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A spring has a natural length of 20 cm. If a 25-dyne force is required to keep it stretched to a length of 25 cm, how much work is required to stretch it from 25 cm to 30 cm?

A spring has a natural length of 20 cm. If a 25-dyne force is required to keep it stretched to a length of 25 cm, how much work is required to stretch it from 25 cm to 30 cm?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. A spring has a natural length of 20 cm. If a 25-dyne force is required to keep it stretched to a length of 25 cm, how much work is required to stretch it from 25 cm to 30 cm? 2. A spring has a natural length of 15 ft. A force of 300 lb compresses the spring to 12 ft. Find the work done in compressing the spring from 13 ft to 10 ft. 3. A cone-shaped water reservoir is 10 feet in diameter across the top and 12 feet deep. If the reservoir is filled to a depth of 10 feet, how much work is required to pump all the water to the top of the reservoir? Use p = 62.4 lb/ft³. 4. Find the force on one end of a parabolic trough full of water if the depth is 2 feet and the width across the top is 2 ft. Use p = 62.4 lb/ft³. 5. Evaluate the iterated integrals. 3 ² S (x + y)dx dy a. 1 0 2 yz b. ſ² ſ² ſ² xyz dx dy dz 0
Transcribed Image Text:1. A spring has a natural length of 20 cm. If a 25-dyne force is required to keep it stretched to a length of 25 cm, how much work is required to stretch it from 25 cm to 30 cm? 2. A spring has a natural length of 15 ft. A force of 300 lb compresses the spring to 12 ft. Find the work done in compressing the spring from 13 ft to 10 ft. 3. A cone-shaped water reservoir is 10 feet in diameter across the top and 12 feet deep. If the reservoir is filled to a depth of 10 feet, how much work is required to pump all the water to the top of the reservoir? Use p = 62.4 lb/ft³. 4. Find the force on one end of a parabolic trough full of water if the depth is 2 feet and the width across the top is 2 ft. Use p = 62.4 lb/ft³. 5. Evaluate the iterated integrals. 3 ² S (x + y)dx dy a. 1 0 2 yz b. ſ² ſ² ſ² xyz dx dy dz 0
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