Mechanics

Mechanics

Vectors & Scalars
1. Vectors
  1. Displacement
  2. Velocity
    1. The rate of change of displacement
    2. If a body is moving in a circular path with a constant speed, the velocity is NOT constant as the direction is changing
    3. Magnitude of velocity = magnitude of displacement / time
  3. Acceleration
    1. Rate of change of velocity
  4. Vectors have both magnitude and direction.
    1. The length of the line represents the magnitude
  5. Two vectors are only equal if they have the same magnitude and direction
  6. Momentum
    1. Mass x Velocity
2. Scalars
  1. Distance
  2. Speed
    1. Rate of change of distance
      1. Distance/time
    2. Speed = MAGNITUDE of velocity (in a straight line where distance=displacement)
    3. Instantaneous Speed = Magnitude of instantaneous velocity
  3. Mass
  4. Scalars have magnitude only
3. Addition and Components of Vectors
  1. Addition
    1. The resultant of two or more vectors is the single vector that produces the same effect (magnitude and direction).
    2. Parallelogram Rule
      1. A+B=R
  2. Components
    1. F can be resolved into two perpendicular vectors
Motion
1. Newton's Laws
  1. 1st Law
    1. Every body continues at a state of rest or of uniform (unaccelerated) motion unless acted on by an external force
  2. 2nd Law
    1. The acceleration of a body is directly proportional to the external force acting on the body and take place in the direction of the force
      1. F=ma
        The Newton (N) is defined as the force to accelerate a mass of 1kg at 1m/s^2
  3. 3rd Law
    1. If A exerts a force on B, then B exerts and equal and opposite force on A
2. SUVAT
  1. For constant velocity
    1. s=vt
  2. For constant acceleration
    1. v=u+at
    2. v^2=u^2+2as
    3. s=ut+½at^2
    4. s=½(u+v)t
3. D-T Graphs
  1. Gradient=velocity
4. V-T Graphs
  1. Gradient = Acceleration
  2. Area under graph = distance
5. Conservation of momentum
  1. The total linear momentum of a system of interacting (colliding) bodies, on which no external force is acting, remains constant
  2. If two bodies A and B collide they exert qual and opposite forces on each other (Newton's 3rd Law), and by Newton's 2nd Law each body experiences the same acceleration. As the changes are oppositely directed the total change in momentum is 0
6. Elastic Collision
  1. No loss of kinetic energy
7. Free Fall
  1. Galileo
    1. Dropped balls from the Leaning Tower of Piza to see acceleration during free fall
    2. He discovered that objects fall at the same speed regardless of their mass
  2. Aristotle
    1. Aristotle assumed that heavier objects would fall faster than lighter ones
  3. Weight = mass x acceleration in free fall (g)
    1. W = mg
Torque (Moments)
1. M = Fd
  1. M = Moment, F = magnitude of Force, d = perpendicular distance
2. Couples
  1. Two forces (equal in magnitude) which are antiparallel.
    1. Can only produce rotation, not translational motion
  2. Moment of couple = One force x separation of forces
3. Total clockwise moment = Total anticlockwise moment (in equilibrium)
Equilibrium, Centre of Mass and COG
1. Conditions for equilibrium
  1. A body is in equilibrium if:
    1. Acceleration on COM is 0 in all directions and angular acceleration is 0
      1. A body may still be moving, but with constant velocity and a constant angular velocity if rotating
    2. The resultant force on COM is 0 and the total torque is 0
2. Concurrent Forces = Forces where the lines of action meet at a single point
  1. Triangle of Forces
  2. Polygon of Forces
3. Types of Equilibrium
  1. Stable
    1. Returns to original position after a slight displacement
  2. Unstable
    1. After displacement, it does not return to its original position or stay in its displaced position
  3. Neutral
    1. A body stays in its displaced position after being displaced slightly
4. Centre of Mass
  1. The MASS of an object can be considered to act at a single point
  2. In a symmetrical and uniform body the COM is in the geometric centre
5. Centre of Gravity
  1. A point where the WEIGHT of a body is considered to act
  2. Can be found by hanging the object with a plumb line
6. Density = mass / volume
7. Pressure = force / area
8. Car Safety
  1. Stopping d = thinking d + braking d
    1. Affected by conditions, tyre tread etc.
  2. KE = braking force x braking distance
  3. Safety features
    1. Seat belts
      1. Seat belts are wide and soft, so produce less injury than hitting the windscreen
      2. Allows time for the airbag to inflate
    2. Crumple zones
      1. The crumple zones increases the distance the force is acting, so in sudden deceleration in a crash they decrease the force enough to save the passengers
    3. Airbags
      1. A flexible nylon bag, an accelerometer detects the crash and starts a chemical reaction, producing nitrogen to fill the airbag
  4. GPS
    1. Trilateration
      1. A satellite sends out a signal and it arrives after a known time at the GPS receiver then , given the speed of EM radiation, the distance of the receiver from the satellite can be found. The more satellites are used the more accurate the location is.
Work, Energy and Power
1. W=Fd
  1. Work done = force x distance moved
2. Force at angle to motion
  1. W = Fdcos(angle)
3. Kinetic energy = ½mv^2
4. GPE = mgh
  1. Therefore, Increase/decrease in GPE = mg(change in h)
5. Power = energy/time
  1. Power is the rate of doing work in Watts
6. A pendulum converts GPE into KE and back to GPE, until it stops as it loses energy in other forms (e.g. heat)
7. Sankey Diagrams
  1. Energy in = Energy out
8. Efficiency
  1. (Useful output energy / total input energy) x 100%
9. Deformation
  1. Elastic
    1. Returns to original state
  2. Plastic
    1. Permanently deformed
  3. Tensile (stretching) force
    1. Ultimate Tensile Strength
      1. The maximum amount of tensile force that can be applied to an object before it breaks
  4. Compressive (squashing) force
10. Hooke's Law
  1. F = kx
  2. Work done = ½kx^2
  3. E = ½Fx = ½kx^2
  4. After an object is stretched beyond its elastic limit it is plastically deformed
11. Young's Modulus
  1. Stress = Force / Area
    1. Ultimate Tensile Stress
      1. The maximum stress an object can take before it breaks
  2. Strain = Extension / Length
  3. Young's Modulus = Stress / Strain
  4. Ductile
    1. Drawn into wires
  5. Brittle
    1. Distort very little

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