As shown in the figure, a 0.480 kg package is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x. The force constant of the spring is 450 N/m. When it is released, the package travels along a frictionless, horizontal surface to point A, the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The speed of the package at the bottom of the track is v= 12.4 m/s, and the package experiences an average frictional force of 7.00 N while sliding up the track. (a) What is x? m + m-MMMM (b) If the package were to reach the top of the track, what would be its speed (in m/s) at that point? m/s (c) Does the package actually reach the top of the track, or does it fall off before reaching the top? O reaches the top of the track O falls off before reaching the top not enough information to tell

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)...
icon
Related questions
icon
Concept explainers
Topic Video
Question
### Description of the Problem

A 0.480 kg package is pushed against a horizontal spring, compressing it by a distance \( x \). The spring has a force constant of 450 N/m. Upon release, the package travels along a frictionless, horizontal surface to point \( A \), located at the base of a vertical circular track with a radius \( R = 1.00 \) m. The package then continues to move up the track. As it reaches the bottom of the track, its speed is \( v_A = 12.4 \) m/s. While sliding up the track, the package experiences an average frictional force of 7.00 N.

### Questions

(a) **What is \( x \)?**

- \( \_\_\_\_ \, \text{m} \)

(b) **If the package were to reach the top of the track, what would be its speed (in m/s) at that point?**

- \( \_\_\_\_ \, \text{m/s} \)

(c) **Does the package actually reach the top of the track, or does it fall off before reaching the top?**

- Reaches the top of the track
- Falls off before reaching the top
- Not enough information to tell

### Diagram Explanation

- The diagram features a side view of a setup including a spring and a circular track.
- On the left, a horizontal line represents the path of the package while it compresses a spring (shown on the right) and upon release, travels towards the circular track.
- A circular track with radius \( R \) is depicted, along which the package moves upwards.
- \( v_A \) indicates the velocity of the package at point \( A \).

This explanation provides insight into solving for the spring compression distance (\( x \)), the speed at the top of the track, and the package's ability to reach the top.
Transcribed Image Text:### Description of the Problem A 0.480 kg package is pushed against a horizontal spring, compressing it by a distance \( x \). The spring has a force constant of 450 N/m. Upon release, the package travels along a frictionless, horizontal surface to point \( A \), located at the base of a vertical circular track with a radius \( R = 1.00 \) m. The package then continues to move up the track. As it reaches the bottom of the track, its speed is \( v_A = 12.4 \) m/s. While sliding up the track, the package experiences an average frictional force of 7.00 N. ### Questions (a) **What is \( x \)?** - \( \_\_\_\_ \, \text{m} \) (b) **If the package were to reach the top of the track, what would be its speed (in m/s) at that point?** - \( \_\_\_\_ \, \text{m/s} \) (c) **Does the package actually reach the top of the track, or does it fall off before reaching the top?** - Reaches the top of the track - Falls off before reaching the top - Not enough information to tell ### Diagram Explanation - The diagram features a side view of a setup including a spring and a circular track. - On the left, a horizontal line represents the path of the package while it compresses a spring (shown on the right) and upon release, travels towards the circular track. - A circular track with radius \( R \) is depicted, along which the package moves upwards. - \( v_A \) indicates the velocity of the package at point \( A \). This explanation provides insight into solving for the spring compression distance (\( x \)), the speed at the top of the track, and the package's ability to reach the top.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Knowledge Booster
Kinetic energy
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON