141 lines
4.0 KiB
Markdown
Executable File
141 lines
4.0 KiB
Markdown
Executable File
---
|
|
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.
|
|
|
|
|
|
|
|
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:
|
|
|
|
|
|
|
|
## 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:
|
|
|
|
|
|
|
|
## Principle of Force Transmissibility
|
|
|
|
A force can be move dalong line of action without affecting equilibrium
|
|
of the body which it acts on:
|
|
|
|
|
|
|
|
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:
|
|
|
|
|
|
|
|
> 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:
|
|
|
|
|
|
|
|
> 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
|