Table of Contents Lecture Topic Slides

Transcription

1 Mechanics 100

2 Table of Contents ecture Topic Slides 1 Fundamental Concepts Force Vectors Equilibrium Of Particles Force Resultants Equilibrium Of Rigid Bodies Structural Analysis Internal Forces: Truss Analysis Centre of Gravity and Centroid Stress Moments of Inertia

3 Fundamental Concepts ecture 1

4 Basic Quantities M ength (mm, cm, m) Used to locate the position of a point in space and to describe the size of a particle Mass (mg, g, Kg) A measure of a quantity of matter that is used to compare the action of one body with that of another T Time (s, hr) Conceived as a succession of events F Force (N) Considered as a push or pull exerted by one body on another; either through direct contact or through a distance

5 Dimensional Analysis Dimensions Properties which can be measured Units Standard elements used to quantify (show magnitude) of the dimensions Dimensional Analysis The analysis of the relationship between identified factors involved in a physical situation Only concerned with nature of dimensions not quantity Dimensional Homogeneity When dimensions on both sides of the equation have the same units Dimensionless Number A number which has no dimensions (Just a number) All numbers have no dimensions Dimensions cancel out to give a number F PA = F = 1 F.

6 Parameter Formula Dimensions S.I Unit Alternative Area Area = l w m Volume Volume = l w h m itres - Density Density = mass area M kg m Rho - ρ Velocity v = s t T m s ms Acceleration a = v u t T m s ms Force F = ma M T M T kg m s kg ms Newton - N Pressure P = F m F m M or T M T N kg m or s (s ) N ms or kg m s Pascal - P Energy Work E = W = Fs F or M T M T kg(m) s kg m s Jules - J Power P = E t = Fs t F T or M T T M T N m s or kg m s m s N ms or kg m s Watt - W Angle m m = 1 Radian - R

7 SI Units

8 Newton s Three aws of Motion First aw Inertia/Equilibrium F = 0 A particle originally at rest, or motion in a straight line with constant velocity, will remain in its state of motion provided that the particle is not subjected to an unbalanced force Second aw F = ma A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and magnitude that is directly proportional to the force Third aw Action Reaction The mutual forces of action and reaction between two particles are equal and opposite (and collinear). For every force applied (action) an equal and opposite force always appears (reaction)

9 Idealisation's (Assumptions) Particle - Negligible Mass and dimensions relative to the scale of motion Rigid Body Combination of a large number of particles which are at a fixed distance from each other. Dimensions are similar to the expected motion Concentrated Force Effect of a loading which is assumed to act at a point on a body

10 Prefixes

11 Procedure of Analysis 1. Read the question and determine what kind of question it is 2. Draw a free body diagram that illustrates the problem Show known and unknown (forces, dimensions, angles) Show axis direction (Positive/Negative direction) Draw it to scale (1cm = ) 3. If you need to make assumptions, indicate them 4. Determine what you need to find out 5. Work out what equation you will need to solve the problem 6. Check units, significant figures, logic (Does your answer seem right?)