A small block slides down a frictionless track whose shape is described by y = (x^2) /d for x<0 and by y = -(x^2)/d for x>0. The value of d is 2.91 m, and x and y are measured in meters as usual. Suppose the block starts on the track at x = 0. What minimum initial velocity (moving to the right) must the block have such that it will leave the track at x = 0 and go into freefall?
A small block slides down a frictionless track whose shape is described by y = (x^2) /d for x<0 and by y = -(x^2)/d for x>0. The value of d is 2.91 m, and x and y are measured in meters as usual. Suppose the block starts on the track at x = 0. What minimum initial velocity (moving to the right) must the block have such that it will leave the track at x = 0 and go into freefall?
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)...
Related questions
Concept explainers
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
Topic Video
Question
9. A small block slides down a frictionless track whose shape is described by y = (x^2) /d for x<0 and by y = -(x^2)/d for x>0. The value of d is 2.91 m, and x and y are measured in meters as usual.
Suppose the block starts on the track at x = 0. What minimum initial velocity (moving to the right) must the block have such that it will leave the track at x = 0 and go into freefall?
|
5.35 m/s
|
||
|
2.27 m/s
|
||
|
3.78 m/s
|
||
|
7.56 m/s
|
Transcribed Image Text:### Educational Diagram
#### Graph of a Cubic Function
The image depicts the graph of a cubic function, which is characterized by the general form \(y = ax^3 + bx^2 + cx + d\). This type of function creates a distinct S-shaped curve. Below is a detailed explanation of the graph's features:
- **Axes**: The graph is placed over a coordinate system, consisting of an **x-axis** (horizontal) and a **y-axis** (vertical), which intersect at the origin (0,0).
- **Curve**: The curve displayed represents the cubic function and showcases its typical behavior:
- The curve starts in the top left quadrant, descends through the origin, and ascends again into the top right quadrant.
- The transition of the curve through the origin indicates an inflection point where the concavity changes.
- **Behavior**:
- **For large negative values of \(x\)**, the curve moves downward, indicating that the function yields large negative values of \(y\).
- **As \(x\) approaches the origin from the left**, the value of \(y\) decreases and then increases after passing through the origin.
- **For positive values of \(x\)**, the curve ascends, indicating that the function yields large positive values of \(y\).
This type of graph provides a visual representation of how cubic functions behave generally, with one real root and typically two inflection points where the concavity changes. Such functions appear frequently in various fields such as physics, engineering, and economics, making understanding their graphical representation crucial.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
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.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
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…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON