A 1200-kg car is being raised with a constant acceleration of 2.53 m/s by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is 200 GPa. What is the change in length of the cable caused by lifting the car?

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is 200 GPa. What is the change in length of the cable caused by lifting the car?

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 48PQ: A company is testing a new material made of recycled plastic for use in construction. Figure P14.48...

See similar textbooks

Related questions

Q: A child slides across a floor in a pair of rubber-soled shoes. The frictional force acting on each…

A: NOTE: As per bartleby guidelines we can answer only first question. For remaining questions please…

Q: 2.0-m-long, 1.0-mm-diameter wire is suspended from the ceiling. Hanging a 4.5 kg mass from the wire…

Q: Humans can bite with a force of approximately 798 N. If a human tooth has the Young's modulus of…

A: Given:- a cross-sectional area A = 1.2 cm2 length L = 1.5 cm…

Q: A 4.0 m steel beam with a cross sectional area of 1.0 x 10-2 m² and a Young's modulus of 2.0 x 1011…

A: Given:- The length of the steel beam L = 4 m The cross-sectional area of the beam is A = 1.0 x…

Q: A 1200-kg car is being raised with a constant acceleration of 2.53 m/s² by a crane, using a 20-m…

Q: A road engineer is planning to build an overpass and wants to support a 2.1 × 10° kg load over a…

A: Given that, Length of the column is L = 5.450 m Diameter of the column is d = 73.60 cm = 0.736 m…

Q: How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume…

A: Answer Option ( c ) = 200 atm

Q: A stainless-steel orthodontic wire is applied to a tooth, as in Figure P9.72. The wire has an…

A: the expression for force is,

Q: After a fall, a 85 kg rock climber finds himself dangling from the end of a rope that had been 18 m…

A: Given Data Mass of the rock climber is m=85 kg Length of the rope is l=18 m Diameter of the rope is…

Q: A (2 m)-long steel wire in a musical instrument has a radius of (0.3 mm). When the wire is under a…

Q: You have a 15 cm^3 block of copper that you wish to make into a cylindrical wire. If the Young's…

A: stiffness of wire is given by, k=A ELwhere V=ALA=VLNow,k=VEL2

Q: After a fall, a 84 kg rock climber finds himself dangling from the end of a rope that had been 13 m…

Q: A wire of 2.0000 m length and 1.0 mm diameter is suspended from the ceiling. Hanging a 4.500 kg…

A: Original length L = 2.0000 m Diameter of wire d = 1.0 mm Radius of wire r = d/2 = 1.0 / 2 mm = 0.5…

Q: A ball has a radius of 1 meter. The Bulk modulus is 4.2 × 1010 N/m2. It is located on the surface of…

Q: A rubber band 20 cm long has a cross-sectional area of 4 mm?. What load will stretch the rubber band…

A: Given data: Length of the rubber band, L=20 cm = 0.20 m Cross section area of the band, A=4…

Q: A 1000-kg object hangs from the lower end of a steel rod 5.0 m long that is suspended vertically.…

Q: What is the compression in the tibia of length l = 30 cm of a person of mass m = 80 kg when standing…

Q: A 45 kg boy whose leg bones are 5 cm? in area and 50 cm long falls through a height of 2 m without…

A: Given data m=45 kg B. S= 0.9×108 N/m2 A= 5cm2 L=50 cm loss in PE = gain energy Stored in leg bones…

Q: 20. A 20-m long steel wire (cross-section 1.0 cm2, Young's modulus 2.0 x 10I N/m²), is subjected to…

A: Given that Original length of wire L = 20 m Cross section area A = 1 cm2 = 1 X 10-4 m2 Young's…

Q: Max (mass = 15 kg) is hanging from one end of a 13-m long bungee cord that has its other end fixed…

Q: A 1.60-meter-long steel piano wire has a diameter of 0.200 cm. How great is the tension (in Newtons)…

A: Length of the wire is l = 1.060 m Diameter is 0.2 cm

Q: An 1800-kg elephant is placed on top of an aluminum cylinder, 4.3 meters high. The area of the top…

A: height of cylinder (h) = 4.3 m Surface area (A) = 0.080 m2mass of elephant (m) = 1800 kg Young's…

Q: After a fall, a 88 kg rock climber finds himself dangling from the end of a rope that had been 14 m…

Q: In a structure you need to place a 7.8 m steel wire that does not stretch more than 8.5 cm when a…

A: Write the given values with suitable variables. L0=7.8 mΔL=8.5 cm=0.085 mF=391.6 NE=20×1010 N/m2…

Q: A stainless-steel orthodontic wire is applied to a tooth, as in Figure P9.14. The wire has an…

A: Given: L = 3.1 cm = 3.1 x 10-2 m radius, r = 0.11 mm = 0.11 x 10-3 m l = 0.1 mm = 1 x 10-4 m Y =…

