Figure 8.5 (Example 8.3) (a) An actor uses some clever staging to make his entrance. (b) The free- body diagram for the actor at the bottom of the circular path. (c) Mactor Mbag Actor Sandbag Mactorg Mbagg The free-body diagram for the sandbag if the normal force from the floor goes to zero. b
You are part of the stage crew for a theatrical company and are designing an apparatus to support an actor of mass 65.0 kg who is to “fly” down to the stage during the performance of a play. You attach the actor’s harness to a 130-kg sandbag by means of a lightweight steel cable running smoothly over two frictionless pulleys as in 8.5a. You need 3.00 m of cable between the harness and the nearest pulley so that the pulley can be hidden behind a curtain. For the apparatus to work successfully, the sandbag must never lift above the floor as the actor swings from above the stage to the floor. Let us call the initial angle that the actor’s cable makes with the vertical θ. What is the maximum value θ can have before the sandbag lifts off the floor?
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