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Question

A new art exhibit featuring mobile works is going up in the Holland, MI, area. One piece is shown in the figure. The 111 N uniform beam has a length of 1.6 m and is pinned to the ground by a pivot. The beam is supported by a cable (attached to the center of the beam) to allow for each of the shoes to hang freely. Each individual shoe has a weight of 11 N. One of the shoes is attached two-fifths of the way along the beam, and the other is attached three-fifths of the way along the beam. The angle the cable makes with the ground is θc = 17∘, and the angle the beam makes with the ground is θb = 31∘.

a) What is the magnitude of tension in the cable, in N?

b) What is the horizontal component of the force at the pivot, in N? Use the coordinate system given in the figure.

c) What is the vertical component of the force at the pivot, in N? Use the coordinate system given in the figure.

The figure: https:// usb06ca.theexpertta.com/images/kyh42kdg.kso.png

Answer 1

General approach works for any number of masses m_i attached to an angled beam (θ₁) of mass m and length L at distances d_i supported by a cable with tension T at a shallower angle (θ₂) attached at distance d.

Balance torque with Tdsin(θ₁-θ₂) = (m L/2 + m₁d₁+ m₂d₂+....)gcos(θ₁) and solve for T. To solve for the forces at the pivot point just balance the vertical and horizontal forces (will need to decompose T into horizontal and vertical components first) and solve for the one missing force in each equation.