Concept explainers
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.
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
University Physics with Modern Physics (14th Edition)
Additional Science Textbook Solutions
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Introduction to Electrodynamics
College Physics: A Strategic Approach (3rd Edition)
College Physics (10th Edition)
Conceptual Physics (12th Edition)
Essential University Physics (3rd Edition)
- A copper rod with length 1.4 m and cross-sectional area 2.0 cm2 is fastened to a steel rod of length L and cross-sectional area 1.0 cm2. The compound structure is pulled on each side by two forces of equal magnitude 6.00 104 N (Fig. P14.57). Find the length L of the steel rod if the elongations (L) of the two rods are equal. Use the values Ysteel = 2.0 1011 Pa and YCu = 1.1 1011 Pa. FIGURE P14.57arrow_forwardThe lintel of prestressed reinforced concrete in Figure P12.27 is 1.50 m long. The concrete encloses one steel reinforcing rod with cross-sectional area 1.50 cm2. The rod joins two strong end plates. The cross-sectional area of the concrete perpendicular to the rod is 50.0 cm2. Youngs modulus for the concrete is 30.0 109 N/m2. After the concrete cures and the original tension T1 in the rod is released, the concrete is to be under compressive stress 8.00 106 N/m2. (a) By what distance will the rod compress the concrete when the original tension in the rod is released? (b) What is the new tension T2 in the rod? (c) The rod will then be how much longer than its unstressed length? (d) When the concrete was poured, the rod should have been stretched by what extension distance from its unstressed length? (e) Find the required original tension T1 in the rod. Figure P12.27arrow_forwardA horizontal, rigid bar of negligible weight is fixed against a vertical wall at one end and supported by a vertical string at the other end. The bar has a length of 50.0 cm and is used to support a hanging block of weight 400.0 N from a point 30.0 cm from the wall as shown in Figure P14.81. The string is made from a material with a tensile strength of 1.2 108 N/m2. Determine the largest diameter of the string for which it would still break. FIGURE P14.81arrow_forward
- Consider a nanotube with a Youngs modulus of 2.130 1012 N/m2 that experiences a tensile stress of 5.3 1010 N/m2. Steel has a Youngs modulus of about 2.000 1011 Pa. How much stress would cause a piece of steel to experience the same strain as the nanotube?arrow_forwardReview. On a day that the temperature is 20.0C, a concrete walk is poured in such a way that the ends of the walk are unable to move. Take Youngs modulus for concrete to be 7.00 109 N/m2 and the compressive strength to be 2.00 109 N/m2. (a) What is the stress in the cement on a hot day of 50.0C? (b) Does the concrete fracture?arrow_forwardA nanotube with a Youngs modulus of 1.000 1012 Pa is subjected to a stress of 3.14 1011 Pa by being pulled at its ends. Assuming the tube had an initial length of 8.12 106 m, what is the new length of the nanotube?arrow_forward
- A carbon nanotube is a nanometer-scale cylindrical tube composed of carbon atoms. One of its interesting properties is a very large Youngs modulus, measured to be more than 1.000 1012 N/m2. A tensile stress of 5.3 1010 N/m2 is exerted on a particular nanotube with a Youngs modulus measured at 2.130 1012 N/m2. Assuming the nanotube obeys Hookes law, by what percentage does the atomic spacing increase?arrow_forwardA steel rod 55 cm long has a diameter of 30.0 cm. The compressive strength (the maximum stress it can support without breaking) of this steel is 550.0 × 106 N/m2. What is the compression force that would break the rod? Answer in MN (meganewtons)arrow_forwardNylon strips are fused to glass plates. When moderately heated the nylon will become soft while the glass stays approximately rigid. Determine the average shear strain in the nylon due to the load P when the assembly deforms as indicated. 2 mm 3 mm 5 mm 3 mm 5 mm 3 mm 0.197 rad 0.297 rad O 0.397 rad O 0.125 rad O none of the abovearrow_forward
- A solid copper cube has an edge length of 89.8 cm. How much stress must be applied to the cube to reduce the edge length to 89 cm? The bulk modulus of copper is 1.4 x 1011 N/m². Number Unitsarrow_forwardA 50-N force is applied to a metal rod with a length of 10 m and a cross-sectional area of 1.0 x 10^(−5) m^2. Supposing that the shear modulus of the rod is 2.5 x 10^10 N/m^2, what would be the shear distance?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning