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Physics: Principles with Applications

Douglas C. Giancoli

Chapter 9

STATIC EQUILIBRIUM; ELASTICITY AND FRACTURE - all with Video Answers

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Chapter Questions

08:52

Problem 1

(I) Three forces are applied to a tree sapling, as shown in Fig. 9-46, to stabilize it. If $\overrightarrow{F}_A = 385 N$ and $\overrightarrow{F}_B = 475 N$, find $\overrightarrow{F}_C$ in magnitude and direction.
FIGURE 9–46 Problem 1. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
06:22

Problem 2

(I) Calculate the mass $m$ needed in order to suspend the leg shown in Fig. 9-47. Assume the leg (with cast) has a mass of 15.0 kg, and its $_{CG}$ is 35.0 cm from the hip joint; the cord holding the sling is 78.0 cm from the hip joint.
FIGURE 9–47 Problem 2. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
09:38

Problem 3

(I) A tower crane (Fig. 9-48a) must always be carefully balanced so that there is no net torque tending to tip it. A particular crane at a building site is about to lift a 2800-kg air-conditioning unit. The crane's dimensions are shown in Fig. 9-48b. $(a)$ Where must the crane's 9500-kg counterweight be placed when the load is lifted from the ground? (The counterweight is usually moved automatically via sensors and motors to precisely compensate for the load.) $(b)$ Determine the maximum load that can be lifted with this counterweight when it is placed at its full extent. Ignore the mass of the beam.
FIGURE 9–48 Problem 3. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
05:42

Problem 4

(I) What is the mass of the diver in Fig. 9-49 if she exerts a torque of $1800 m\cdot N$ on the board, relative to the left (A) support post?
FIGURE 9–49 Problems 4 and 5.(Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
08:37

Problem 5

(II) Calculate the forces $F_A$ and $F_B$ that the supports exert on the diving board of Fig. 9-49 when a 52-kg person stands at its tip. $(a)$ Ignore the weight of the board. $(b)$ Take into account the board's mass of 28 kg. Assume the board's $_{CG}$ is at its center.

Kebur Fantahun
Kebur Fantahun
Numerade Educator
08:13

Problem 6

(II) Figure 9-50 shows a pair of forceps used to hold a thin plastic rod firmly. If the thumb and finger each squeeze with a force $F_T = F_F = 11.0 N$, what force do the forceps jaws exert on the plastic rod?
FIGURE 9–50 Problem 6.(Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:25

Problem 7

(II) Two cords support a chandelier in the manner shown in Fig. 9-4 except that the upper cord makes an angle of 45$^{\circ}$ with the ceiling. If the cords can sustain a force of 1660 N without breaking, what is the maximum chandelier weight that can be supported?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
16:59

Problem 8

(II) The two trees in Fig. 9-51 are 6.6 m apart. A backpacker is trying to lift his pack out of the reach of bears. Calculate the magnitude of the force $\overrightarrow{F}$ that he must exert downward to hold a 19-kg backpack so that the rope sags at its midpoint by $(a)$ 1.5 m, $(b)$ 0.15 m.
FIGURE 9–51 Problems 8 and 70.(Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:46

Problem 9

(II) A 110-kg horizontal beam is supported at each end. A 320-kg piano rests a quarter of the way from one end. What is the vertical force on each of the supports?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
11:24

Problem 10

(II) Calculate $F_A$ and $F_B$ for the uniform cantilever shown in Fig. 9-9 whose mass is 1200 kg.

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:46

Problem 11

(II) A 75-kg adult sits at one end of a 9.0-m-long board. His 25-kg child sits on the other end. $(a)$ Where should the pivot be placed so that the board is balanced, ignoring the board's mass? $(b)$ Find the pivot point if the board is uniform and has a mass of 15 kg.

Kebur Fantahun
Kebur Fantahun
Numerade Educator
09:34

Problem 12

(II) Find the tension in the two cords shown in Fig. 9-52. Neglect the mass of the cords, and assume that the angle $\theta$ is 33$^{\circ}$ and the mass $m$ is 190 kg.
FIGURE 9–52 Problem 12. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:15

Problem 13

(II) Find the tension in the two wires supporting the traffic light shown in Fig. 9-53.
FIGURE 9–53 Problem 13. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
08:52

Problem 14

(II) How close to the edge of the 24.0-kg table shown in Fig. 9-54 can a 66.0-kg person sit without tipping it over?
FIGURE 9–54 Problem 14. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
03:13

Problem 15

(II) The force required to pull the cork out of the top of a wine bottle is in the range of 200 to 400N. What range of forces $F$ is required to open a wine bottle with the bottle opener shown in Fig. 9-55?
FIGURE 9–55 Problem 15. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
11:55

Problem 16

(II) Calculate $F_A$ and $F_B$ for the beam shown in Fig. 9-56. The downward forces represent the weights of machinery on the beam. Assume the beam is uniform and has a mass of 280 kg.
FIGURE 9–56 Problem 16. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
05:11

Problem 17

(II) Three children are trying to balance on a seesaw, which includes a fulcrum rock acting as a pivot at the center, and a very light board 3.2 m long (Fig. 9-57). Two playmates are already on either end. Boy A has a mass of 45 kg, and boy B a mass of 35 kg. Where should girl C, whose mass is 25 kg, place herself so as to balance the seesaw?
FIGURE 9–57 Problem 17. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
23:20

Problem 18

(II) A shop sign weighing 215 N hangs from the end of a uniform 155-N beam as shown in Fig. 9-58. Find the tension in the supporting wire (at 35.0$^{\circ}$), and the horizontal and vertical forces exerted by the hinge on the beam at the wall. [$Hint$: First draw a free-body diagram.]
FIGURE 9–58 Problem 18. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
23:40

Problem 19

(II) A traffic light hangs from a pole as shown in Fig. 9-59. The uniform aluminum pole AB is 7.20 m long and has a mass of 12.0 kg. The mass of the traffic light is 21.5 kg. Determine (a) the tension in the horizontal massless cable CD, and (b) the vertical and horizontal components of the force exerted by the pivot A on the aluminum pole.
FIGURE 9–59 Problem 19 (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
15:19

Problem 20

(II) A uniform steel beam has a mass of 940 kg. On it is resting half of an identical beam, as shown in Fig. 9-60. What is the vertical support force at each end?
FIGURE 9–60 Problem 20. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:00

Problem 21

(II) A 2500-kg trailer is attached to a stationary truck at point B, Fig. 9-61. Determine the normal force exerted by the road on the rear tires at A, and the vertical force exerted on the trailer by the support B.
FIGURE 9–61 Problem 21. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
22:40

Problem 22

(II) A 20.0-m-long uniform beam weighing 650 N rests on walls A and B, as shown in Fig. 9-62. (a) Find the maximum weight of a person who can walk to the extreme end D without tipping the beam. Find the forces that the walls A and B exert on the beam when the person is standing: (b) at D; (c) 2.0 m to the right of A.
FIGURE 9–62 Problem 22. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
07:05

Problem 23

(II) A 0.75-kg sheet is centered on a clothesline as shown in Fig. 9-63. The clothesline on either side of the hanging sheet makes an angle of 3.5$^{\circ}$ with the horizontal. Calculate the tension in the clothesline (ignore its mass) on either side of the sheet.Why is the tension so much greater than the weight of the sheet?
FIGURE 9–63 Problem 23. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
08:50

Problem 24

(II) A 172-cm-tall person lies on a light (massless) board which is supported by two scales, one under the top of her head and one beneath the bottom of her feet (Fig. 9-64). The two scales read, respectively, 35.1 and 31.6 kg. What distance is the center of gravity of this person from the bottom of her feet?
FIGURE 9–64 Problem 24. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
03:00

Problem 25

(II) A man doing push-ups pauses in the position shown in Fig. 9-65. His mass $m = 68 kg$. Determine the normal force exerted by the floor (a) on each hand; (b) on each foot.
FIGURE 9–65 Problem 25. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
09:48

Problem 26

(III) Two wires run from the top of a pole 2.6 m tall that supports a volleyball net. The two wires are anchored to the ground 2.0 m apart, and each is 2.0 m from the pole (Fig. 9-66). The tension in each wire is 115 N. What is the tension in the net, assumed horizontal and attached at the top of the pole?
FIGURE 9–66 Problem 26. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:30

Problem 27

(III) A uniform rod AB of length 5.0 m and mass $M = 3.8 kg$ is hinged at A and held in equilibrium by a light cord, as shown in Fig. 9-67. A load $W = 22 N$ hangs from the rod at a distance $d$ so that the tension in the cord is 85N. (a) Draw a free-body diagram for the rod. (b) Determine the vertical and horizontal forces on the rod exerted by the hinge. (c) Determine $d$ from the appropriate torque equation.
FIGURE 9–67 Problem 27. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
09:24

Problem 28

(III) You are on a pirate ship and being forced to walk the plank (Fig. 9-68). You are standing at the point marked C. The plank is nailed onto the deck at point A, and rests on the support 0.75 m away from A. The center of mass of the uniform plank is located at point B. Your mass is 65 kg and the mass of the plank is 45 kg. What is the minimum downward force the nails must exert on the plank to hold it in place?
FIGURE 9–68 Problem 28. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:01

Problem 29

(III) A door 2.30 m high and 1.30 m wide has a mass of 13.0 kg. A hinge 0.40 m from the top and another hinge 0.40 m from the bottom each support half the door's weight (Fig. 9-69). Assume that the center of gravity is at the geometrical center of the door, and determine the horizontal and vertical force components exerted by each hinge on the door.
FIGURE 9–69 Problem 29. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
14:59

Problem 30

(III) A uniform ladder of mass $m$ and length $\ell$ leans at an angle $\theta$ against a frictionless wall, Fig. 9-70. If the coefficient of static friction between the ladder and the ground is $\mu_s$, determine a formula for the minimum angle at which the ladder will not slip.
FIGURE 9–70 Problem 30. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
01:33

Problem 31

(I) Suppose the point of insertion of the biceps muscle into the lower arm shown in Fig. 9-13a (Example 9-8) is 6.0 cm instead of 5.0 cm; how much mass could the person hold with a muscle exertion of 450 N?

Supratim Pal
Supratim Pal
Numerade Educator
10:29

Problem 32

(I) Approximately what magnitude force, $F_M$, must the extensor muscle in the upper arm exert on the lower arm to hold a 7.3-kg shot put (Fig. 9-71)? Assume the lower arm has a mass of 2.3 kg and its $_{CG}$ is 12.0 cm from the elbow-joint pivot.
FIGURE 9–71 Problem 32. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:39

Problem 33

(II) Redo Example 9-9, assuming now that the person is less bent over so that the 30$^{\circ}$ in Fig. 9-14b is instead 45$^{\circ}$. What will be the magnitude of $F_V$ on the vertebra?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
12:37

Problem 34

(II) (a) Calculate the magnitude of the force, $F_M$, required of the "deltoid" muscle to hold up the outstretched arm shown in Fig. 9-72. The total mass of the arm is 3.3 kg. (b) Calculate the magnitude of the force $F_J$ exerted by the shoulder joint on the upper arm and the angle (to the horizontal) at which it acts.
FIGURE 9–72 Problems 34 and 35. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:04

Problem 35

(II) Suppose the hand in Problem 34 holds an 8.5-kg mass. What force, $F_M$, is required of the deltoid muscle, assuming the mass is 52 cm from the shoulder joint?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
04:04

Problem 36

(II) The Achilles tendon is attached to the rear of the foot as shown in Fig. 9-73. When a person elevates himself just barely off the floor on the "ball of one foot," estimate the tension $F_T$ in the Achilles tendon (pulling upward), and the (downward) force $F_B$ exerted by the lower leg bone on
the foot. Assume the person has a mass of 72 kg and $D$ is twice as long as $d$.
FIGURE 9–73 Problem 36. (Figure can't copy)

Vishal Gupta
Vishal Gupta
Numerade Educator
04:30

Problem 37

(II) If 25 kg is the maximum mass m that a person can hold in a hand when the arm is positioned with a 105$^{\circ}$ angle at the elbow as shown in Fig. 9-74, what is the maximum force $F_{max}$ that the biceps muscle exerts on the forearm? Assume the forearm and hand have a total mass of 2.0 kg with a $_{CG}$ that is 15 cm from the elbow, and that the biceps muscle attaches 5.0 cm from the elbow.
FIGURE 9–74 Problem 37. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
02:19

Problem 38

(II) The Leaning Tower of Pisa is 55 m tall and about 7.7 m in radius. The top is 4.5 m off center. Is the tower in stable equilibrium? If so, how much farther can it lean before it becomes unstable? Assume the tower is of uniform composition.

Suzanne W.
Suzanne W.
Numerade Educator
13:56

Problem 39

(III) Four bricks are to be stacked at the edge of a table, each brick overhanging the one below it, so that the top brick extends as far as possible beyond the edge of the table. (a) To achieve this, show that successive bricks must extend no more than (starting at the top) \(\frac{1}{2}\), \(\frac{1}{4}\), \(\frac{1}{6}\) and \(\frac{1}{8}\) of their length beyond the one below (Fig. 9-75a). (b) Is the top brick completely beyond the base? (c) Determine a general formula for the maximum total distance spanned by $n$ bricks if they are to remain stable. (d) A builder wants to construct a corbeled arch (Fig. 9-75b) based on the principle of stability discussed in (a) and (c) above.What minimum number of bricks, each 0.30 m long and uniform, is needed if the arch is to span 1.0 m?
FIGURE 9–75 Problem 39. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
08:22

Problem 40

(I) A nylon string on a tennis racket is under a tension of 275 N. If its diameter is 1.00 mm, by how much is it lengthened from its untensioned length of 30.0 cm?

Paul A.
Paul A.
California State Polytechnic University, Pomona
03:03

Problem 41

(I) A marble column of cross-sectional area $1.4 m^2$ supports a mass of 25,000 kg. (a) What is the stress within the column? (b) What is the strain?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
09:17

Problem 42

(I) By how much is the column in Problem 41 shortened if it is 8.6 m high?

Paul A.
Paul A.
California State Polytechnic University, Pomona
03:04

Problem 43

(I) A sign (mass 1700 kg) hangs from the bottom end of a vertical steel girder with a cross-sectional area of $0.012 m^2$. (a) What is the stress within the girder? (b) What is the strain on the girder? (c) If the girder is 9.50 m long, how much is it lengthened? (Ignore the mass of the girder itself.)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
08:24

Problem 44

(II) One liter of alcohol $(1000 cm^3)$ in a flexible container is carried to the bottom of the sea, where the pressure is $2.6 \times 10^6 N/m^2$. What will be its volume there?

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:42

Problem 45

(II) How much pressure is needed to compress the volume of an iron block by 0.10%? Express your answer in $N/m^2$, and compare it to atmospheric pressure $(1.0 \times 10^5 N/m^2)$.

Kebur Fantahun
Kebur Fantahun
Numerade Educator
09:48

Problem 46

(II) A 15-cm-long tendon was found to stretch 3.7 mm by a force of 13.4 N. The tendon was approximately round with an average diameter of 8.5 mm. Calculate Young's modulus of this tendon.

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:28

Problem 47

(II) A steel wire 2.3 mm in diameter stretches by 0.030% when a mass is suspended from it. How large is the mass?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
08:14

Problem 48

(II) At depths of 2000 m in the sea, the pressure is about 200 times atmospheric pressure (1 $atm = 1.0 \times 10^5 N/m^2$). By what percentage does the interior space of an iron bathysphere's volume change at this depth?

Paul A.
Paul A.
California State Polytechnic University, Pomona
09:14

Problem 49

(III) A scallop forces open its shell with an elastic material called abductin, whose Young's modulus is about $2.0 \times 10^6 N/m^2$. If this piece of abductin is 3.0 mm thick and has a cross-sectional area of $0.50 cm^2$, how much potential energy does it store when compressed 1.0 mm?

WA
Walter Allen
Numerade Educator
04:07

Problem 50

(I) The femur bone in the human leg has a minimum effective cross section of about $3.0 cm^2 (= 3.0 \times 10^{-4} m^2)$. How much compressive force can it withstand before breaking?

