From c0d6190132205c59718ea50f8cccb241b5256434 Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Mon, 4 Oct 2021 10:43:27 +0100 Subject: [PATCH] Create notes on mmme1028 lectures L1.1, L1.2 --- ...ot-2021-10-04T09:14:41,378027532+01:00.png | Bin 0 -> 26775 bytes ...ot-2021-10-04T09:23:03,892292648+01:00.png | Bin 0 -> 218897 bytes ...ot-2021-10-04T09:41:56,080077960+01:00.png | Bin 0 -> 183962 bytes ...ot-2021-10-04T09:43:04,689667620+01:00.png | Bin 0 -> 40996 bytes ...ot-2021-10-04T09:44:05,581697277+01:00.png | Bin 0 -> 15155 bytes ...ot-2021-10-04T09:55:59,773394306+01:00.png | Bin 0 -> 41449 bytes .../mmme1028_l1.1_exercises_2021-09-30.pdf | Bin 0 -> 3836246 bytes .../mmme1028_l1.2_exercises_2021-10-04.pdf | Bin 0 -> 1429677 bytes .../mmme1028_statistics_and_dynamics.md | 140 ++++++++++++++++++ 9 files changed, 140 insertions(+) create mode 100644 mechanical/images/vimscrot-2021-10-04T09:14:41,378027532+01:00.png create mode 100644 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1.2 + +### Lecture 1.1 (L1.1) Exercises + +Can be found [here](./lecture_exercises/mmme1028_l1.1_exercises_2021-09-30.pdf). + +### Lecture 1.2 (L1.2) Exercises + +Can be found here [here](./lecture_exercises/mmme1028_l1.2_exercises_2021-10-04.pdf) + +## Newton's Laws + +1. Remains at constant velocity unless acted on by external force + +2. Sum of forces on body is equal to mass of body multiplied by + acceleration + + > 1st Law is a special case of 2nd + +3. When one body exerts a force on another, 2nd body exerts force + simultaneously of equal magnitude and opposite direction + +## Equilibrium + +- Body is in equilibrium if sum of all forces and moments acting on + body are 0 + +### Example + +Determine force $F$ and $x$ so that the body is in equilibrium. + +![](./images/vimscrot-2021-10-04T09:14:41,378027532+01:00.png) + +1. Check horizontal equilibrium + + $\sum{F_x} = 0$ + +2. Check vertical equilibrium + + $\sum{F_y} = 8 - 8 + F = 0$ + + $F = 2$ + +3. Take moments about any point + + $\sum{M(A)} = 8\times{}2 - F(2+x) = 0$ + + $F(2+x) = 16)$ + + $x = 6$ + +## Free Body Diagrams + +A free body diagram is a diagram of a single (free) body which shows all +the external forces acting on the body. + +Where there are several bodies or subcomponents interacting as a complex +system, each body is drawn separately: + +![](./images/vimscrot-2021-10-04T09:23:03,892292648+01:00.png) + +## Friction + +- Arises between rough surfaces and always acts at right angles to the + normal reaction force ($R$) in the direction to resist motion. +- The maximum value of friction $F$ is $F_{max} = \mu{}R$, where + $\mu{}$ is the friction coefficient +- $F_{max}$ is also known as the point of slip + +## Reactions at Supports + +There are three kinds of supports frequently encountered in engineering +problems: + +![](./images/vimscrot-2021-10-04T09:41:56,080077960+01:00.png) + +## Principle of Force Transmissibility + +A force can be move dalong line of action without affecting equilibrium +of the body which it acts on: + +![](./images/vimscrot-2021-10-04T09:43:04,689667620+01:00.png) + +This principle can be useful in determining moments. + +## Two-Force Bodies + +- If a body has only 2 forces, then the forces must be collinear, + equal, and opposite: + + ![](./images/vimscrot-2021-10-04T09:44:05,581697277+01:00.png) + + > The forces must be collinear so a moment is not created + +## Three-Force Bodies + +- If a body in equilibrium has only three forces acting on it, then + the lines of actions must go through one point: + + ![](./images/vimscrot-2021-10-04T09:55:59,773394306+01:00.png) + + > This is also to not create a moment + +- The forces must form a closed triangle ($\sum{F} = 0$) + +## Naming Conventions + +| Term | Meaning | +|----------------------|----------------------------------------------------------| +| light | no mass | +| heavy | body has mass | +| smooth | there is no friction | +| rough | contact has friction | +| at the point of slip | one tangential reaction is $F_{max}$ | +| roller | a support only creating normal reaction | +| rigid pin | a support only providing normal and tangential reactions | +| built-in | a support proviting two reaction components and a moment | + +## Tips to Solve (Difficult) Problems + +1. Make good quality clear and big sketches +2. Label all forces, dimensions, relevant points +3. Explain and show your thought process---write complete equations +4. Follow standard conventions in equations and sketches +5. Solve everything symbolically (algebraicly) until the end +6. Check your answers make sense +7. Don't forget the units

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