Explanation Given data: A weight is attached to 10 m length of climbing rope, and the rope stretches by 20 cm. The single rope is replaced by a doubled rope. The doubled rope means that, two pieces of rope next to each other. It is required to find the stretching length when the single rope is replaced by the doubled rope. Formula used: Refer to the equation (8.6) textbook, and write the expression for the stress of the climbing rope as follows. F A = Y ( Δ L L ) (1) Here, F is the restoring force, A is the cross-sectional area of the climbing rope, Y is the Young’s modulus of the climbing rope, L is the length of the climbing rope (resting length), Δ L is the change in length (stretching length) of the climbing rope. ( F A ) is the stress, and ( Δ L L ) is the strain. Explanation: Rearrange the expression in equation (1) for the stretching length of the rope as follows. Δ L = F L Y A (2) From the given data, a single rope is replaced by the doubled rope (two pieces of rope next to each other). As the single rope is replaced by the doubled rope, the cross-sectional area of the rope becomes double and the Young’s modulus remains same. As the weight is same in both the cases (single and doubled rope), the restoring force is not varied from one case to the other. As the two pieces are placed next to the other, the length of the rope does not change from one case to the other. Modify the expression in equation (2) for the stretching length when the load is attached to the sing rope as follows. ( Δ L ) single = ( F L Y ) ( 1 A single ) (3) Modify the expression in equation (2) for the stretching length when the load is attached to the doubled rope as follows. ( Δ L ) double = ( F L Y ) ( 1 A double ) (4) Calculation of stretching length of the rope when the load is attached to the doubled rope [ ( Δ L ) double ] : Divide equation (4) with equation (3) as follows

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 8, Problem 25MCQ

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College Physics: A Strategic Approach (4th Edition)

Ch. 8 - Prob. 1CQ Ch. 8 - Could a ladder on a level floor lean against a...Ch. 8 - Prob. 3CQ Ch. 8 - Prob. 4CQ Ch. 8 - Prob. 5CQ Ch. 8 - Prob. 6CQ Ch. 8 - Prob. 7CQ Ch. 8 - A spring exerts a 10 N force after being stretched...Ch. 8 - Prob. 9CQ Ch. 8 - A typical mattress has a network of springs that...

Ch. 8 - Take a spring and cut it in half to make two...Ch. 8 - A wire is stretched right to its breaking point by...Ch. 8 - Prob. 13CQ Ch. 8 - Prob. 14CQ Ch. 8 - Steel nails are rigid and unbending. Steel wool is...Ch. 8 - Two children hold opposite ends of a lightweight,...Ch. 8 - Prob. 19MCQ Ch. 8 - Prob. 20MCQ Ch. 8 - Prob. 21MCQ Ch. 8 - Prob. 22MCQ Ch. 8 - Prob. 23MCQ Ch. 8 - Prob. 24MCQ Ch. 8 - Prob. 25MCQ Ch. 8 - Prob. 26MCQ Ch. 8 - You have a heavy piece of equipment hanging from a...Ch. 8 - Prob. 1P Ch. 8 - Prob. 2P Ch. 8 - Prob. 3P Ch. 8 - Prob. 4P Ch. 8 - Youre carrying a 3.6-m-long, 25 kg pole to a...Ch. 8 - Prob. 6P Ch. 8 - Prob. 7P Ch. 8 - Prob. 9P Ch. 8 - Prob. 11P Ch. 8 - Prob. 13P Ch. 8 - Prob. 14P Ch. 8 - Prob. 15P Ch. 8 - The stability of a vehicle is often rated by the...Ch. 8 - Prob. 18P Ch. 8 - A car manufacturer claims that you can drive its...Ch. 8 - Prob. 20P Ch. 8 - An orthodontic spring, connected between the upper...Ch. 8 - Prob. 22P Ch. 8 - Experiments using optical tweezers measure the...Ch. 8 - Prob. 24P Ch. 8 - One end of a 10-cm-long spring is attached to the...Ch. 8 - Prob. 26P Ch. 8 - A spring has an unstretched length of 10 cm. It...Ch. 8 - A spring stretches 5.0 cm when a 0.20 kg block is...Ch. 8 - You need to make a spring scale to measure the...Ch. 8 - Prob. 30P Ch. 8 - A force stretches a wire by 1.0 mm. a. A second...Ch. 8 - Prob. 32P Ch. 8 - What hanging mass will stretch a 2.0-m-long,...Ch. 8 - An 80-cm-long, 1.0-mm-diameter steel guitar string...Ch. 8 - A mineshaft has an ore elevator hung from a single...Ch. 8 - The normal force of the ground on the foot can...Ch. 8 - A three-legged wooden bar stool made out of solid...Ch. 8 - Prob. 38P Ch. 8 - Prob. 39P Ch. 8 - Prob. 40P Ch. 8 - A glass optical fiber in a communications system...Ch. 8 - The Achilles tendon connects the muscles in your...Ch. 8 - Prob. 44P Ch. 8 - Prob. 47P Ch. 8 - Prob. 48P Ch. 8 - Prob. 49P Ch. 8 - Prob. 51GP Ch. 8 - Prob. 52GP Ch. 8 - Prob. 53GP Ch. 8 - Prob. 55GP Ch. 8 - Two identical, side-by-side springs with spring...Ch. 8 - Prob. 57GP Ch. 8 - Prob. 58GP Ch. 8 - Prob. 59GP Ch. 8 - A 25 kg child bounces on a pogo stick. The pogo...Ch. 8 - Prob. 61GP Ch. 8 - In the hammer throw, an athlete spins a heavy mass...Ch. 8 - There is a disk of cartilage between each pair of...Ch. 8 - Orb spiders make silk with a typical diameter of...Ch. 8 - Larger animals have sturdier bones than smaller...Ch. 8 - Prob. 67GP Ch. 8 - Prob. 68GP Ch. 8 - Prob. 69MSPP Ch. 8 - Prob. 70MSPP Ch. 8 - Prob. 71MSPP Ch. 8 - Prob. 72MSPP

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