knowledge-6 FEM

• Scalar quantities only have magnitude
• Vector quantities have both magnitude and direction
• Vector addition (by calculation):

  to add two vectors , V1 and V2, at right angles to each other:

  1. sketch a right angled triangle formed by adding V1 and V2 , the resultant is the hypotenuse
  2. calculate magnitude of resultant by using Pythagoras theorem.
  3. calculate the angle between V1 and resultant using tan =V1/V2
• Vector addition ( by scale drawing):

  to add two or more vectors:

  1. choose an appropriate scale
  2. use a protractor and a ruler to draw the first vector to scale and in the correct direction.
  3. draw the next vector starting at the other end of the first vector
  4. repeat with other vectors
  5. draw a line straight from the start of the first vector to the end of the last vector.
  6. measure angle of resultant
  7. measure length of final line and use scale to determine magnitude.
• Resolving vectors:

  • horizontal = Vcos
  • vertical = Vsin
  • to resolve a vector:
  • sketch a right angled triangle where the vector is the hypotenuse and the perpendicular components form either side.
  • apply trigonometry to find value for each component.
• Conditions for equilibrium:

  An object at equilibrium is either at rest or moving with constant velocity.

  • the resultant force must be zero
  • the total clockwise moment must be equal to the anitclockwise point at any point.
• if an object in equilibrium has:

  • two forces acting on it , the force vectors will be equal in size and act in opposite directions.
  • three forces acting on it , adding the vectors will form a closed triangle when placed nose to tail.
• Centre of mass:

  the centre of mass of an object is the point which a single force has no turning effect when applied.
• An object will topple over if its line of action of its weight is outside its base.
• A distance-time graph shows how total distance travelled by an object changes with time
• A displacement time graph shows the same as a distance time graph but from a particular point and in a fixed direction.
• on a displacement time graph:

  • the gradient gives its velocity
  • a straight line with a constant gradient shows steady speed
  • a curved line shows acceleration
• Velocity time graph shows how an objects speed changes over time in a particular direction.
• on a velocity time graph:

  • the gradient of the line gives the objects acceleration
  • a straight line shows constant acceleration
  • horizontal line shows steady speed.
• acceleration time graphs show how acceleration changes with time.
• on a acceleration time graph:

  • the area under the line shows change in velocity
  • a value of zero shows an object is moving with constant velocity.
• Acceleration due to gravity:

  an object in free fall only has its weight acting on it , all objects in free fall accelerate at the same rate, regardless of their mass.
• Friction:

  is the force that opposes the relative motion between two surfaces in contact with each other, or an object moving through a fluid.
• Friction:

  • acts in the opposite direction to objects movement
  • increases with increasing viscosity of a liquid
  • increases with increasing speed of an object
  • depends on size and shape of an object
• streamlining an object reduces drag