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Presentation On The Mechanics

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Published in: Physics
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This presentation describes introduction to mechanics 1

Athumani R / Dubai

4 years of teaching experience

Qualification: Bachelor Of Pharmacy

Teaches: Others, Biology, Chemistry, Physics

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  1. MATHEMATICS FORM 5 MECHANICS 1
  2. MECHANICS 1 CONTENTS Mathematical Models in Mechanics *Constant Acceleration *Vector in Mechanics *Dynamic of Particle Moving in Straight line *Force and Friction *Momentum and Impulse
  3. Modelling Assumptions Modelling Assumptions can simplify a problem and allow you to analyze a real life situation using known mathematical techniques. • You need to understand the significance of different modelling assumptions and how they affect calculations in a particular problem.
  4. • Modelling assumptions can affect the validity of a model. For example, when modelling the landing of an aero plane flight, it would not be appropriate to ignore the effects of Wind and air resistance. •The following are models and their explanations as will be used in solving mechanics problems in Mathematics. •Understand each model and use it in solving the problems in Mechanics.
  5. Model Particle - Dimensions of the object are negligible. Rod - All dimensions but one are negligible, like a pole or a beam. Lamina - Object with area but negligible thickness, like a sheet of paper. Modelling assumptions mass of the object is concentrated at a single point rotational forces (i.e. moving around a central fixed point) and air resistance can be ignored mass is concentrated along a line no thickness rigid (does not bend or buckle) mass is distributed across a flat surface
  6. Uniform body - Mass is distributed evenly. Light object - Mass of the object is small compared to other masses, like a string or a pulley. Inextensible string- A string that does not stretch under load. mass of the object is concentrated at a single point at the geometric Centre of the body - the Centre of mass treat object as having zero mass tension the same at both ends of a light string acceleration is the same in objects connected by a taut inextensible string
  7. Smooth surface - a surface on which it can be assumed there is no friction. Rough surface - a surface on which there is friction. Wire - Rigid thin length of metal. assume that there is no friction between the surface and any object on it objects in contact with the surface experience a frictional force if they are moving, or are acted on by a force treated as one-dimensional
  8. Bead - Particle with a hole in it for threading on a wire or string (i.e. passing the wire or string through the hole). Peg- A support from which a body can be suspended or rested. pulley has no mass tension is the same on either side of the pulley a smooth bead moves freely along a wire or string for a smooth bead, tension is the same on either side of the bead dimensionless and fixed can be rough or smooth as specified in the question
  9. Air resistance - Resistance experienced ak ak object moves throug t e air. Gravity - Force of • g = 9.8 ms-z attraction between all objects. Acceleration due to gravity is denoted by g. • usually modelled as being negligible assume all objects with mass are attracted toward the Earth acceleration due to Earth's gravity is uniform (i.e. the same in all parts, at all times) and acts vertically downward g is constant and is taken as 9.8 m s-2, unless otherwise stated in the question
  10. Example A mass is attached to a length of string which is fixed to the ceiling. The mass is drawn to one side with the string stretched tightly and allowed to swing. State the effect of the following assumptions on any calculations made using this model. a. The string is light and inextensible (unable to be stretched further). b. The mass is modelled as a particle.
  11. Answers a. Ignore the mass of string and any stretching effect caused by mass. b. Ignore the rotational effect of any external forces that are acting on it, and effect of air resistance.
  12. Example 2 A football is kicked by the goalkeeper from one end of the football pitch. State the effect of the following assumptions on any calculations made using this model. a. The football is modelled as a particle. b. Air resistance is negligible.
  13. EXERCISE 1. An ice hockey puck is hit and slides across the ice. State the effect of the following assumptions on any calculations made using this model. a. The ice hockey puck is modelled as a particle. b. The ice is smooth. 2. A parachutist wants to model her descent from an aero plane to the ground. She models herself and her parachute as particles connected by a light inextensible string. Explain why this may not be a suitable modelling assumption for this situation.
  14. EXERCISE conts 3. A fishing rod manufacturer constructs a mathematical model to predict the behavior of a particular fishing rod. The fishing rod is modelled as a light rod. a. Describe the effects of this modelling assumption. b. Comment on its validity in this situation.
  15. Summary of key points 1. Mathematical models can be constructed to simulate real-life situations. 2. Modelling assumptions can be used to simplify your calculations.
  16. Next part Units and Quantities in Measurements Thank You My Friend See You In Next Part

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