# 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.

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.