A.3 Two builders, both of mass m, have devised an unusual (and potentially dangerous)

scheme to lift themselves and a steel beam of mass M off the ground, using a rope and

pulley system as shown below. Assume the builders are positioned directly underneath

the pulleys, and the ropes are massless and inextensible. The system is in equilibrium,

and the ropes attached to the beam are at angle 9 to the vertical direction.

a. Draw free body diagrams for the forces acting (i) on one of the builders, and (ii) on

the beam. Clearly identify all forces.

b. Show that the normal contact force FN exerted by the beam on each builder is given

by

FN

mg cos 0 - Mg

1 + cos 0

c. What is the maximum beam mass M that the builders could pull up to a specific

angle 0?

d. One builder argues that to get higher, they would need to put the pulleys closer

together; the other argues they should be further apart. Which one is right? Explain

your reasoning.

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