You are designing an apparatus to support an actor of mass77.7kg who is to \"fly

Question

You are designing an apparatus to support an actor of mass77.7kg who is to "fly" down to the stage during the performance of a play. You attach the actor's harness to a133.8kg sandbag by means of a lightweight steel cable running smoothly over two frictionless pulleys as in the figure. You need5.0m 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?. What is the maximum value?can have before the sandbag lifts off the floor?

The director and his staff forget it is the body-double stuntman who is flying, not the actor. The stuntman's mass is20kg more than the actor. At the last second, you are asked to calculate how muchextramass,?Mto add to the sandbag in order to maintain the same maximum angle?.

You are designing an apparatus to support an actor of mass77.7kg who is to fly down to the stage during the performance of a play. You attach the actor's harness to a133.8kg sandbag by means of a lightweight steel cable running smoothly over two frictionless pulleys as in the figure. You need5.0m 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?. What is the maximum value?can have before the sandbag lifts off the floor? The director and his staff forget it is the body - double stuntman who is flying, not the actor. The stuntman's mass is20kg more than the actor. At the last second, you are asked to calculate how muchextramass,?Mto add to the sandbag in order to maintain the same maximum angle?. * just answer what is ?M

Explanation / Answer

By conservation of mechanical energy at the point where the actor is in the figure and at the bottom (WHen the tension in the rope will be max and sandbag will be most likely to lift off)

Ki + Ui = Kf + Uf
0 + mactor.g.yi = 1/2 mactor v2 + 0

also, yi = R - R cos

Using above 2 equations we get,

v2 = 2gR (1 - cos )

Now, as the actor moves in a circular arc he experiences a centripetal acceleration v2/R in upward direction

Using force equilibrium in y direction :

T - mactorg =  mactor v2/R

Also, T = mbagg

mbag g = mactorg + mactor (2gR (1 - cos ))/R

or, cos = [3 mactor - mbag ] / 2 mactor

or, cos = (3 x 77.7 - 133.8) / (2 x 77.7) = 0.6389

= 50.28 degree

Now, mst = 97.7 kg

mbag= 3 x mst - 2 x mst x cos = 168.258 kg

M = 168.258 kg - 133.8 kg = 34.45 kg

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.