3. A wire has a mass 5.3 g and length 2.50m. A force of 50 N can extend it by 2.3 mm.Determine(a) the Young's Modulus for the metal of the wire [ans: 6.9 × 101º Pa](b) the strain energy stored in the stretched wire [ans: 5.8 x 10-² J][Density of the metal of the wire = 2.7x10³ kg m³ 1

we know that density = mass/volume 2.7x103=5.3x10-3A x 2.5Area = A = 7.85 x10-7 m2

A wire has a mass 5.3 g and length 2.50m. A force of 50 N can extend it by 2.3 mm. Determine (a) the Young's Modulus for the metal of the wire [ans: 6.9 x 1010 Pa] (b) the strain energy stored in the stretched wire [ans: 5.8 × 10-² J] [Density of the metal of the wire = 2.7x103 kg m3 ]

A wire has a mass 5.3 g and length 2.50m. A force of 50 N can extend it by 2.3 mm. Determine (a) the Young's Modulus for the metal of the wire [ans: 6.9 x 1010 Pa] (b) the strain energy stored in the stretched wire [ans: 5.8 × 10-² J] [Density of the metal of the wire = 2.7x103 kg m3 ]

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 47PQ

See similar textbooks

Related questions

Q: 2 This is a stress-strain graph for a metal wire. 1.6 1.4 breaks 1.2 elastic limit 1.0 0.8 0.6 0.4…

Q: A solid copper cube has an edge length of 89.6 cm. How much stress must be applied to the cube to…

A: Write the given values with the suitable variables. Li=89.6 cmLf=89 cmk=1.4×1011 N/m2 Here, Li, Lf,…

Q: A steel wire of length 4.7 m and cross-sectional area 3.0 × 10-5 m2stretches by the same amount as a…

Q: 3 x 10, then find out the percentage change in its volume. is applied on it due to which it suffers…

A: Poisson's ratio is defined as the ratio between transverse strain and longitudinal strain.

Q: A metal rod is 4.00m long and has a cross-sectional area of 0.50cm^2. It stretches 0.20cm under a…

A: Given data: Original Length (L) = 4.00 m Cross section area (A) = 0.50 cm2 = 0.50×10-4 m2 Stretch…

Q: An aluminium wire, initially 2.45 m long and diameter of 1.5 mm, is suspended from a rigid support…

Q: A 0.800 m-long metal wire has a circular cross section of diameter 0.900 mm. One end of the wire is…

A: Given that, Length of the wire(L)= 0.8 m Diameter (d)= 0.9× 10-³ m So, radius (r)= (0.9×10-³)/2=…

Q: The figure represents an insect caught at the midpoint of a spider-web thread. The thread breaks…

A: Given,breaking stress of the string, 9.2 ×108 N/m2strain, 2.00lengthh of the thread, L = 3.0 cmcross…

Q: What is the pressure required to reduce the volume of a brass block by 10%?[Given the Bulk Modulus…

A: To solve the question we will use the formula: Bulk modulus, k=PdVV

Q: A 2 m long steel rod has a cross-sectional area of 0.3 cm?. The rod is a part of a vertical support…

A: The stress of the rod is given by F/A Strain is given by dL/L where F= Force…

Q: A copper wire of length 4.4 m, cross sectional area 2.8 x 10 m and Young's modulus 11 x 10-0 N/m2…

Q: A solid copper cube has an edge length of 89.6 cm. How much stress must be applied to the cube to…

Q: The steel rod with a diameter 15 mm is applied by a load of 15KN due to the load the diameter of the…

Q: A solid copper cube has an edge length of 89.3 cm. How much stress must be applied to the cube to…

Q: Human bones have a Young's modulus of 1.5 x 1010 Pa. The bone breaks if stress exceeds 1.5 x 10° Pa.…

Q: Calculate the strain of a brass rod of length 250 mm which is subjected to a tensile load of 50 kN…

A: Length , L = 250 mm Elongation , ∆L = 0.2 mm Load , F = 50 kN To find = Strain

Q: A metal wire 1.0 mm in diameter and 2.0 m long hangs vertically with a 6 kg mass suspended from it.…

Q: A wire of uniform cross sectional area of 0.25 mm2 is stretched at both ends by a total force of 65…

A: Given data The cross-sectional area is given as Ac = 0.25 mm2. The total force at both ends is…

Q: A 0.900 m-long metal wire has a circular cross section of diameter 0.950 mm. One end of the wire is…

A: Write the expression for young’s modulus.

Q: A 200-kg load is hung on a wire of length 4.00 m, cross-sectional area 0.200 x 10-4 m2, and Young's…

A: Given Data: Mass, Wire length, Cross-sectional area, Young’s modulus, Standard Data Used:…

Q: Due to loading, a line segment has length 2 m with consta normal strain 0.25. What is the original…

Q: An aluminum wire is 0.850 m long and has a circular cross section of diameter 0.780 mm. Fixed at the…

Q: A copper wire of length 7.9 m , cross sectional area 2 x 10-m²and Young's modulus 11 x 1010 N/m² has…

Q: Young's modulus of iron rod is 21 x 1010 N/m². A force of 7.0 × 105 N is applied to a 1.5-m length…

A: Youngs modulus = stressstrain=F/A∆L/L

Q: A system requires a metal component with the design specification that it not experience more than…

A: Given data: The stain is ε=0.1%=1×10-3 The range of the stress is σ=0,1000 kPa First, calculate…

Q: Find the minimum diameter of a (50 m)-long nylon string that will stretch no more than (1 cm) when a…

