A traffic light hangs from a structure as shown in the figure. The uniform alumi

Question

A traffic light hangs from a structure as shown in the figure. The uniform aluminum pole AB is 8 m long and has a mass of 16.0 kg. The mass of the traffic light is 12.0 kg. CD is a steel cable with a round cross-sectional diameter of 1.0 cm. A steel pin with a round cross-sectional diameter of 0.5 cm holds the pivot in place at point A. Both cable CD and the bolt at point A must hold for this to be a safe and stable construction. Suggest a material that both these parts could be manufactured out of and back up your suggestion with computations that show the construction will be safe.

Answers-4.2 million Newtons per square meter and 22 million Newtons per square meter

Explanation / Answer

Given that

The mass of the traffic light (m) =12kg

Weight of the traffic light (WL) =mg =12*9.81 =117.72N

Mass of the pole is (M) =16kg

Then weight of the pole is (Wp) =mg =16*9.81 =156.96N

The acceleration due to gravity is (g) =9.81m/s2

Now applying the static equilibrium condition we get

sigmaTorque =0

(156.96)(4.00)sin53+(117.72N)(8.0)sin53-T(7.99)sin(37) =0

501.415+752.122-T(4.808)=0

T =260.719N

The horizontal component of force exerted at the pivot A on the aluminum pole is

Hcostheta =T =260.719N

now the vertical component of the force exerted by the pivot A on the aluminum pole is

Hsintheta =Wp+WL =117.72N+156.96N=274.68N

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