A traffic light consists of a horizontal member attached to a vertical support post. The horizontal member extends 7 m to the left of the support post and has a constant mass density of 15 kg/m. Each traffic light has mass of 10 kg, and the street sign has a mass of 4.5 kg. Make sure the connection between the horizontal member and the vertical support post is strong enough to withstand the forces exerted on the horizontal member. Calculate the effects of the forces resulting from the two traffic lights and the street sign on the horizontal member.

τ = 539 N m

Explanation:

Let's use the rotational equilibrium relationship, where we set our reference system at the junction of the poles and the counterclockwise rotations we consider positive

               τ = Σ τ_i

the mass of the traffic lights is m₁ = 10 kg, the mass of the sign m₂ = 4.5kg and suppose the worst case all the elements connected at the end (x = 7 m)

               τ = 2 m₁  x + m₂ x + m₃ x / 2

we calculate the mass of the horizontal pole using the concept of linear density

               λ = m₃ / l

               m₃ = λ l

we substitute

                τ = (2m₁ + m₂) x + λ l x / 2

                τ = x (2m₁ + m₂ +λ l / 2)

let's calculate

               τ = 7 (2 10 + 4.5 + 15 7/2)

               τ = 539 N m

therefore, this is the torque that the joint between the two posts must resist