Paul A.
Paul A.
California State Polytechnic University, Pomona
05:02

Problem 51

(II) (a) What is the maximum tension possible in a 1.00-mm-diameter nylon tennis racket string? (b) If you want tighter strings, what do you do to prevent breakage: use thinner or thicker strings? Why? What causes strings to break when they are hit by the ball?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:09

Problem 52

(II) If a compressive force of $3.3 \times 10^4 N$ is exerted on the end of a 22-cm-long bone of cross-sectional area $3.6 cm^2$, (a) will the bone break, and (b) if not, by how much does it shorten?

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:18

Problem 53

(II) (a) What is the minimum cross-sectional area required of a vertical steel cable from which is suspended a 270-kg chandelier? Assume a safety factor of 7.0. (b) If the cable is 7.5 m long, how much does it elongate?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
17:15

Problem 54

(II) Assume the supports of the uniform cantilever shown in Fig. 9-76 $(m = 2900 kg)$ are made of wood. Calculate the minimum cross-sectional area required of each, assuming a safety factor of 9.0.
FIGURE 9–76 Problem 54. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:46

Problem 55

(II) An iron bolt is used to connect two iron plates together. The bolt must withstand shear forces up to about 3300 N. Calculate the minimum diameter for the bolt, based on a safety factor of 7.0.

Dading Chen
Dading Chen
Numerade Educator
10:25

Problem 56

(III) A steel cable is to support an elevator whose total (loaded) mass is not to exceed 3100 kg. If the maximum acceleration of the elevator is $1.8 m/s^2$, calculate the diameter of cable required. Assume a safety factor of 8.0.

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:51

Problem 57

(II) How high must a pointed arch be if it is to span a space 8.0 m wide and exert one-third the horizontal force at its base that a round arch would?

Keshav Singh
Keshav Singh
Numerade Educator
07:20

Problem 58

(II) The subterranean tension ring that exerts the balancing horizontal force on the abutments for the dome in Fig. 9-34 is 36-sided, so each segment makes a 10$^{\circ}$ angle with the adjacent one (Fig. 9-77). Calculate the tension $F$ that must exist in each segment so that the required force of $4.2 \times 10^5 N$ can be exerted at each corner (Example 9-13).
FIGURE 9–77 Problem 58. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
13:53

Problem 59

A woman holds a 2.0-m-long uniform 10.0-kg pole as shown in Fig. 9-78. (a) Determine the forces she must exert with each hand (magnitude and direction). To what position should she move her left hand so that neither hand has to exert a force greater than (b) 150 N? (c) 85N?
FIGURE 9–78 Problem 59. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
08:58

Problem 60

A cube of side $\ell$ rests on a rough floor. It is subjected to a steady horizontal pull $F$, exerted a distance $h$ above the floor as shown in Fig. 9-79. As $F$ is increased, the block will either begin to slide, or begin to tip over. Determine the coefficient of static friction $\mu_s$ so that (a) the block begins to slide rather than tip; (b) the block begins to tip. [$Hint$: Where will the normal force on the block act if it tips?]
FIGURE 9–79 Problem 60. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
07:17

Problem 61

A 50-story building is being planned. It is to be 180.0 m high with a base 46.0 m by 76.0 m. Its total mass will be about $1.8 \times 10^7 kg$, and its weight therefore about $1.8 \times 10^8 N$. Suppose a 200-km/h wind exerts a force of over the 76.0-m-wide face (Fig. 9-80). Calculate the torque about the potential pivot point, the rear edge of the building (where $\overrightarrow{F}_E$ acts in Fig. 9-80), and determine whether the building will topple. Assume the total force of the wind acts at the midpoint of the building's face, and that the building is not anchored in bedrock. [Hint: $\overrightarrow{F}_E$ in Fig. 9-80 represents the force that the Earth would exert on the building in the case where the building would just begin to tip.]
FIGURE 9-80 Forces on a building subjected to wind $\left(\overrightarrow{\mathbf{F}}_{\mathrm{A}}\right)$, gravity $(m \overrightarrow{\mathbf{g}})$, and the force $\overrightarrow{\mathbf{F}}_{\mathrm{E}}$ on the building due to the Earth if the building were just about to tip. Problem 61 . (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
07:43

Problem 62

The center of gravity of a loaded truck depends on how the truck is packed. If it is 4.0 m high and 2.4 m wide, and its $_{CG}$ is 2.2 m above the ground, how steep a slope can the truck be parked on without tipping over (Fig. 9-81)?
FIGURE 9–81 Problem 62. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
09:36

Problem 63

A uniform meter stick with a mass of 180 g is supported horizontally by two vertical strings, one at the 0-cm mark and the other at the 90-cm mark (Fig. 9-82). What is the tension in the string (a) at 0 cm? (b) at 90 cm?
FIGURE 9–82 Problem 63. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
13:13

Problem 64

There is a maximum height of a uniform vertical column made of any material that can support itself without buckling, and it is independent of the cross-sectional area (why?). Calculate this height for (a) steel (density $7.8 \times 10^3 kg/m^3$), and (b) granite (density $2.7 \times 10^3 kg/m^3$).

Paul A.
Paul A.
California State Polytechnic University, Pomona
08:07

Problem 65

When a mass of 25 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12$^{\circ}$ with the horizontal as shown in Fig. 9-83. Determine the radius of the wire.
FIGURE 9–83 Problem 65. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
15:14

Problem 66

A 65.0-kg painter is on a uniform 25-kg scaffold supported from above by ropes (Fig. 9-84). There is a 4.0-kg pail of paint to one side, as shown. Can the painter walk safely to both ends of the scaffold? If not,
which end(s) is dangerous, and how close to the end can he approach safely?
FIGURE 9–84 Problem 66. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
08:50

Problem 67

A 15.0-kg ball is supported from the ceiling by rope A. Rope B pulls downward and to the side on the ball. If the angle of A to the vertical is 22$^{\circ}$ and if B makes an angle of 53$^{\circ}$ to the vertical (Fig. 9-85), find the tensions in ropes A and B.
FIGURE 9–85 Problem 67. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
09:35

Problem 68

The roof over a 9.0-m $\times$ 10.0-m room in a school has a total mass of 13,600 kg. The roof is to be supported by vertical wooden $"2 \times 4s"$ (actually about $4.0cm \times 9.0cm$) equally spaced along the 10.0-m sides. How many supports are required on each side, and how far apart must they be? Consider only compression, and assume a safety factor of 12.

Paul A.
Paul A.
California State Polytechnic University, Pomona
05:28

Problem 69

A 25-kg object is being lifted by two people pulling on the ends of a 1.15-mm-diameter nylon cord that goes over two 3.00-m-high poles 4.0 m apart, as shown in Fig. 9-86. How high above the floor will the object be when the cord breaks?
FIGURE 9–86 Problem 69. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
13:43

Problem 70

A 23.0-kg backpack is suspended midway between two trees by a light cord as in Fig. 9-51. A bear grabs the backpack and pulls vertically downward with a constant force, so that each section of cord makes an angle of 27$^{\circ}$ below the horizontal. Initially, without the bear pulling, the angle was 15$^{\circ}$; the tension in the cord with the bear pulling is double what it was when he was not. Calculate the force the bear is exerting on the backpack.

Paul A.
Paul A.
California State Polytechnic University, Pomona
15:23

Problem 71

Two identical, uniform beams are symmetrically set up against each other (Fig. 9-87) on a floor with which they have a coefficient of friction $\mu_s = 0.50$. What is the minimum angle the beams can make with the floor and still not fall?
FIGURE 9–87 Problem 71. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
11:07

Problem 72

A steel rod of radius $R = 15 cm$ and length $\ell _0$ stands upright on a firm surface. A 65-kg man climbs atop the rod. (a) Determine the percent decrease in the rod's length. (b)When a metal is compressed, each atom moves closer to its neighboring atom by exactly the same fractional amount. If iron atoms in steel are normally $2.0 \times 10^{-10}m$ apart, by what distance did this interatomic spacing have to change in order to produce the normal force required to support the man? [$Note$: Neighboring atoms repel each other, and this repulsion accounts for the observed normal force.]