Q: 20. A 20 cm cylindrical brass rod with diameter 6 cm is held vertically on its one circular flat…

Q: A vertical steel girder with a crosssectional area of 0.15 m2 has a 1550 kg sign hanging from its…

Q: A 0.490-m-long guitar string, of cross-sectional area 1.00 x 10 ^-6 m^2, has Young's modulus Y =…

A: The elongation of the wire, using Hooke's law, ∆L=FLAY

Q: A hollow metal post is 10 ft long, and the cross-sectional area of the material is 2.5in² . When a…

A: Stress is defined as the force per unit area. Strain is defined as the ratio of change in…

Q: The base of an aluminum block, which is fixed in place, measures 10 cm by 10 cm, and the height of…

A: Given data: Dimensions of block is, 10 cm×10 cm. Height of block is, L=80 cm=0.8 m. Magnitude of…

Q: A 195-kg load is hung on a wire of length of 3.80 m, cross-sectional area 2.00 10-5 m2, and Young's…

A: According to stress by strain relation , stress is defined as the product of Young's modulus to the…

Q: an (1 cm) when a load of (70 kg) is suspended from its lower end. Assume that the Young modulus…

A: we know that γ = F/A△L/L L=50 m A= πR2 △L= 1X10-2 m γ= 3.51x 109 n/m2 let R=r min…

Q: A small steel cube (side length 2.54 cm) is being tested by subjecting it to compressive forces of…

Q: A solid copper cube has an edge length of 81.9 cm. How much stress must be applied to the cube to…

A: Given Initial length l1 = 81.9 cm = 0.819 m Final length l2 = 81 cm = 0.81 m Bulk modulus B =…

Q: A 1.0 x 10-3 kg spider is hanging vertically by a thread that has a Young’s modulus of 4.5 x 109 N/m…

Q: A 439 kg load is hung on a wire of length 9 m, cross-sectional area 0.200 x 10–4 m2, and Young's…

Q: The young's modulus of a material whose elastic strain and stress are 0.33 and 145.23 N/m?…

A: Given information: The strain in a material is, ε=0.33 The stress inside the material is, σ=145.23…

Q: A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 cm and…

Q: A solid copper cube has an edge length of 89.6 cm. How much stress must be applied to the cube to…

A: The stress that must be applied to the cube is 2.726 x 109 N/m2

Q: A copper wire of length 3-m and 1-mm diameter is subjected to a tension of 5-N. Calculate the…

A: Given: The length of the wire is 3 m. The diameter of the wire is 1 mm. The tenson in the wire is 5…

Q: A solid copper cube has an edge length of 85.3 cm. Ho w much st The bulk modulus of copper is 1.4x…

A: givenLi=85.3 cmLf=85 cmK=1.4×1011 N/m2

Q: A solid copper cube has an edge length of 88.3 cm. How much stress must be applied to the cube to…

Q: When water freezes, it expands by about 9.00%. What would be the pressure increase inside your…

A: Given ∆VV=0.09 Bulk modulus (B)=2.0*109 N/m2 Required ∆P=?

Concept explainers

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).

Question

3. A wire has a mass 5.3 g and length 2.50m. A force of 50 N can extend it by 2.3 mm.
Determine
(a) the Young's Modulus for the metal of the wire [ans: 6.9 × 101º Pa]
(b) the strain energy stored in the stretched wire [ans: 5.8 x 10-² J]
[Density of the metal of the wire = 2.7x10³ kg m³ 1

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

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 P14.57
Assume Youngs modulus for bone is 1.50 1010 N/m2. The bone breaks if stress greater than 1.50 108 N/m2 is imposed on it. (a) What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.50 cm? (b) If this much force is applied compressively, by how much does the 25.0-cm-long bone shorten?
The 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 P12.27
A high-speed lifting mechanism supports an 800.-kg object with a steel cable that is 25.0 m long and 4.00 cm2 in cross-sectional area. (a) Determine the elongation of the cable. (b) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 3.0 m/s2? (c) What is the greatest mass that can be accelerated upward at 3.0 m/s2 if the stress in the fable is not to exceed the elastic limit of the cable, which is 2.2 108 Pa?
Review. A wire of length L, Youngs modulus Y, and cross-sectional area A is stretched elastically by an amount L. By Hookes law, the restoring force is kL. (a) Show that k = YA/L. (b) Show that the work done in stretching the wire by an amount L is W=12YA(L)2/L.
A 100-N weight is attached to a free end of a metallic wire that hangs from the ceiling. When a second 100-N weight is added to the wire, it stretches 3.0 mm. The diameter and the length of the wire are 1.0 mm and2.0 m, respectively. What is Young’s modulus of the metal used to manufacture the wire?
Review. 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?
(a) When water freezes, its volume increases by 9.05% (that is, V/V0=9.05102 ). 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?
A company is testing a new material made of recycled plastic for use in construction. Figure P14.48 is a graph of the stress as a function of strain for this material. Find Youngs modulus for this material and compare your result with the data for conventional building materials listed in Table 14.1.
A high-speed lifting mechanism supports an 800.-kg object with a steel cable that is 25.0 m long and 4.00 cm2 in cross-sectional area. (a) Determine the elongation of the cable. (b) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 3.0 m/s2? (c) What is the greatest mass that can be accelerated upward at 3.0 m/s2 if the stress in the fable is not to exceed the elastic limit of the cable, which is 2.2 108 Pa?
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 1109 N /m2. The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter.
An aluminium (=2.7g/cm3) wire is suspended from the ceiling and hangs vertically. How long must the wire be before the stress at its upper end reaches the proportionality limit, which is 8.0107N/m2 ?