Question

Calculate the torques about pivot P provided by the forces shown in the Figure 3, if L = 4.5 m

Answer 1

The definition of torque of a force we can find the total torque on the bar is

           τ = 246.2 N m

The torque of a force is defined by the relation

         τ = F x r

where the bold letters indicate vectors, τ is the torque, f the force, and r the distance from the pivot point.

We can calculate the magnitude of this expression

       τ = F r sin θ

where in the angle between the forces and the candidate

In this case, we have five forces

• the force at point P does not create torque since its distance is zero.

• The force applied to the end of the bar, the angle is zero and the sine value zero.

The other forces create a torque:

F₁ =   80 N, the distance is x₁ = 0.5L,  θ₁ = 37º

F₂ = -60 N, the distance is x₂ = 0.5L, angle θ = 90º

F₃ =  70 N the distance is x₃ = L, angles θ = 30º

with respect to the vertical, this angle with respect to the horizontal is

         θ’ = θ + 90

         θ‘ = 30+ 90

         θ₃' = 120º

substitute

         τ = F₁ x₁ sin θ₁ + F₂ x₂ sin θ₂ + F₃ x₃ sin  θ₃'

let's calculate

          τ = 80 0.5L sin 37 - 60 0.5L sin 90 + 70 L sin 120

          τ = 54.7L

indicate that the length of the bar is L + 4.5 m

           τ = 54.7  4.5

           τ = 246.2 Nm

Using the defined torque we can find the total torque on the bar is

           τ = 246.2 N m

Learn more about torque here:

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