Concept explainers
Runaway Car Using Hooke's Law, we can show that the work done in compressing a spring a distance of feet from its at-rest position is , where is a stiffness constant depending on the spring. It can also be shown that the work done by a body in motion before it comes to rest is given by , Where weight of the object (in Ibs), acceleration due to gravity( ), and object’s velocity (in ft/sec). A parking garage has a spring shock absorber at the end of a ramp to stop runaway cars. The spring has a stiffness constant and must be able to stop a 4000-lb car traveling at 25 mph. What is the least compression required of the spring? Express your answer using feet to the nearest tenth.
[Hint: Solve ].
Source: www.scifonims.com
To find: What is the least compression required of the spring? Express your answer using feet to the nearest tenth.
Answer to Problem 38AYU
Solution:
4 feet
Explanation of Solution
Given:
Runaway Car Using Hooke’s Law, we can show that the work done in compressing a spring a distance of feet from its at rest position is where is a stiffness constant depending on the spring. It can also be shown that the work done by a body in motion before it comes to rest is given by , where = weight of the object (lb), = acceleration due to gravity , = object’s velocity (in ft/sec). A parking garage has a spring shock absorber at the end of a ramp to stop runaway cars. The spring has a stiffness constant and must be able to stop a 4000-lb car traveling at 25 mph.
The least compression required of the spring is 4 feet.
Chapter 3 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning