3.4 Mechanics and Materials
3.4.1 Force, Energy and Momentum
3.4.1.1 Scalars and Vectors
A scalar quantity consists of only magnitude (eg speed). It is one-dimensional.
A vector quantity consists of both direction and magnitude (eg velocity). It is
two-dimensional.
Scalar Vector
Speed Velocity
Mass Momentum
Time Vector
Power Force
Energy Weight
3.4.1.2 Moments
F = f orce × perpendicular distance f rom pivot
Conditions for Equilibrium
● Sum of clockwise moments = sum of anticlockwise moments
● Sum of forces on system = 0 → forces in equilibrium
Classes of Lever
, Mechanical Advantage
● Load force ÷ Effort force
● Mechanical advantage of lever classes:
○ Class 1: Definable
○ Class 2: Always greater than 1
○ Class 2: Always less than 1
3.4.1.3 Motion Along a Straight Line
● s = displacement
● u = initial velocity
● v = final velocity
● a = acceleration
● t = time taken
3.4.1.4 Projectile Motion
Time of Flight
● Calculated from vertical component of velocity
● Calculate time to reach max height then double to get time of flight (time
of flight = up to max height then back down to ground)
● Max height at v = 0
● Calculate:
○ Initial speed vertically upwards = u sinθ
○ a = -g
○ Sub into v = u + at
0 = u sinθ − gt
u sinθ
t = g
2u sinθ
time of f light = 2t = g
3.4.1 Force, Energy and Momentum
3.4.1.1 Scalars and Vectors
A scalar quantity consists of only magnitude (eg speed). It is one-dimensional.
A vector quantity consists of both direction and magnitude (eg velocity). It is
two-dimensional.
Scalar Vector
Speed Velocity
Mass Momentum
Time Vector
Power Force
Energy Weight
3.4.1.2 Moments
F = f orce × perpendicular distance f rom pivot
Conditions for Equilibrium
● Sum of clockwise moments = sum of anticlockwise moments
● Sum of forces on system = 0 → forces in equilibrium
Classes of Lever
, Mechanical Advantage
● Load force ÷ Effort force
● Mechanical advantage of lever classes:
○ Class 1: Definable
○ Class 2: Always greater than 1
○ Class 2: Always less than 1
3.4.1.3 Motion Along a Straight Line
● s = displacement
● u = initial velocity
● v = final velocity
● a = acceleration
● t = time taken
3.4.1.4 Projectile Motion
Time of Flight
● Calculated from vertical component of velocity
● Calculate time to reach max height then double to get time of flight (time
of flight = up to max height then back down to ground)
● Max height at v = 0
● Calculate:
○ Initial speed vertically upwards = u sinθ
○ a = -g
○ Sub into v = u + at
0 = u sinθ − gt
u sinθ
t = g
2u sinθ
time of f light = 2t = g