Q: A large 75-kg lighting fixture can be hung from wires of identical size and shape made of aluminum,…

A: Given: The mass is 75 kg. The Young's modulus of aluminum is 0.70x1011 Pa. The Young's modulus of…

Q: A horizontal aluminum rod 4.7 cm in diameter projects 4.4 cm from a wall. A 1100 kg object is…

A: Given: Diameter of aluminum rod, d=4.7 cm projects at a distance L= 4.4 cm from a wall. Mass of…

Q: A child slides across a floor in a pair of rubber-soled shoes. The frictional force acting on each…

Q: One end of a steel rod of radius R = 10mm and length L = 80 cm is held in a vise. A force of…

A: We need to calculate the elongation of the rod when the given force is applied.

Q: Humans can bite with a force of approximately 792 N. If a human tooth has the Young's modulus of…

A: Force exerted (F) = 792 N Cross sectional area (A) = 1.3 cm2= 0.00013 m2Length of bone (L) = 1.7cm =…

Q: After a fall, a 84 kg rock climber finds himself dangling from the end of a rope that had been 13 m…

Q: A 1000-kg object hangs from the lower end of a steel rod 5.0 m long that is suspended vertically.…

Q: A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load.…

Q: TOW TRUCK IS PULLING A CAR OUT OF A DITCH BY MEANS OF STEEL CABLE THAT IS 8.3m LONG AND HAS A RADIUS…

Q: When water freezes, it expands by about 9%. What would be the pressure increase inside your…

Q: After a fall, a 84 kg rock climber finds himself dangling from the end of a rope that had been 13 m…

A: By observing the scenario, Climber finds that he dangling from the end of the rope i.e., the only…

Q: A steel wire, 3.0 m long, has a diameter of 1.0 mm. If a 10 kg load is hung from the wire how far…

Q: 6. What is the compression in the tibia of length /= 30 cm of a person of mass m = 80 kg when…

Q: A 1.6 x 10-3-kg house spider is hanging vertically by a thread that has a Young's modulus of 4.3 x…

Q: How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume…

Q: In her gymnastic routine, Regina dismounts from the uneven-parallel bars and lands straight-legged…

Q: A material rod that is 4.00 m long and 0.50 cm2 in cross- section area is found to stretch 0.20 cm…

A: The Young's Modulus, Y=Fl0A∆l

Q: A brass wire which is 4.00 m long and 4.00 mm in diameter hangs from the ceiling. If a mass of 5.00…

Q: After a fall, a 110 kg rock climber finds himself dangling from the end of a rope that had been 15 m…

A: Given, massm= 110kg Length of ropel= 15m diameterd= 9.9×10-3m=9.9 mm change in…

Q: A weight of 125 Newton is attached to a brass wire of 7.5 meters long. Young's modulus for brass is…

A: Given data: Weight of the load P=125N Length of the wire L=7.5m Radius of the wire r=0.7mm Young's…

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

Accepted file types
PDF document pdf
A 1200-kg car is being raised with a constant acceleration of 253 m/s by a crane, using a 20-m long steel cable that is 1.5 cm in diameter.
Young's modulus for steel is 200 GPa. What is the change in length of the cable caused by lifting the car?

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 1 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

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 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, V/V0=2103 ) relative to the space available. Calculate the magnitude of the normal force exerted by the juice per square centimeter if its bulk modulus is 1.8109 N/m2, assuming the bottle does not break. In view of your answer, do you think the bottle will survive?
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.
(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?
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?
Use the graph in Figure P14.46 to list the three materials from greatest Youngs modulus to smallest. Explain your reasoning. FIGURE P14.46
During heavy lifting, a disk between spinal vertebrae is subjected to a 5000-N compressional force. (a) What pressure is created, assuming that the disk has a uniform circular cross section 2.00 cm in radius? (b) What deformation is produced if the disk is 0.800 cm thick and has a Young's modulus of 1.5109N/m2 ?
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?
The “lead” in pencils is a graphite composition with a Young’s modulus of approximately 1.0109N/m2 . Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0N . The lead is 0.50mm in diameter and 60mm long.
Artificial diamonds can be made using high-pressure, high-temperature presses. Suppose an artificial diamond of volume 1.00 106 m3 is formed under a pressure of 5.00 GPa. Find the change in its volume when it is released from the press and brought to atmospheric pressure. Take the diamonds bulk modulus to be B = 194 GPa.
(a) By how much does a 65.0-kg mountain climber stretch her 0.800-cm diameter nylon rope when she hangs 35.0 m below a rock outcropping? (b) Does the answer seem to be consistent with what you have observed for nylon ropes? Would it make sense if the rope were actually a bungee cord?