# 1 Introduction In this course, we spend a large part of our time l...

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1 Introduction In this course, we spend a large part of our time learning how to analyze systems, both engineered and natural, with the principles of dynamics. The objects considered are in moest cases extracted from realistic situations with the purpose to provide a strong connection to actual engineering practice. Analyzing engineering problems requires more than just a mere knowledge of the physical and mathematical principles of mechanics, engineering students must also have the ability to visualize physical configurations in terms of resal materials, actual constraints, and the practical limitations which governs the behavior of machines and structures. In the course of the semester you will be conducting two engineering mechanics projects. The project report is due by the end of the last day of the semester. Your final report should: Include a title page with your name, the class, and date of submission. Be complete, clear, and include detailed answers to each design projects in separate pages Include appropriate organization and logical flow of information you will also be graded on the quality of the documentation - including drawings, programming, etc. 2 Design Project 1 The proposed design for an energy-absorbing bumper for a car (fig.1 exerts a force of magnitude bs + CU on the car when it collides with a rigid obstacle, where & is the distance the car travels from the point where it contacts the obestacle and v is the cars velocity. Thus the force exerted on the car by the bumper is a function of the car's position and velocity. 1. Suppose that at t = 0 the car contacts the obstacle with initial velocity Prove that the car's position is given a function of time by (1) where & = c/2m, h = /d² - b/m, and m is the mass of the car. 2. Investigate the effects of the car's mass, the initial velocity, and the constant 6 and c on the motion of the car when it strikes the obstacle. (Assume that d² > b/m.) Pay particular attention to how your choices for the constants 5 and e affect the maximum deceleration to which the occupants of the car would be subjected. Write a brief report presenting the results of your analysis and giving your conclusions concerning the design of energy-absorbing bumpers.

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