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A 20.0-m tall hollow aluminum flagpole is equivalent in stiffness to a solid cylinder 4.00 cm in diameter. A strong wind bends the pole much as a horizontal force of 900 N exerted at the top would. How far to the side does the top of the pole flex?

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As an oil well is drilled, each new section of drill pipe supports its own weight and that of the pipe and drill bit beneath it. Calculate the stretch in a new 6.00 m length of steel pipe that supports 3.00 km of pipe having a mass of 20.0 kg/m and a 100-kg drill bit. The pipe is equivalent in stiffness to a solid cylinder 5.00 cm in diameter.

8.59 mm

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Calculate the force a piano tuner applies to stretch a steel piano wire 8.00 mm, if the wire is originally 0.850 mm in diameter and 1.35 m long.

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A vertebra is subjected to a shearing force of 500 N. Find the shear deformation, taking the vertebra to be a cylinder 3.00 cm high and 4.00 cm in diameter.

1 . 49 × 10 7 m size 12{1 "." "49" times "10" rSup { size 8{ - 7} } m} {}
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A disk between vertebrae in the spine is subjected to a shearing force of 600 N. Find its shear deformation, taking it to have the shear modulus of 1 × 10 9 N / m 2 size 12{5 "." "00" times "10" rSup { size 8{7} } N/m rSup { size 8{2} } } {} . The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter.

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When using a pencil eraser, you exert a vertical force of 6.00 N at a distance of 2.00 cm from the hardwood-eraser joint. The pencil is 6.00 mm in diameter and is held at an angle of 20.0º to the horizontal. (a) By how much does the wood flex perpendicular to its length? (b) How much is it compressed lengthwise?

(a) 3 . 99 × 10 7 m size 12{3 "." "99" times "10" rSup { size 8{ - 7} } m} {}

(b) 9 . 67 × 10 8 m size 12{9 "." "67" times "10" rSup { size 8{ - 8} } m} {}

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To consider the effect of wires hung on poles, we take data from [link] , in which tensions in wires supporting a traffic light were calculated. The left wire made an angle 30.0º below the horizontal with the top of its pole and carried a tension of 108 N. The 12.0 m tall hollow aluminum pole is equivalent in stiffness to a 4.50 cm diameter solid cylinder. (a) How far is it bent to the side? (b) By how much is it compressed?

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A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.2% (that is, Δ V / V 0 = 2 × 10 3 size 12{ΔV/V rSub { size 8{0} } =2 times "10" rSup { size 8{ - 3} } } {} ) relative to the space available. Calculate the magnitude of the normal force exerted by the juice per square centimeter if its bulk modulus is 1 . 8 × 10 9 N/m 2 size 12{1 "." 8 times "10" rSup { size 8{9} } `"N/m" rSup { size 8{2} } } {} , assuming the bottle does not break. In view of your answer, do you think the bottle will survive?

4 × 10 6 N/m 2 size 12{4 times "10" rSup { size 8{6} } `"N/m" rSup { size 8{2} } "." } {} . This is about 36 atm, greater than a typical jar can withstand.

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(a) When water freezes, its volume increases by 9.05% (that is, Δ V / V 0 = 9 . 05 × 10 2 size 12{ΔV/V rSub { size 8{0} } =9 "." "05" times "10" rSup { size 8{ - 2} } } {} ). What force per unit area is water capable of exerting on a container when it freezes? (It is acceptable to use the bulk modulus of water in this problem.) (b) Is it surprising that such forces can fracture engine blocks, boulders, and the like?

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This problem returns to the tightrope walker studied in [link] , who created a tension of 3 . 94 × 10 3 N size 12{3 "." "94" times "10" rSup { size 8{3} } } {} in a wire making an angle 5.0º below the horizontal with each supporting pole. Calculate how much this tension stretches the steel wire if it was originally 15 m long and 0.50 cm in diameter.

1.4 cm

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The pole in [link] is at a 90.0º bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is 4 . 00 × 10 4 N size 12{4 "." "00" times "10" rSup { size 8{4} } N} {} , at the angles shown. The pole is 15.0 m tall, has an 18.0 cm diameter, and can be considered to have half the stiffness of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of 30.0º with the vertical. (Clearly, the guy wire must be in the opposite direction of the bend.)

A telephone pole is located at a ninety degree bend in a power line. Each part of the line is at an angle of eighty degrees with the pole and has a tension labeled T. A guy wire is attached to the top of the pole at an angle of thirty degrees with the vertical.
This telephone pole is at a 90 º size 12{"90"°} {} bend in a power line. A guy wire is attached to the top of the pole at an angle of 30 º size 12{"30"°} {} with the vertical.
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Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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