Create notes on mmme1028 lectures L1.1, L1.2

mechanical/mmme1028_statistics_and_dynamics.md

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+---
+author: Alvie Rahman
+date: \today
+tags:
+- uni
+- nottingham
+- mmme1028
+- maths
+- statics
+- dynamics
+title: MMME 1028 // Statics and Dynamics
+---
+
+# Lecture 1.1, 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