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:57

Problem 73

A home mechanic wants to raise the 280-kg engine out of a car. The plan is to stretch a rope vertically from the engine to a branch of a tree 6.0 m above, and back to the bumper (Fig. 9-88). When the mechanic climbs up a stepladder and pulls horizontally on the rope at its midpoint, the engine rises out of the car. (a) How much force must the mechanic exert to hold the engine 0.50 m above its normal position? (b) What is the system's mechanical advantage?
FIGURE 9–88 Problem 73. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
10:04

Problem 74

A 2.0-m-high box with a 1.0-m-square base is moved across a rough floor as in Fig. 9-89. The uniform box weighs 250 N and has a coefficient of static friction with the floor of 0.60. What minimum force must be exerted on the box to make it slide? What is the maximum height $h$ above the floor that this force can be applied without tipping the box over? Note that as the box tips, the normal force and the friction force will act at the lowest corner.
FIGURE 9–89 Problem 74. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
08:41

Problem 75

A tightly stretched horizontal "high wire" is 36 m long. It sags vertically 2.1 m when a 60.0-kg tightrope walker stands at its center. What is the tension in the wire? Is it possible to increase the tension in the wire so that there is no sag?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
11:32

Problem 76

Parachutists whose chutes have failed to open have been known to survive if they land in deep snow. Assume that a 75-kg parachutist hits the ground with an area of impact of $0.30 m^2$ at a velocity of 55 m/s, and that the ultimate strength of body tissue is $5 \times 10^5 N/m^2$. Assume that the person is brought to rest in 1.0 m of snow. Show that the person may escape serious injury.

Paul A.
Paul A.
California State Polytechnic University, Pomona
03:46

Problem 77

If the left vertical support column in Example 9-5 is made of steel, what is its cross-sectional area? Assume that a safety factor of 3 was used in its design to avoid fracture.

Kebur Fantahun
Kebur Fantahun
Numerade Educator
32:26

Problem 78

The mobile in Fig. 9-90 is in equilibrium. Object B has mass of 0.748 kg. Determine the masses of objects A, C, and D. (Neglect the weights of the crossbars.)
FIGURE 9–90 Problem 78. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:18

Problem 79

In a mountain-climbing technique called the "Tyrolean traverse," a rope is anchored on both ends (to rocks or strong trees) across a deep chasm, and then a climber traverses the rope while attached by a sling as in Fig. 9-91. This technique generates tremendous forces in the rope and anchors, so a
basic understanding of physics is crucial for safety. A typical climbing rope can undergo a tension force of perhaps 29 kN before breaking, and a "safety factor" of 10 is usually recommended. The length of rope used in the Tyrolean traverse must allow for some "sag" to remain in the recommended safety range. Consider a 75-kg climber at the center of a Tyrolean traverse, spanning a 25-m chasm. (a) To be within its recommended safety range, what minimum distance x must the rope sag? (b) If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in (a), determine the tension in the rope. Ignore stretching of the rope.Will the rope break?
FIGURE 9–91 Problem 79. (Figure can't copy)

Kebur Fantahun
Kebur Fantahun
Numerade Educator
13:42

Problem 80

When a wood shelf of mass 6.6 kg is fastened inside a slot in a vertical support as shown in Fig. 9-92, the support exerts a torque on the shelf. (a) Draw a free-body diagram for the shelf, assuming three vertical forces (two exerted by the support slot-explain why). Then calculate (b) the magnitudes of the three forces and (c) the torque exerted by the support (about the left end of the shelf).
FIGURE 9–92 Problem 80. (Figure can't copy)

Paul A.
Paul A.
California State Polytechnic University, Pomona
01:36

Problem 81

A cubic crate of side $s = 2.0 m$ is top-heavy: its $_{CG}$ is 18 cm above its true center. How steep an incline can the crate rest on without tipping over? [$Hint$: The normal force would act at the lowest corner.]

Massimo Antonelli
Massimo Antonelli
Numerade Educator