Forces and motion (3)

• Instantaneous speed is the speed of the object at a specific point of time. You draw a tangent then calculate the gradient

  
• The area under a velocity time graph is the displacement (from the area)
• Deriving v= u + at

  a = Δv/ Δt = v-u/t

  
• Deriving s=ut + 1/2at^2

  Displacement = area under graph so ut

  Displacement of triangle area 1/2 x (v-u) x t.

  (v-u) also = at so therefore when substituted in:

  s = ut + 1/2 at^2

  
• deriving the equation s = 1/2 (u +v)t

  If you treat the area under the graph as a trapezium (u and v being the parallel sides and t is distance between them)

  
• Deriving v^2 = u^2 +2as.

  T = (v-u) / a

  this can be substituted into s = 1/2 (u+v)t

  so s=1/2 (u+v) x (v-u)/a

  when rearranged (u+v)(v-u) = 2as

  v^2= u^2 + 2as.

  
• To determine G:

  plot a displacement t^2 graph

  use Suvat equation s= ut + 1/2at^2. Since we know u= 0 we can cancel that out so s= 1/2gt^2 (as g = a)
• Finding centre of gravity:

  Attach cork and pin onto the end of a clamp

  hole punch three holes into an irregular 2d shape

  put one of the holes through the pin and add a string with a mass weight on the end

  draw the cotton line’s direction

  see where they all cross over.

  
• Moment = the turning effect of a force around an axis. Moment = force x perpendicular distance from the axis. Moment = fx
• Principle of moments = the sum of the anti clockwise moments about a point is equal to the clockwise moments.
• Couple = 2 forces being applied in parallel along different lines.

  a good example for this is a bike pedal

  The moment of a couple is known as a torque. Torque of a couple = one of the forces x perpendicular separation between forces.

  
• Uncertanties:

  when adding or taking away simply add the uncertainties.

  when x or dividing, add the uncertainties.

  when There is a power, you times the uncertainty by the power.
• Moment = force x perpendicular distance from the line of action of the point of rotation