MECHANICS 1

1. Distance Travelled = area under graph
   1. Trapezium rule: Area = average parallel sides x height
      1. A = 1/2(a+b)h
   2. Objects meet when they have the same distance travelled

1. Ignore air resistance

1. s=displacement u=initial velocity v = final velocity a=acceleration t=time
2. v=u+at s=(u+v)t/2 v^2=u^2+2as s=ut+1/2at^2 s=vt-1/2at^2
3. State which way is positive

1. Conservation of momentum
   1. Momentum before = momentum after
      1. m1u1 + m2u2 = m1v1 + m1v1 + m2v2

1. = force x time
   1. Impulse = area under force - time graph
2. = final momentum - initial momentum
   1. =mv-mu
3. Newtons 3rd Law: Objects exert equal and opposite forces (and so impulse) on eachother

1. Strings
   1. One string: Tension equal
   2. Two separate strings: Tension different
   3. In-extensible
      1. Does not change length so accelerations and velocity of two particles attached are equal
   4. Becomes slack
      1. No tension so change in acceleration, must resolve again

1. Rods
   1. Uniform
      1. Weight acts at the centre of the rod
   2. Light
      1. Adds no weight to the system
   3. Straight and does not bend, all forces remain perpendicular

Annotations:

• u is Mue

1. In limiting equilibrium (on the point of movement), otherwise equal to or less than

1. No friction

1. 0 < u <1

1. R(^): R - mg

1. Component of F = Fcos0

   Annotations:

   • 0 is Theta