Homework Help is Here – Start Your Trial Now!
Science
Physics
A block of mass 4.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 410 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 19° 1. The block, starting from rest, slides down the ramp a distance 32 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest?  2. After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring?  3. What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?

A block of mass 4.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 410 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 19° 1. The block, starting from rest, slides down the ramp a distance 32 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest?  2. After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring?  3. What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?

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)...
See similar textbooks
icon
Related questions
Question

A block of mass 4.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 410 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 19°

1. The block, starting from rest, slides down the ramp a distance 32 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest? 

2. After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring? 

3. What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed? 

### Physics Concept: Motion of a Mass on an Inclined Plane with a Spring #### Diagram Explanation The diagram illustrates a mass \(M\) resting on an inclined plane with an angle \(\theta\) relative to the horizontal. A spring is attached to the mass, and the spring is also anchored to the base of the incline. The system appears to be set up to study the dynamics of the mass-spring system on an inclined plane. #### Key Features: 1. **Inclined Plane**: The surface on which the mass \(M\) rests is inclined at an angle \(\theta\) with respect to the horizontal ground. 2. **Mass \(M\)**: This is the object of mass \(M\) resting on the inclined plane. 3. **Spring**: A spring with a rest length \(l\) is connected to the mass. The spring is positioned such that it can either be compressed or stretched depending on the position of the mass relative to its equilibrium position. 4. **Distances**: - \(l\) represents the rest length of the spring when it is neither compressed nor stretched. - \(d\) is the distance from the point where the spring anchors to the mass \(M\) when the spring is stretched. #### Analysis: This type of system is typically analyzed by applying principles of mechanics such as Hooke's Law for springs, Newton's Second Law for motion, and concepts of potential and kinetic energy. When the mass is displaced from its equilibrium position, the system can exhibit oscillatory motion due to the restoring force exerted by the spring. The inclined plane adds complexity to the problem by introducing components of gravitational force along and perpendicular to the incline. Equation of motion might include: - **Spring Force**: \( F_s = -k (d - l) \), where \(k\) is the spring constant. - **Gravitational Force Components**: - Along the incline: \( F_{\parallel} = Mg \sin(\theta) \) - Perpendicular to the incline: \( F_{\perp} = Mg \cos(\theta) \) #### Applications: This setup is ideal for studying: - Simple harmonic motion in systems involving inclined planes. - Energy transformations between kinetic, potential, and elastic forms. - The effect of incline angle \(\theta\) on the dynamics of mechanical systems. Students learning this topic would benefit from understanding how forces and motion
Transcribed Image Text:### Physics Concept: Motion of a Mass on an Inclined Plane with a Spring #### Diagram Explanation The diagram illustrates a mass \(M\) resting on an inclined plane with an angle \(\theta\) relative to the horizontal. A spring is attached to the mass, and the spring is also anchored to the base of the incline. The system appears to be set up to study the dynamics of the mass-spring system on an inclined plane. #### Key Features: 1. **Inclined Plane**: The surface on which the mass \(M\) rests is inclined at an angle \(\theta\) with respect to the horizontal ground. 2. **Mass \(M\)**: This is the object of mass \(M\) resting on the inclined plane. 3. **Spring**: A spring with a rest length \(l\) is connected to the mass. The spring is positioned such that it can either be compressed or stretched depending on the position of the mass relative to its equilibrium position. 4. **Distances**: - \(l\) represents the rest length of the spring when it is neither compressed nor stretched. - \(d\) is the distance from the point where the spring anchors to the mass \(M\) when the spring is stretched. #### Analysis: This type of system is typically analyzed by applying principles of mechanics such as Hooke's Law for springs, Newton's Second Law for motion, and concepts of potential and kinetic energy. When the mass is displaced from its equilibrium position, the system can exhibit oscillatory motion due to the restoring force exerted by the spring. The inclined plane adds complexity to the problem by introducing components of gravitational force along and perpendicular to the incline. Equation of motion might include: - **Spring Force**: \( F_s = -k (d - l) \), where \(k\) is the spring constant. - **Gravitational Force Components**: - Along the incline: \( F_{\parallel} = Mg \sin(\theta) \) - Perpendicular to the incline: \( F_{\perp} = Mg \cos(\theta) \) #### Applications: This setup is ideal for studying: - Simple harmonic motion in systems involving inclined planes. - Energy transformations between kinetic, potential, and elastic forms. - The effect of incline angle \(\theta\) on the dynamics of mechanical systems. Students learning this topic would benefit from understanding how forces and motion
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Nonconservative forces
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
SEE MORE TEXTBOOKS