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momentofforces

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momentofforces

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  1. Find the tension T in each cable and the magnitude and direction of the force exerted on the strut by the pivot in each of the arrangements in Fig. below. In each case let w be the weight of the suspended crate full of priceless art objects. The strut is uniform and also has weight w. Start each case with a free-body diagram of the strut. • [ T = 2.60w , 3.28w, 37.60 ; T = 4.10w, 5.39w, 48.80 ]

  2. A museum of modem art is displaying an irregular 358-N sculptore by hanging it from two thin vertical wires, A and B, that are 1.25 m apart . The center of gravity of this piece of art is located 48.0 cm from its extreme right tip. Find the tension in each wire. • [ 66 N , 292 N ]

  3. A beam of mass M and length L is supported horizontally at its ends by two cables making angles θ and Φ with the horizontal ceiling. (a) Show that if the beam is uniform, these two angles must be equal and the tensions in the cables must also be equal. (b) Suppose now that the center of gravity is 3L/4 from the left end of the beam. Show that the angles are not completely independent but must obey the equation tan θ = 3 tan Φ.

  4. A uniform solid cylinder of mass M is supported on a ramp that rises at an angle θ above the horizontal by a wire that is wrapped around its rim and pulls on it tangentially parallel to the ramp. (a) Show that there must be friction on the surface for the cylinder to balance this way. (b) Show that the tension in the wire must be equal to the friction force, and find this tension. • [ (Mg/2) sin θ ]

  5. A uniform, 250-kg beam is supported by a cable connected to the ceiling, as shown in Fig. below. The lower end the beam rests on the floor. (a) What is the tension in the cable? (b) What is the minimum coefficient of static friction between the beam and the floor required for the beam to remain in this position? • [ 2700 N , 19 ]

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