball m2 will move off at a speed slightly lower than the velocity of the original ball. In a perfectly elastic collision ball m2’s velocity would be identical to the pre collision velocity of m1. After the collision the ball will slow down as energy is lost due to air and rolling resistance. If m1 strikes m2 at an angle then they will both move off in different directions that are perpendicular to each other. In this case only partial energy and momentum is transferred to the stationary ball. However the combined kinetic energies and momentums will add up to the initial pre-collision kinetic energy and momentum of the ball m1. The kinetic energy and momentum of m1 and m2 individually will depend on the angle of the collision. In all these cases, after the collision these balls will transfer their kinetic energy into energy lost through both air and rolling frictions as heat until they come to rest.