141 lines
4.0 KiB
Markdown
Executable File
141 lines
4.0 KiB
Markdown
Executable File
---
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author: Alvie Rahman
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date: \today
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tags:
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- uni
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- nottingham
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- mmme1028
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- maths
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- statics
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- dynamics
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title: MMME1028 // Statics and Dynamics
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---
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# Lecture L1.1, L1.2
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### Lecture L1.1 Exercises
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Can be found [here](./lecture_exercises/mmme1028_l1.1_exercises_2021-09-30.pdf).
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### Lecture L1.2 Exercises
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Can be found here [here](./lecture_exercises/mmme1028_l1.2_exercises_2021-10-04.pdf)
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## Newton's Laws
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1. Remains at constant velocity unless acted on by external force
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2. Sum of forces on body is equal to mass of body multiplied by
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acceleration
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> 1st Law is a special case of 2nd
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3. When one body exerts a force on another, 2nd body exerts force
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simultaneously of equal magnitude and opposite direction
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## Equilibrium
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- Body is in equilibrium if sum of all forces and moments acting on
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body are 0
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### Example
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Determine force $F$ and $x$ so that the body is in equilibrium.
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1. Check horizontal equilibrium
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$\sum{F_x} = 0$
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2. Check vertical equilibrium
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$\sum{F_y} = 8 - 8 + F = 0$
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$F = 2$
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3. Take moments about any point
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$\sum{M(A)} = 8\times{}2 - F(2+x) = 0$
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$F(2+x) = 16)$
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$x = 6$
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## Free Body Diagrams
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A free body diagram is a diagram of a single (free) body which shows all
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the external forces acting on the body.
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Where there are several bodies or subcomponents interacting as a complex
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system, each body is drawn separately:
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## Friction
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- Arises between rough surfaces and always acts at right angles to the
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normal reaction force ($R$) in the direction to resist motion.
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- The maximum value of friction $F$ is $F_{max} = \mu{}R$, where
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$\mu{}$ is the friction coefficient
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- $F_{max}$ is also known as the point of slip
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## Reactions at Supports
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There are three kinds of supports frequently encountered in engineering
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problems:
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## Principle of Force Transmissibility
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A force can be move dalong line of action without affecting equilibrium
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of the body which it acts on:
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This principle can be useful in determining moments.
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## Two-Force Bodies
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- If a body has only 2 forces, then the forces must be collinear,
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equal, and opposite:
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> The forces must be collinear so a moment is not created
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## Three-Force Bodies
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- If a body in equilibrium has only three forces acting on it, then
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the lines of actions must go through one point:
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> This is also to not create a moment
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- The forces must form a closed triangle ($\sum{F} = 0$)
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## Naming Conventions
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| Term | Meaning |
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|----------------------|----------------------------------------------------------|
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| light | no mass |
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| heavy | body has mass |
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| smooth | there is no friction |
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| rough | contact has friction |
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| at the point of slip | one tangential reaction is $F_{max}$ |
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| roller | a support only creating normal reaction |
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| rigid pin | a support only providing normal and tangential reactions |
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| built-in | a support proviting two reaction components and a moment |
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## Tips to Solve (Difficult) Problems
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1. Make good quality clear and big sketches
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2. Label all forces, dimensions, relevant points
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3. Explain and show your thought process---write complete equations
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4. Follow standard conventions in equations and sketches
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5. Solve everything symbolically (algebraicly) until the end
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6. Check your answers make sense
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7. Don't forget the units
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