Holding Up Under Stress. A string or rope will break apart if it is placed under too much tensile stress [see Eq. (11.8)]. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7800 kg/m 3 and will break if the tensile stress exceeds 7.0 × 10 8 N/m 2 . You want to make a guitar string from 4.0 g of this type of steel. In use, the guitar siring must be able to withstand a tension of 900 N without breaking. Your job is to determine (a) the maximum length and minimum radius the string can have; (b) the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.
Holding Up Under Stress. A string or rope will break apart if it is placed under too much tensile stress [see Eq. (11.8)]. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7800 kg/m 3 and will break if the tensile stress exceeds 7.0 × 10 8 N/m 2 . You want to make a guitar string from 4.0 g of this type of steel. In use, the guitar siring must be able to withstand a tension of 900 N without breaking. Your job is to determine (a) the maximum length and minimum radius the string can have; (b) the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.
Holding Up Under Stress. A string or rope will break apart if it is placed under too much tensile stress [see Eq. (11.8)]. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7800 kg/m3 and will break if the tensile stress exceeds 7.0 × 108 N/m2. You want to make a guitar string from 4.0 g of this type of steel. In use, the guitar siring must be able to withstand a tension of 900 N without breaking. Your job is to determine (a) the maximum length and minimum radius the string can have; (b) the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.
A string or rope will break apart if it is placed under too much tensile stress. Thicker ropes can
withstand more tension without breaking because the thicker the rope, the greater the cross-sectional
area and the smaller the stress. One type of steel has density 7870 kg/m³ and will break if the
tensile stress exceeds 7.0 x 108 N/m². You want to make a guitar string from a mass of 4.5 g of
this type of steel. In use, the guitar string must be able to withstand a tension of 900 N without
breaking. Your job is the following.
Express your answer in meters.
L =
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Part B
Determine the minimum radius the string can have.
Express your answer in meters.
T=
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▼ Part C
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m
m
Determine the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.
Express your answer in hertzes.
ΜΕ ΑΣΦ
f =
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A 480 mm long thighbone (femur), which is the largest and longest bone in the human body, has a cross sectional area of 7.7 × 10–4 m2. A safety factor of 4 applies and the maximum compressional stress that a bone can withstand is 1.6 × 108 N/m2 before it breaks. Young’s Modulus (E ) of a bone at room temperature is 15 × 109 Pa. How much will it compress to support a weight of 1.2 × 105 N?
Human bones have a Young's modulus of 1.5 x 1010 Pa. The bone breaks if
stress exceeds 1.5 x 10° Pa. If, for example, a femur of length 25.31 cm
experiences this stress compressively, what will be the new length of the
bone?
Answer must be in cm and in two decimal places.
Chapter 15 Solutions
University Physics with Modern Physics Plus Mastering Physics with eText -- Access Card Package (14th Edition)
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