Physics in the context of MAE3 Machine Design and Analysis:List of Topics: Units: When to use what? Vectors decomposition Statics vs Dynamics Forces Torques/moments Energy Units: When to use what? Table of common units:
Use English for design. Why? Because all the materials and machines readily available in the United States are English. For example: The mills in the machine shop have English lead screws, so each rotation of the handle corresponds to .1 inches. Use Metric for analysis. Why? because metric system is the scientific measurement system. Analysis is MUCH easier. For example: English system often confuses with mass and weight. There are two types of "pounds", poundforce and poundmass. If you mistakenly use poundforce, your answer will be off by a factor of g = 32.2ft/s^2 Vector Decomposition: A vector is a mathematical representation of a magnitude and direction. Examples: Forces, velocities, accelerations, etc... Anything with a direction and an amount. Decomposition: We often strategically decompose vectors into the sum of vectors in order to simplify problems. The geometric decomposition of vectors is often called to as "tip to tail" method. Mathematical Decomposition: <3,4> = <3,0> + <0,4> =work in progress= Geometric Decomposition ("tip to tail"): *TIP TO TAIL EXAMPLE* Vectors The following vector combinations are equivalent: VECTOR IMAGE Common misconception: Tips and tails do not matter! Statics vs Dynamics Basics:
xtranslation: ΣF_{x} = ma_{x} ytranslation: ΣF_{y} = ma_{y} rotation: ΣM_{p }= Iα ΣF_{x} = 0 ΣF_{y} = 0 ΣM_{p }= 0 Quasi Static: Quasi means "seemingly". So what does "seemingly static" apply?
Dynamics: Dynamics occur when an object is in motion. An objects motion is described by the applied forces and its mass. Using the follow equations, we can calculate the motion of an object. ΣF_{x} = ma_{x} ΣF_{y} = ma_{y} ΣM_{p }= Iα Realizing that:
We can solve complicated dynamics problems using 2nd order differential equations. Solving the differential equations will give us the equations of motion of the object. This can be a very advanced topic and is taught in MAE3. Forces: Forces are always vectors applied at a location. It causes a tendency for an object to translate in space. Important: Forces are applied at a point Examples: Pushes, pulls, springs, gravity, etc... Moments (aka: Torques) A moment (synonymous with torques) is a 'force' that causes the object to rotate. Important: Moments are applied onto the entire body but always calculated relative to a point. Examples: motors, torsional springs, screwdrivers Torques dude to forces are calculated by: t=r*F where t=torque, r=length of moment arm, and F=perpendicular force component Common Mistakes:
Basic Force Balance Examples: For the following examples, solve for force F, such that the "seesaw" does not move, aka static. In order to solve all of these problems, the first thing to realize is that if the object in static equilibrium, it neither translates nor rotates. Thus, the sum of forces and sum of moments are equal to zero. Tips:
Example 1: Discussion: This example is so simple any kindergartner will tell you that F=3N using common sense and playground expertise. However, the proper way to solve this problem is to sum the moments about point P: ΣM_{p }= 3*3  3*F = 0 F = 3N Example 2: Discussion: This one is a bit more complicated. It is possible to solve this equation using intuition. However, using the moment balance equation will allow us to solve this problem systematically: ΣM_{p }= 2*3  4*F = 0 F = 1.5N Example 3: Discussion: It should be immediately apparent that this problem has the exact same solution as example 2. If it is not, the most common mistake people people make for this problem is to take the length of the moment arm to be 5m. The red line is not the correct moment arm! Example 4: Discussion: the moment arm can be visualized as: Example 5:Physics Fundamentals Refresher for MAE3MAE3 uses material from mechanics and statics that are covered in Physics 2A. Some review and refresher material includes:
