A wire of length L, Young’s modulus Y, and crosssectional area A is stretched elastically by an amount ΔL. By Hooke’s law, the restoring force is -k ΔL. (a) Show that k = YA/L. (b) Show that the work done in stretching the wire byan amount ΔL is W = 1/2 YA(ΔL)2/L .

A wire of length L, Young’s modulus Y, and crosssectional area A is stretched elastically by an amount ΔL. By Hooke’s law, the restoring force is -k ΔL. (a) Show that k = YA/L. (b) Show that the work done in stretching the wire byan amount ΔL is W = 1/2 YA(ΔL)2/L .

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter12: Static Equilibrium And Elasticity

Section: Chapter Questions

Problem 68P: An aluminium (=2.7g/cm3) wire is suspended from the ceiling and hangs vertically. How long must the...

See similar textbooks

Related questions

Q: Tensile load of 2 MN is applied to an Aluminium cord with original diameter of 5 mm, the measured…

A: Given: Tensile load, F = 2MN = 2 x 106 N Diameter of rod = d = 5 mm = 5 x 10-3 m Length stretched =…

Q: 50. The work done in stretching an elastic string of natural length 5 m and modulus of elasticity…

A: Work done is the difference of elastic potential energy stored in form of elastic potential energy…

Q: steel cable with a cross-sectional area of 3.00 cm^2 has an elastic limit of 2.40x10^8 Pa. Find the…

Q: Draw the shear and moment diagram for the beam shown and find the maximum moment. 7N A B, C 6m 4m

Q: A bar ACB has is subjected to an external load at C, and it is supported either end by a cable as…

A: We need to calculate the smallest area of cross section possible for the two cables at the end of…

Q: One end of a steel wire of length 0.2 m and radius 2 x 10-m is fixed. If the work done in wisting…

Q: For an elastic wire under tension there is, under certain conditions, a simple rela- tion between…

A: Tension = tension is produced in body due to internal molecule when we applied a external force on…

Q: A specimen of aluminum having a rectangular cross section 10 mm x 12.7 mm. is pulled in tension with…

A: Given data: Rectangular cross section = 10 mm × 12.7 mm Force (F) = 35,500 N The modulus of…

Q: Without fracture of the Femur, determine the maximum height, in cm, from which a 70-kg woman can…

Q: Two wires are made of the same material, their Young’s Modulus constant is 10 x10^10 Pa. Wire X is 4…

A: Given: Two wires are X & Y. Young's modulus constant, γ=10×1010 Pa Considered wire Y length be…

Q: Two violin strings have the same length, tied down at both ends, and are stretched with the same…

A: Speed of wave in string = ( T/μ)1/2 μ = mass per unit lengh Since μ is different so wave speed will…

Q: A basket of negligible weight hangs from a vertical spring scale of force constant 1500 N/m. (a) If…

A: Given data The force constant is k=1500 N/m The mass is m=3.0 kg The height is d=1.0 m (a)…

Q: The stress - strain relationship become nonlinear in the elastic region. O True O False O O

Q: A 15 cm long animal tendon ( وتر ) was found to stretch 3.7 mm by a force of 13.4 N. The tendon was…

A: Given: length of animal lo=15 cm =150 mm force F=13.4 N Diameter=D =…

Q: What is maximum diameter of brass rod if it has to support a 400N load without exceeding its elastic…

A: Let Y be the stress on the brass rod, F be the load, A be the cross-sectional area, and D be the…

Q: е. The elastic limit of a steel elevator cable is 275 MPa. What is the maximum upward acceleration…

Q: A metal has a flexural stress of 564 Pa. The W is measured to be 1 meter, while the load was 10 N.…

A: Given data: The flexural stress is σf=564 Pa. The width of beam is w=1 m. The applied load is P=10…

Q: nal area of 3.00cm2 has an elastic limit of 2.40x108 Pa. Find the maximum upward acceleration that…

A: Given-Cross-sectional area A= 3.00cm2=3×10-4 m2Force is perpendicular to the cross-section of the…

Q: In normal motion, the load exerted on the hip joint is 2.5 times body weight. (a) Calculate the…

Q: Determine the strain if a rod is experiencing a stress of 70,000 kPa with a modulus of elasticity of…

A: Given: The stress is 70000 kPa. The modulus of elasticity is 175 GPa.

Q: Bar AB of Fig. with weight W and length L has a uniform cross section. Rotation of the bar is…

Q: The stress-strain curve during elastic deformation is non-linear. Is this true or false?

