mechanical/mmme1028_statistics_and_dynamics.md

@@ -1,140 +0,0 @@
----
-author: Alvie Rahman
-date: \today
-tags:
-- uni
-- nottingham
-- mmme1028
-- maths
-- statics
-- dynamics
-title: MMME 1028 // Statics and Dynamics
----
-
-# Lecture L1.1, L1.2
-
-### Lecture L1.1 Exercises
-
-Can be found [here](./lecture_exercises/mmme1028_l1.1_exercises_2021-09-30.pdf).
-
-### Lecture 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