Mechanics (M1) Mindmap

Created by: Keryn
Created on: 11-05-13 14:02

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M1 Revision Mindmap
- Kinematics
  - SUVAT
    - v=u+at
    - s=(u+v)/2 x t
    - s=ut+1/2 at^2
    - v^2=u^2+2as
    - State which direction is positive.
      - Take care with +ve's and -ve's
    - gravity= 9.8ms^2
    - Only use when a is constant.
  - Velocity-time graphs.
    - Slope= acceleration
    - Area= distance travelled.
      - If people meet they have travelled the same distance.
    - Can use SUVAT when acceleration is uniform.
- Statics
  - Forces.
    - 1N causes 1kg to accelerate at 1ms^2.
    - force = mass x acceleration
    - Weight is the force due to gravity / N.
    - Resultant forces
      - Resolve ^ and > then Pythagoras.
  - Forces on an inclined palne.
    - Resolve perpendicular and parallel to the plane.
    - Resolved component = fcosx
      - cos(90-x) = sinx
    - apply f=ma when moving, f=ur when in limiting equilibrium (point of moving).
- Dynamics
  - Momentum
    - Conservation of momentum: momentum before= momentum after
    - Impulse= final momentum -initial momentum
      - Ns
    - momentum= mass x velocity
      - Ns
  - Connected Particles.
    - Resolve in direction of motion.
      - accelerations and tensions are equal.
    - Consider each particle separately, unless towing.
    - If string becomes slack.
      - On inclined plane: no tension so accelerations different. Resolve ^ again.
      - Projectile - SUVAT.
- Moments
  - Resolve ^ or take moments (force x distance) about a point to eliminate a force.
  - May need simultaneous equations.
  - If rod is about to tiklt, one support force will be 0.
- Vectors
  - Have a magnitude and direction.
  - Are represented by a line showing its magnitude as length.
    - An arrow is also important to show the direction of the vector.
  - Notation
    - O->C= bold c underlined
    - Vector i =east, Vector j=north.
    - Subtraction rule: BC=OC-OB
    - Addition rule: OF+FG=OG
  - position vector at time t=(original position vector) + t (velocity vector)
    - collide if same position vector at same time.
    - speed= magnitude of velocity vector
      - Use Pythagoras.
    - Parallel
      - multiple, use k and find factor multiplied by. speed of 5->8=x1.6
    - bearing =SOH CAH TOA
- Assumptions
  - Pulley is smooth.
    - No friction therefore the tensions in all parts of the string are equal.
  - String is in-extensible.
    - The string doesn't change length so the accelerations and velocity of both particles are equal.
  - String/ pulley is light.
    - adds no weight to the system do acceleration is constant throughout the motion.
  - Surface is smooth.
    - No friction.
  - Air projectile q's.
    - Assume that acceleration due to gravity is 9.8. Must ignore air resistance.
  - Object is a particle.
    - No size so weight acts at one point only, also no air resistance.
  - Rod
    - Straight and doesn't bend, all forces remain perpendicular.
  - Uniform rod.
    - Weight acts at the centre of the rod.

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Mechanics (M1) Mindmap

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