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
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