The paper “ The Spring and Damper Mechanism as the Major Principle Applied in the Design of the Safety Apparatus” is an intriguing version of a lab report on engineering and construction. It is paramount to note that the energy equations shall be of great importance when calculating the potential energy that is contained in the spring coupled by the momentum to be applied to the moving mass. In accordance with Hooke’ s law, the elasticity of a material is directly proportional to the load applied to it. Therefore in this case: Where is the elongation or compression of the spring and is the spring constant.
Since there is a change in the elongation value, on integration: or, DampingDamping in a vibrational mechanism is usually achieved by the introduction of frictional forces which in turn transfer the motion away through intermolecular interactions. The damper is meant to absorb the force in order to slow down the moving mass on impact. For harmonic vibrations the energy equation is stated as: The frictional force acting on the damper shall be stated as: Where is the coefficient of damping? For all forces acting on a harmonic vibrating mass to balance, then: On differential simplification of the above equation: Breaking down the above equation, it is evident that angular frequency for un-damped vibration of a moving mass shall be: The expression for the damping ratio shall be expressed as: Apparatus DesignThe project design shall be based on the third law of Newton that relates to action-reaction.
In his definition, Newton stated that there is an equal to every action force exerted, but rather in the opposite direction. Where is the action force and is a reaction force that is equal but acting in the opposite direction?
Therefore, in the design of the system that is going to protect the mass from damaging, it is a requirement that these two forces be considered. For the sake of experimental setup, considering we have to protect as moving mass of 5,000 kilograms, then the safety apparatus’ threshold reaction force shall be, where is the top acceleration of the mass. For example, if the maximum acceleration of the mass such as a vehicle or a train is then the force shall be 50,000 Newton. The apparatus shall be set in such a way that it absorbs the shock on hard impact just the same as the shock absorbers are built.
This is based on the fact that the mass to be protected has to be equipped with proper safety apparatus to counter the reaction the damper and the spring should nullify the forces to be encountered. To illustrate this, the damper should possess the capability to damp up to the mass’ maximum attainable force of 50,000 Newton. Figure 2 below shows the suggested design setup of the safety apparatus to be used in absorbing the reaction energy as a result of a collision. Figure 2: Safety apparatus design. Experimental SetupThe experimental setup shall be entirely dependent on the pioneer spring-mass experiment as shown in figure 3 below.
The main aim of this experiment though shall be; to establish the perfect spring and damper types suitable for the kind of safety apparatus. The suitability of these gadgets should be in line with their ability to counter the reaction force.