A man is attempting to raise a 7.5 m-long, 35 kg flagpole that has a hinge at the base by pulling on a rope attached to the top of the pole, as shown in the figure below.
With what force does the man have to pull on the rope to hold the pole motionless in this position?
The torque of this weight around the pivot is
τ = Frcosθ
F= 35kg x 9.8m/s/s
r=3.75m
θ= 30°
35kg x 9.8m/s/s x 3.75m x cos(30) = 1113.92
torque =1113.92 Nm clockwise
the torque due to the tension:
τ x 7.5 m x sin20
This must have the same magnitude as the torque due to the weight
1113.92 Nm = 7.5 sin(20)τ
=434 Nm
rounded would be
τ= 430 Nm
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