Question 7.QE.1: Rank the magnitudes of the torques Suppose that five strings......

Rank the magnitudes of the torques

Suppose that five strings pull one at a time on a horizontal beam that can pivot about a pin through its left end, which is the axis of rotation. The magnitudes of the forces exerted by the strings on the beam are either T or T/2. Rank the magnitudes of the torques that the strings exert on the beam, listing the largest magnitude torque first and the  smallest magnitude torque last. Indicate if any torques have equal magnitudes. Try to answer the question before looking at the answer below.

Represent mathematically     A mathematical expression for the torque produced by each force is shown below. To understand why each torque is positive, imagine in what direction each string would turn the beam about the axis of rotation, if that were the only force exerted on it. You will see that each string tends to turn the beam counterclockwise (except string 5) .

\text { Torque due to string 1: } \tau_1=+T(l / 2) \sin 60^{\circ}=+0.43 \mathrm{Tl} \text {. }

\text { Torque due to string 2: } \tau_2=+T(l / 2) \sin 90^{\circ}=+0.50 \mathrm{Tl} \text {. }

\text { Torque due to string 3: } \tau_3=+T(l / 2) \sin 150^{\circ}=+0.25 \mathrm{Tl} \text {. }

\text { Torque due to string } 4: \tau_4=+(T / 2) l \sin 90^{\circ}=+0.50 \mathrm{Tl} \text {. }

\text { Torque due to string 5: } \tau_5=+T l \sin 0^{\circ}=0 \text {. }