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The massless spring of a spring gun has a force constant k = 14.5 N/cm. When the gun is aimed vertically, a 10-g projectile is shot to a height of 5.0 m above the end of the expanded spring. How much was the spring compressed initially? 5.0 m ? T. Image Description d cm |NNNNNNN-

The massless spring of a spring gun has a force constant k = 14.5 N/cm. When the gun is aimed vertically, a 10-g projectile is shot to a height of 5.0 m above the end of the expanded spring. How much was the spring compressed initially? 5.0 m ? T. Image Description d cm |NNNNNNN-

College Physics
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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A 4.5×1054.5×105 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.65 m by a large spring bumper at the end of its track. What is the spring constant kk of the spring?

k=k=  N/m

The massless spring of a spring gun has a force constant k=14.5k=14.5 N/cm. When the gun is aimed vertically, a 10-g projectile is shot to a height of 5.0 m above the end of the expanded spring. How much was the spring compressed initially?


Image Description

 

d=d=  cm

 

The image presents a physics problem involving a spring gun. The spring gun has a force constant \( k = 14.5 \, \text{N/cm} \). A 10-gram projectile is launched vertically from the spring gun to a height of 5.0 meters above the spring's fully expanded position. The question asks for the initial compression distance \( d \) of the spring. **Diagrams:** 1. **First Diagram (Left):** - The spring is in a compressed state with the projectile resting on top. The compression distance \( d \) is marked but unknown. 2. **Second Diagram (Middle):** - The spring expands, launching the projectile upwards. An arrow indicates the upward velocity \( v \) of the projectile as it leaves the spring. 3. **Third Diagram (Right):** - The projectile reaches a height of 5.0 meters above the spring’s original position. This setup conveys a typical energy transformation problem, where the potential energy stored in the compressed spring is converted into kinetic energy and then gravitational potential energy at the projectile's peak. At the bottom is a text input box labeled "Image Description" and another box with "d = __ cm" for recording the calculated compression distance of the spring.
Transcribed Image Text:The image presents a physics problem involving a spring gun. The spring gun has a force constant \( k = 14.5 \, \text{N/cm} \). A 10-gram projectile is launched vertically from the spring gun to a height of 5.0 meters above the spring's fully expanded position. The question asks for the initial compression distance \( d \) of the spring. **Diagrams:** 1. **First Diagram (Left):** - The spring is in a compressed state with the projectile resting on top. The compression distance \( d \) is marked but unknown. 2. **Second Diagram (Middle):** - The spring expands, launching the projectile upwards. An arrow indicates the upward velocity \( v \) of the projectile as it leaves the spring. 3. **Third Diagram (Right):** - The projectile reaches a height of 5.0 meters above the spring’s original position. This setup conveys a typical energy transformation problem, where the potential energy stored in the compressed spring is converted into kinetic energy and then gravitational potential energy at the projectile's peak. At the bottom is a text input box labeled "Image Description" and another box with "d = __ cm" for recording the calculated compression distance of the spring.
**Problem Statement:** A \(4.5 \times 10^5\) kg subway train is brought to a stop from a speed of 0.500 m/s in 0.65 m by a large spring bumper at the end of its track. What is the spring constant \(k\) of the spring? **Solution:** \( k = \) [ ] N/m *Explanation:* The problem involves calculating the spring constant \(k\) based on the given information about a subway train's mass, its initial speed, and the distance over which it is stopped by a spring. To solve this, you would typically apply the work-energy principle, equating the initial kinetic energy of the train with the elastic potential energy stored in the spring at maximum compression.
Transcribed Image Text:**Problem Statement:** A \(4.5 \times 10^5\) kg subway train is brought to a stop from a speed of 0.500 m/s in 0.65 m by a large spring bumper at the end of its track. What is the spring constant \(k\) of the spring? **Solution:** \( k = \) [ ] N/m *Explanation:* The problem involves calculating the spring constant \(k\) based on the given information about a subway train's mass, its initial speed, and the distance over which it is stopped by a spring. To solve this, you would typically apply the work-energy principle, equating the initial kinetic energy of the train with the elastic potential energy stored in the spring at maximum compression.
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