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Chapter 12: Equilibrium and Elasticity

Fundamentals Of Physics
Pages: 327 - 353

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98 Questions for Chapter 12: Equilibrium and Elasticity

  1. Figure 12-49ashows a vertical uniform beam of length Lthat is hinged at its lower end. A horizontal forceFa→ is applied tothe beam at distance yfrom the lower end. The beam remainsvertical because of a cable attached at the upper end, at angleθwith the horizontal. Figure12-49agives the tension Tin the cableas a function of the position of the applied force given as a fraction y/Lof the beam length. The scale of the Taxis is set byTs=600N.Figuregives the magnitude Fhof the horizontal force on thebeam from the hinge, also as a function of y/L. Evaluate (a) angleθand (b) the magnitude of Fa

    Found on Page 348
  2. In the Figure, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by AA=2AB; the Young’s moduli of the cylinders are related by EA=2EB. The cylinders had identical lengths before the brick was placed on them. What fraction of the brick’s mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are dA for cylinder A and dB for cylinder B. (c) What is the ratio dA/dB ?

    Found on Page 344
  3. Figure 12-57 shows an approximate plot of stress versus strain for a spider-web thread, out to the point of breaking at a strain of 0.200. The vertical axis scale is set by values a=0.12 GN/m2, b=0.30 GN/m2, and c=0.80 GN/m2 . Assume that the thread has an initial length of 0.80 cm, an initial cross-sectional area of 8.0x10-12 m2, and (during stretching) a constant volume. Assume also that when the single thread snares a flying insect, the insect’s kinetic energy is transferred to the stretching of the thread. (a) How much kinetic energy would put the thread on the verge of breaking? What is the kinetic energy of (b) a fruit fly of mass 6.00 mg and speed 1.70 m/s and (c) a bumble bee of mass 0.388 g and speed 0.420 m/s ? Would (d) the fruit fly and (e) the bumble bee break the thread?

    Found on Page 344
  4. A tunnel of length L=150 m, height H=7.2 m, and width 5.8 m (with a flat roof) is to be constructed at distance d=60 m beneath the ground. (See the Figure.) The tunnel roof is to be supported entirely by square steel columns, each with a cross-sectional area of 960 cm2. The mass of 1.0 cm3 of the ground material is 2.8 g. (a) What is the total weight of the ground material the columns must support? (b) How many columns are needed to keep the compressive stress on each column at one-half its ultimate strength?

    Found on Page 344
  5. In Fig. 12-60, a 103 kguniform log hangs by two steel wires, Aand B, both of radiuses 1.20 mm. Initially, wire Awas 2.50 mlong and 2.0 mmshorter than wire B. The log is now horizontal. What are the magnitudes of the forces on it from (a) wire Aand (b) wire B? (c) What is the ratio dA/dB?

    Found on Page 344
  6. Figure 12-23 shows a horizontal block that is suspended by two wires, Aand B, which are identical except for their original lengths. The center of mass of the block is closer to wire Bthan to wire A.

    Found on Page 344
  7. Question: Figure 12-29 shows a diver of weight 580 N standing at the end of a diving board with a length of L =4.5 mand negligible v mass. The board is fixed to two pedestals (supports) that are separated by distance d = 1 .5 m. Of the forces acting on the board, what are the (a) magnitude and (b) direction (up or down) of the force from the left pedestal and the (c) magnitude and (d) direction (up or down) of the force from the right pedestal? (e) Which pedestal (left or right) is being stretched, and (f) which pedestal is being compressed?

    Found on Page 346
  8. The table gives the initial lengths of three rods and the changes in their lengths when forces are applied to their ends to put them under strain. Rank the rods according to their strain, greatest first.

    Found on Page 344
  9. Question: In Fig 12-30, trying to get his car out of mud, a man ties one end of a rope around the front bumper and the other end tightly around a utility pole 18 maway. He then pushes sideways on the rope at its midpoint with a force of 550 N , displacing the center of the rope 0.30 m, but the car barely moves. What is the magnitude of the force on the car from the rope? (The rope stretches somewhat.)

    Found on Page 346
  10. A physical therapist gone wild has constructed the (stationary) assembly of massless pulleys and cords seen in Fig. 12-24. One long cord wraps around all the pulleys, and shorter cords suspend pulleys from the ceiling or weights from the pulleys. Except for one, the weights (in newtons) are indicated.

    Found on Page 344

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