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A 7000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law and have spring constants with k = 1700 N/m and ką = 3100 N/m. After the first spring compresses a distance of 29.4 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 49.0 cm after first contacting the two-spring system. Find the car's initial speed. 311 Your response differs from the correct answer by more than 10%. Double check your calculations. m/s k2 ki kjXz + kz(xz – x)} Total force (N) X2 Distance (cm)

A 7000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law and have spring constants with k = 1700 N/m and ką = 3100 N/m. After the first spring compresses a distance of 29.4 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 49.0 cm after first contacting the two-spring system. Find the car's initial speed. 311 Your response differs from the correct answer by more than 10%. Double check your calculations. m/s k2 ki kjXz + kz(xz – x)} Total force (N) X2 Distance (cm)

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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I am not sure why I am not getting the answer. I looked all around the interwebs and I keep on finding the same way to solve the problem and when I do it that way I keep getting .311. That answer is wrong and im not sure what im doing wrong. 

 

Im using U=.5kx^2 ( both springs)

and 

U=.5mv^2 (kenetic) 

A 7000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke’s law and have spring constants with \( k_1 = 1700 \, \text{N/m} \) and \( k_2 = 3100 \, \text{N/m} \). After the first spring compresses a distance of 29.4 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 49.0 cm after first contacting the two-spring system. Find the car’s initial speed. \(.311 \) Your response differs from the correct answer by more than 10%. Double check your calculations. m/s **Diagram:** The image of the two coiled springs system shows a freight car on rails compressing two springs mounted in series. The first spring with constant \( k_1 \) is being compressed initially, followed by the second spring with constant \( k_2 \), which further increases the force. **Graph Explanation:** The graph illustrates the relationship between the total force (in Newtons) and the distance (in cm) for the spring system. - The x-axis represents the distance, starting from 0 to \( x_2 \) with \( x_1 \) being an intermediate point at 29.4 cm. - The y-axis represents the total force (N). - The sloped line shows the increase in force as the first spring is compressed to 29.4 cm (point \( k_1 x_1 \)). - At this point, the second spring begins to compress, leading to a further linear increase in force up to 49.0 cm, following the equation \( k_1 x_2 + k_2 (x_2 - x_1) \). **Submit Answer:** Button: "Submit Answer" **Need Help?** Button: "Read It"
Transcribed Image Text:A 7000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke’s law and have spring constants with \( k_1 = 1700 \, \text{N/m} \) and \( k_2 = 3100 \, \text{N/m} \). After the first spring compresses a distance of 29.4 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 49.0 cm after first contacting the two-spring system. Find the car’s initial speed. \(.311 \) Your response differs from the correct answer by more than 10%. Double check your calculations. m/s **Diagram:** The image of the two coiled springs system shows a freight car on rails compressing two springs mounted in series. The first spring with constant \( k_1 \) is being compressed initially, followed by the second spring with constant \( k_2 \), which further increases the force. **Graph Explanation:** The graph illustrates the relationship between the total force (in Newtons) and the distance (in cm) for the spring system. - The x-axis represents the distance, starting from 0 to \( x_2 \) with \( x_1 \) being an intermediate point at 29.4 cm. - The y-axis represents the total force (N). - The sloped line shows the increase in force as the first spring is compressed to 29.4 cm (point \( k_1 x_1 \)). - At this point, the second spring begins to compress, leading to a further linear increase in force up to 49.0 cm, following the equation \( k_1 x_2 + k_2 (x_2 - x_1) \). **Submit Answer:** Button: "Submit Answer" **Need Help?** Button: "Read It"
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