College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Question
Transcribed Image Text:**Physics Problem: Object on an Incline and Spring Compression**
An object of mass 15 kg is released at point A, slides to the bottom of a 30-degree incline, then collides with a horizontal massless spring, compressing it a maximum distance of 0.50 m. The spring constant is 400 N/m, the height of the incline is 2.0 m, and the horizontal surface is frictionless. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)
**Diagram Explanation:**
- The diagram features an incline with a 30-degree angle from the horizontal.
- Point A is at the top of the incline, 2.0 meters above the horizontal ground.
- The object on point A is shown as a blue block.
- At the base of the incline, there's a horizontal spring.
**Questions:**
(a) What is the speed of the object (in m/s) at the bottom of the incline?
- __ m/s
(b) What is the work of friction (in J) on the object while it is on the incline?
- __ J
(c) The spring recoils and sends the object back toward the incline. What is the speed of the object (in m/s) when it reaches the base of the incline?
- __ m/s
(d) What vertical distance (in m) does it move back up the incline?
- __ m
Transcribed Image Text:**Title: Analyzing Roller Coaster Dynamics**
**Introduction:**
In an amusement park, a car rolls on a track as shown in the diagram. We are tasked with finding the speed (in m/s) of the car at three points: A, B, and C. It's important to note that the work done by the rolling friction is zero, as the point at which the rolling friction acts on the tires is momentarily at rest, resulting in zero displacement.
**Track Description:**
- The track begins at the highest point, with the car's velocity \( v = 0 \).
- The initial height of the car at the top is 38 meters.
- The track descends to point A, which is 14 meters above the ground level.
- It then rises to point B, which is 28 meters above the ground level.
- Finally, the track ends at point C, at ground level (0 meters).
**Graphical Representation:**
1. **Path of the Car:**
- The track is depicted with a blue line, showing the car's descending and ascending path between points.
- Heights are marked with red lines for clarity.
2. **Points of Interest:**
- **A:** Height of 14 meters.
- **B:** Height of 28 meters.
- **C:** Ground level.
**Objective:**
Calculate the speed of the car at points A, B, and C.
**Calculation Fields:**
- \( v_A = \) ____ m/s
- \( v_B = \) ____ m/s
- \( v_C = \) ____ m/s
**Conclusion:**
By understanding the principles of energy conservation and the absence of frictional work, one can calculate the speeds at the specified points on the track. This exercise demonstrates the conversion of potential energy to kinetic energy and vice versa in a frictionless environment, typical of amusement park rides.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps with 3 images
Knowledge Booster
Similar questions
- While riding on an elevator, a person has twoforces acting on him, a normal force and a gravity force. Suppose the person has mass m is on an elevator that 1 descends a distance d. If the total work on the person is Wiotal = -mgd, what is 4 the magnitude of the normal force? Is the elevator speeding up or slowing down? The knowns in this problem are m and g.arrow_forwardA 1680 kg car skids on a level road with coefficient of kinetic friction 0.64 between the tires of the car and the road. The car skids a distance of 102 m and comes to a complete stop. The work done on the car by the force of kinetic friction is (enter your answer with two significant figures) possibly useful: W = (Fcosθ)d w = mg g = 9.81 m/s2arrow_forwardA Net Force Fnet=(x-3x2)i + (2y2-y3)j acts on a 3.5 kg particle. a) Calculate the net work done on the particle as it moves from (1.0m,0.0m) to (1.0m,4.0m). b) At (x,y) = (1.0m,0.0m), the particle's speed is 5.0 m/s. Find the particle's speed at (x,y) = (1.0m,4.0m).arrow_forward
- A 4.5-kg block slides down a frictionless incline making an angle of 55.0° with the horizontal. (a) What is the total work done on the block when the block slides 1.4 m (measured along the incline)? (b) What is the speed of the block after it has slid 1.2 m if it starts from rest? m/s (c) What is its speed after 1.2 m if it starts with an initial speed of 1.6 m/s? m/s You can use the definition of work as the scalar product of a constant force and displacement to find the work done by each force acting on the block. Then use the work- kinetic energy theorem the find the speed of the block at any given location and for any initial kinetic energy it may have.arrow_forwardA) A 1390 kg car accelerates uniformly from rest to 10.4 m/s in 2.87 s. Find the work done on the car in this time interval. Answer in units of kJ. B) Find the average power delivered by the en- gine in this time interval. Answer in units of hp. C) Find the instantaneous power delivered by the engine at t = 1.5 s. Answer in units of hp.arrow_forwardA particle moves in the x-axis from x = 12.8 m to x = 23.7 m under the influence of a force where F is expressed in newtons and x is expressed in meters. Use numerical integration to determine the total work done by the force during the displacement. In the networks there are Various calculators for integrals are available.arrow_forward
- The force required to compress a non-standard spring varies as the spring is compressed, as shown by the plot of force vs displacement. Distances are x1 = 10, x2 = 25 cm, x3 = 55 cm, and x4=75cm, and the forces are F1 = 110 N and F2 = -60N. Calculate the work done in Joules, on the spring as it is compressed from origin to point x4.arrow_forwardA mechanic pushes a 2480-kg car from rest to a speed of ?v, doing 4.66e3 J of work in the process. During this time, the car moves 25.7 m. (Neglect the friction between car and road.) (a) Find ?v. m/s ( ± 0.02 m/s) (b) Determine the horizontal force exerted on the car. N ( ± 2 N)arrow_forward1. A force of F = 5.6 Ni + 9.7 Nj + 7.9 Nk is applied to a particle in space to move it at a distance r = 2.6mi - 5.8mj - 9.7mk . Determine the work done by force.arrow_forward
- A 12.0 kg box is given an initial push that starts it sliding across the floor. It eventually comes to a stop. If the box has an initial velocity of 3.5 m/s, how much work is done by friction to cause it to come to a stop? (Yes, you are correct, you do not know the coefficient of friction.)arrow_forwardThe spring-flex exercise system consists of a spring with one end fixed and a handle on the other end. The idea is that you exercise your muscles by stretching the spring from its natural length, which is 48 cm. If a 200 Newton force is required to keep the spring stretched to a length of 66 cm, how much work is required to stretch it from 62 cm to 76 cm? Your answer must include the correct units. Work=arrow_forward6. A force and a displacement are given in component form. What is the work done by this force? F =(si+2j+k)N Ar=(2i-3 +2%)m 24 )marrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press 
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
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