The Claw

Length of the Pendulum
Trigonometry was used in order to calculate the unknown length of the arm of the claw.

tanθ = o/a tanθ = x/18 x = 18tan42° = 16.21m

Length of the pendulum
= 16.21 + 1.54
= 17.7m

Observation Point
Approximately 18 meters. Triangular device used to measure the angle of elevation to the centre axis of the claw - 42° angle.

It was estimated that the pendulum would be off the floor at the height of a person’s hip.

One of the class member height was measured to a total of 154cm, where the length from their toes to their hips were measured. – 0.7m

Total length of the pendulum
L = 17.7m
H = 0.7m

L + H = Total Length
17.7 – 0.7 = L
L = 17m

Total length of the pendulum equals to 17 metres.

Height of the claw at full swing

A

b
17m

a2 = b2 + c2 - 2bcCosA a2 = 172 + 27.152 – 2(17)(27.15)Cos60° = 289 + 737.12 – 923.1Cos60° = 564.57 a = √564.57 = 23.76m
60

C

120°

c
27.15

a

B

A pendulum which obeys simple harmonic motion will have a given period by T = 2π √l/g (where l is the length of the pendulum, and g standing for gravity).

g = 9.8 l = 17m t = 2π√l/g = 2π√17/9.8 = 1.73s

Acceleration (Pendulum)

v = u + at 6 = 0 + a (90) 6 – 0/90 = a a = 0.06 m/s2

Velocity (Pendulum)

2s/t – u = v 2 (270)/90 – 0 = v V = 6 m/s

Centripetal Force (Pendulum)

Fe = mv2/r = 72446.4(6)2/5.48 = 475925.25N

Net Acceleration
Centripetal Force + Gravity
= 475925.25 + 9.8
= 475935.05

Radius
D : R
L : l
R : r

15950 : 17

R/r = L/l
R/2 = 17/6.2
R = 17x 2/6.2
R = 5.48m

Weight

Weight of the claw
= 70000kg

Average Female
= 67kg
Estimate weight of passengers
Average Male
= 85.9kg

= 85.9 +67/2
=76.42

Average of genders x numbers of passengers
76.42 x 32
= 2446.4
Weight of passengers + the claw weight
70000 +2446.4
=72446.4
Total weight = 7244.4

Kinetic Energy
½ mv2
½ (72446.4) x 62
= 1304035.2 J

Potential Energy m x g x h
72446.4 x 9.8 x 17
= 12069570.24 J

The net force (Fnet) acting upon an object moving in circular motion is directed inwards. While there may be more than one force acting upon the object, the vector sum of them should add up to the net force.
Circular Motion

Fnet = m x (v2/r) = 700 x (62/5.718) = 440713.54N

Acceleration = 4 x π2 x r/t = 4 x π2 x 5.48/1.73 = 123.05 m/s2

Velocity = √ar v = √123.05 x 5.48 = 25.98 m/s