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Suppose a force of 60 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.6 m from its equilibrium position? c. How much work is required to stretch the spring 0.2 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. k=

Suppose a force of 60 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.6 m from its equilibrium position? c. How much work is required to stretch the spring 0.2 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. k=

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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## Hooke's Law and Work Done on a Spring Suppose a force of 60 N is required to stretch and hold a spring 0.1 m from its equilibrium position. ### Problems **a.** Assuming the spring obeys Hooke's law, find the spring constant \( k \). \[ \text{k =} \] *(Type an integer or a decimal.)* **b.** Set up the integral that gives the work done in compressing the spring 0.6 m from its equilibrium position. Use decreasing limits of integration. \[ \int_{}^{} (\:\;\;\;\,\;) \, dx \] *(Type exact answers.)* **Find the work done in compressing the spring.** The work is \[ \boxed{} \] *(Type an integer or a decimal.)* **c.** Set up the integral that gives the work done in stretching the spring 0.2 m from its equilibrium position. Use increasing limits of integration. \[ \int_{}^{} (\:\;\;\;\,\;) \, dx \] *(Type exact answers.)* **Find the work done in stretching the spring.** The work is \[ \boxed{} \] *(Type an integer or a decimal.)* **d.** Set up the integral that gives the work done to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium. Use increasing limits of integration. \[ \int_{}^{} (\:\;\;\;\, \;) \, dx \] *(Type exact answers.)* ## Explanation of Diagrams There are no visual diagrams or graphs in this document. However, the problem involves setting up integrals to compute the work done on a spring according to Hooke's Law, illustrated as follows: 1. **Spring Constant Calculation (Part a)**: - The spring constant \( k \) is calculated using Hooke's Law \( F = kx \), where \( F \) is the force in Newtons and \( x \) is the displacement in meters. 2. **Work Done Computation using Integrals (Parts b, c, and d)**: - **Part b:** Compressing the spring by 0.6 m. - **Part c:** Stretching the spring by 0.2 m. - **Part d:** Additional work done to stretch the spring further by
Transcribed Image Text:## Hooke's Law and Work Done on a Spring Suppose a force of 60 N is required to stretch and hold a spring 0.1 m from its equilibrium position. ### Problems **a.** Assuming the spring obeys Hooke's law, find the spring constant \( k \). \[ \text{k =} \] *(Type an integer or a decimal.)* **b.** Set up the integral that gives the work done in compressing the spring 0.6 m from its equilibrium position. Use decreasing limits of integration. \[ \int_{}^{} (\:\;\;\;\,\;) \, dx \] *(Type exact answers.)* **Find the work done in compressing the spring.** The work is \[ \boxed{} \] *(Type an integer or a decimal.)* **c.** Set up the integral that gives the work done in stretching the spring 0.2 m from its equilibrium position. Use increasing limits of integration. \[ \int_{}^{} (\:\;\;\;\,\;) \, dx \] *(Type exact answers.)* **Find the work done in stretching the spring.** The work is \[ \boxed{} \] *(Type an integer or a decimal.)* **d.** Set up the integral that gives the work done to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium. Use increasing limits of integration. \[ \int_{}^{} (\:\;\;\;\, \;) \, dx \] *(Type exact answers.)* ## Explanation of Diagrams There are no visual diagrams or graphs in this document. However, the problem involves setting up integrals to compute the work done on a spring according to Hooke's Law, illustrated as follows: 1. **Spring Constant Calculation (Part a)**: - The spring constant \( k \) is calculated using Hooke's Law \( F = kx \), where \( F \) is the force in Newtons and \( x \) is the displacement in meters. 2. **Work Done Computation using Integrals (Parts b, c, and d)**: - **Part b:** Compressing the spring by 0.6 m. - **Part c:** Stretching the spring by 0.2 m. - **Part d:** Additional work done to stretch the spring further by
### Problem Statement #### c. Set up the integral that gives the work done in stretching the spring 0.2 m from its equilibrium position. Use increasing limits of integration. \[ \int_{0}^{0.2} kx \, dx \] (Type exact answers.) **Find the work done in stretching the spring.** The work is \[ \boxed{} \] (Type an integer or a decimal.) #### d. Set up the integral that gives the work done to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium. Use increasing limits of integration. \[ \int_{0.1}^{0.2} kx \, dx \] (Type exact answers.) **Find the additional work required.** The additional work is \[ \boxed{} \] (Type an integer or a decimal.)
Transcribed Image Text:### Problem Statement #### c. Set up the integral that gives the work done in stretching the spring 0.2 m from its equilibrium position. Use increasing limits of integration. \[ \int_{0}^{0.2} kx \, dx \] (Type exact answers.) **Find the work done in stretching the spring.** The work is \[ \boxed{} \] (Type an integer or a decimal.) #### d. Set up the integral that gives the work done to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium. Use increasing limits of integration. \[ \int_{0.1}^{0.2} kx \, dx \] (Type exact answers.) **Find the additional work required.** The additional work is \[ \boxed{} \] (Type an integer or a decimal.)
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