A: When a material is elastically deformed its stress-strain curve is linear in nature till the elastic…

Q: The figure shows an approximate plot of stress versus strain for a spider-web thread, out to the…

A: We have, stress=forcearea and strain=change in lengthoriginal lengthHence, work…

Q: Hooke's Law may also be stated in the same relation as Young's Modulus where "the strain in a solid…

A: Hooke's law is define as that the strain in a solid body is directly proportional to the applied…

Q: The bulk modulus of K, modulus of elasticity E and Poisson's ratio is then which of m the following…

A: The relation between the bulk modulus(K), modulus of Elasticity(E) and the Poisson's ratio(ν) is…

Q: The plot of tensile stress vs tensile strain of a certain rod has a slope of 25-GPa in the elastic…

Q: What is the Young's modulus (in N/m2) for this material? On a graph with a starting point of (0,0) a…

A: Young's modulus = stress÷strain Young's modulus = slope of stress-strain curve. Coordinates of curve…

Q: Consider a structure including the horizontal beam AB hinged to the wall at point A and supported by…

A: According to our policies, I can answer only first three subparts of this problem. The detailed…

Q: A 15 cm long animal tendon was found to stretch 3.7 mm by a force of 13.4 N. The tendon was…

A: Given : Lo = 15 cm = 0.15 m ∆L = 3.7 mm = 3.7 x 10-3 m F = 13.4 N d = 8.5 mm = 8.5 x 10-3 m

Q: When a tensile load (F) is applied to a solid homogeneous rod, the rod undergoes a change in length…

A: Required : Alternate expression for the strain energy.

Q: the point that identifies the proportional limit of the material whosee graph of stress as a…

Q: Find the modulus of elasticity of a brass rod of cross section 20 mm x 20 mm, and length 248 mm…

A: Tensile load(T)= 50 KN Elongation (e)= 0.25 mm = 2.5× 10-⁴ m Length of the rod(L)= 248 mm= 0.248 m…

Q: Two wires are made of the same material, their Young’s Modulus constant is 10 x10^10 Pa. Wire X is 5…

Q: The ratio of stress to strain (o-4 / ɛ ) in the linear elastic region is . . called Young's

A: Y = streas/strain

Q: A bar of an advanced alloy having an elastic modulus of 107 GPa and an original diameter of 3.8 mm…

Q: When the material is in the region of the stress-strain curve, the material can go back to its…

A: Answer (C) Elastic, temporarily

Q: A particular human hair has a Young's modulus of 3.63×109 N/m2 and a diameter of 145 μm. If a 228 g…

A: Write the expression for Young’s modulus, and solve for the change in length of the hair.

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

A: When the thread is stretched under the weight of the insect, calculate the total length of the…

Q: Figure below shows a two-member truss supporting a block of weight W. The cross-sectional areas of…

A: Given that:- Cross sectional area of AB=800mm^2

Q: A steel rectangular block, a = 2.4cm wide and b =1.2 cm deep, is subjected to an axial tensile load…

A: Modulus of elasticity for a volume object is known as Bulk modulus of elasticity.

Q: Jsing the circle (radius = r =2 cm) and ellipse (long axis = 3 cm, short axis = 1.5 cm) of Figure…

Q: GO Depending on how you fall, you can break a bone easily. The severity of the break depends on how…

A: Spring constant can be calculated as k=YAl where Y= young's modulus, A= Area, and l= length.

Q: A 15 cm long animal tendon was found to stretch 3.7 mm by a force of 13.4 N. The tendon was…

A: Given Data : The length of the animal tendon is given as l=15cm=15cm×1m100cm=15×10-2m. The change in…

Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

A wire of length L, Young’s modulus Y, and crosssectional area A is stretched elastically by an amount ΔL. By Hooke’s law, the restoring force is -k ΔL. (a) Show that k = YA/L. (b) Show that the work done in stretching the wire by
an amount ΔL is W = 1/2 YA(ΔL)²/L .

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 with 2 images

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

Describe a system in which elastic potential energy is stored.
Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.
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 ?
A wire of original length L and cross sectional area A is stretched within its elastic limit by a stress S.Show that the density of stored elastic energy in the stretched wire is S2/2Y.
A 15 cm long animal tendon ( وتر ) 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. the elastic modulus of this tendon?
A 15 cm long animal 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. the elastic modulus of this tendon?
A steel rectangular block, a = 2.4cm wide and b =1.2 cm deep, is subjected to an axial tensile load as shown in the figure. Measurements show the block to increase in length by x = 7.11×10−5m (initial length=10cm) and to decrease width by δ z = 0.533×10−5m, when P is 45 kN. Calculate the modulus of elasticity and Poisson's ratio for the material.
Proof that the energy stored in the compact bone is given by E = AL0 (Sb) ^ 2 / 2γ. When Sb is bone stress. *
The 90-kg uniform rectangular plate is supported by an ideal pivot at O and a spring which must be compressed prior to being slipped into place at point A. If the modulus of the spring is k = 2,200 N/m, what must be its undeformed length L in mm?
A copper wire and a steel wire having the same cross-section area are fastened end to end stretched by a force F. the lengths of copper and steel wires are in the ratio of 2:1 and their modulus of elasticity are in the ratio of 1:2. What is the ratio (Ec/es) of their extensions a. 2:1 b. 1:2 c. 1:4 d. 4:1
Your biceps muscle is attached to your elbow by the distal biceps tendon. An average adults tendon has a 6 mm by 3 mm rectangular cross-section and is 63 mm in length. A tendon has a Young’s modulus of 1.5x10^9 N/m^2. How much work must be done to stretch the length of the distal biceps tendon by 10%? Assume that the tendon is a linearly elastic material and that stretching does not alter it’s cross-section.
An axial tensile load of 1.5 kN is applied to the St37 steel plate with a central crack as shown in the figure. The steel plate has an Elasticity modulus of 210 GPa, and a fracture energy value of 54 N/m. Calculate the surface energy value caused by the central crack on the plate.