Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 8, Problem 70PQ
A block is attached to a spring, and the block makes contact with a frictionless surface. Sketch a graph of the potential energy of the block–spring system as a function of position along with the corresponding system as in Figure 8.16 (page 224). Use this sketch to show how the block can move to the left from a positive position to a negative position and decrease the elastic potential energy of the system.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 8.1 - Comet Halleys Orbital Parameters Figure 8.1 shows...Ch. 8.2 - Prob. 8.2CECh. 8.2 - Prob. 8.3CECh. 8.3 - In Figure 8.11, a person launches a ball off of a...Ch. 8 - Case Study From Figure 8.1B for Comet Halley, is...Ch. 8 - Estimate the kinetic energy of the following: a....Ch. 8 - Prob. 3PQCh. 8 - Prob. 4PQCh. 8 - A 0.430-kg soccer ball is kicked at an initial...Ch. 8 - Prob. 6PQ
Ch. 8 - According to a scaled woman, a 67.7-kg man runs...Ch. 8 - Prob. 8PQCh. 8 - Prob. 9PQCh. 8 - Prob. 10PQCh. 8 - Prob. 11PQCh. 8 - Prob. 12PQCh. 8 - Prob. 13PQCh. 8 - In each situation shown in Figure P8.12, a ball...Ch. 8 - Prob. 15PQCh. 8 - Prob. 16PQCh. 8 - Prob. 17PQCh. 8 - Prob. 18PQCh. 8 - A ball of mass 0.40 kg hangs straight down on a...Ch. 8 - Prob. 20PQCh. 8 - Prob. 21PQCh. 8 - Prob. 22PQCh. 8 - One type of toy car contains a spring that is...Ch. 8 - A block is placed on top of a vertical spring, and...Ch. 8 - Rubber tends to be nonlinear as an elastic...Ch. 8 - A block is hung from a vertical spring. The spring...Ch. 8 - A spring of spring constant k lies along an...Ch. 8 - A block on a frictionless, horizontal surface is...Ch. 8 - A falcon is soaring over a prairie, flying at a...Ch. 8 - A stellar black hole may form when a massive star...Ch. 8 - A newly established colony on the Moon launches a...Ch. 8 - The Flybar high-tech pogo stick is advertised as...Ch. 8 - An uncrewed mission to the nearest star, Proxima...Ch. 8 - A small ball is tied to a string and hung as shown...Ch. 8 - Prob. 35PQCh. 8 - Prob. 36PQCh. 8 - Prob. 37PQCh. 8 - Prob. 38PQCh. 8 - Figure P8.39 shows two bar charts. In each, the...Ch. 8 - Prob. 40PQCh. 8 - If a spacecraft is launched from the Moon at the...Ch. 8 - A 1.50-kg box rests atop a massless vertical...Ch. 8 - A man unloads a 5.0-kg box from a moving van by...Ch. 8 - Starting at rest, Tina slides down a frictionless...Ch. 8 - Prob. 45PQCh. 8 - Karen and Randy are playing with a toy car and...Ch. 8 - An intrepid physics student decides to try bungee...Ch. 8 - A block of mass m = 1.50 kg attached to a...Ch. 8 - Prob. 49PQCh. 8 - A jack-in-the-box is actually a system that...Ch. 8 - A side view of a half-pipe at a skateboard park is...Ch. 8 - Prob. 52PQCh. 8 - Prob. 53PQCh. 8 - Prob. 54PQCh. 8 - A particle moves in one dimension under the action...Ch. 8 - Prob. 56PQCh. 8 - Prob. 57PQCh. 8 - Prob. 58PQCh. 8 - Prob. 59PQCh. 8 - Much of the mass of our Milky Way galaxy is...Ch. 8 - A stellar black hole may form when a massive star...Ch. 8 - Prob. 62PQCh. 8 - Prob. 63PQCh. 8 - FIGURE 8.38 Comparison of a circular and an...Ch. 8 - A 50.0-g toy car is released from rest on a...Ch. 8 - Prob. 66PQCh. 8 - The Earths perihelion distance (closest approach...Ch. 8 - After ripping the padding off a chair you are...Ch. 8 - A In a classic laboratory experiment, a cart of...Ch. 8 - A block is attached to a spring, and the block...Ch. 8 - At the start of a basketball game, a referee...Ch. 8 - At the start of a basketball game, a referee...Ch. 8 - Prob. 73PQCh. 8 - Prob. 74PQCh. 8 - At 220 m, the bungee jump at the Verzasca Dam in...Ch. 8 - Prob. 76PQCh. 8 - A block of mass m1 = 4.00 kg initially at rest on...Ch. 8 - A Eric is twirling a ball of mass m = 0.150 kg...Ch. 8 - Prob. 79PQCh. 8 - Prob. 80PQCh. 8 - Prob. 81PQCh. 8 - Prob. 82PQCh. 8 - Prob. 83PQCh. 8 - Prob. 84PQ
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.Similar questions
- A particle moves in one dimension under the action of a conservative force. The potential energy of the system is given by the graph in Figure P8.55. Suppose the particle is given a total energy E, which is shown as a horizontal line on the graph. a. Sketch bar charts of the kinetic and potential energies at points x = 0, x = x1, and x = x2. b. At which location is the particle moving the fastest? c. What can be said about the speed of the particle at x = x3? FIGURE P8.55arrow_forwardA horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P8.35. (a) The block is pulled to a position xi = 6.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 6.00 cm from equilibrium and when the block passes through equilibrium. (b) Find the speed of the block as it passes through the equilibrium point. (c) What is the speed of the block when it is at a position xi/2 = 3.00 cm? (d) Why isnt the answer to part (c) half the answer to part (b)? Figure P8.35arrow_forwardConsider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position x=0 , is moving with speed v in the x-direction. What is the total kinetic energy of the spring? (Hint: First express the kinetic energy of an infinitesimal element of the spring dm in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)arrow_forward
- A jack-in-the-box is actually a system that consists of an object attached to the top of a vertical spring (Fig. P8.50). a. Sketch the energy graph for the potential energy and the total energy of the springobject system as a function of compression distance x from x = xmax to x = 0, where xmax is the maximum amount of compression of the spring. Ignore the change in gravitational potential energy. b. Sketch the kinetic energy of the system between these points the two distances in part (a)on the same graph (using a different color). FIGURE P8.50 Problems 50 and 79arrow_forwardA block on a frictionless, horizontal surface is attached to two springs as shown in Figure P8.28. The block is displaced, compressing one spring and stretching the other. a. Find an expression for the change in the blocksprings systems potential energy in terms of the parameters given in the figure. b. Is it possible to displace the block in such a way that the systems potential energy does not change? FIGURE P8.28arrow_forwardAfter ripping the padding off a chair you are refurbishing, you notice that there are six springs beneath, which are intended to contribute equally in supporting your weight when you sit. You find a tag that indicates that the springs are identical and that each has a spring constant of 1.5 103 N/m. What would be the elastic potential energy stored in the six-spring system if you were to sit on the chair?arrow_forward
- (a) Sketch a graph of the potential energy function U(x)=kx2/2+Aex2 where k , A, and are constants. (b) What is the force corresponding to this potential energy? (c) Suppose a particle of mass in moving with this potential energy has a velocity v when its position is x = . Show that the particle does not pass 2+2 through the origin unless Amv2=k22(1e a 2 ) .arrow_forwardA nonconstant force is exerted on a particle as it moves in the positive direction along the x axis. Figure P9.26 shows a graph of this force Fx versus the particles position x. Find the work done by this force on the particle as the particle moves as follows. a. From xi = 0 to xf = 10.0 m b. From xi = 10.0 to xf = 20.0 m c. From xi = 0 to xf = 20.0 m FIGURE P9.26 Problems 26 and 27.arrow_forwardA small 0.65-kg box is launched from rest by a horizontal spring as shown in Figure P9.50. The block slides on a track down a hill and comes to rest at a distance d from the base of the hill. The coefficient of kinetic friction between the box and the track is 0.35 along the entire track. The spring has a spring constant of 34.5 N/m, and is compressed 30.0 cm with the box attached. The block remains on the track at all times. a. What would you include in the system? Explain your choice. b. Calculate d. c. Compare your answer with your answer to Problem 50 if you did that problem.arrow_forward
- A particle moves in the xy plane (Fig. P9.30) from the origin to a point having coordinates x = 7.00 m and y = 4.00 m under the influence of a force given by F=3y2+x. a. What is the work done on the particle by the force F if it moves along path 1 (shown in red)? b. What is the work done on the particle by the force F if it moves along path 2 (shown in blue)? c. What is the work done on the particle by the force F if it moves along path 3 (shown in green)? d. Is the force F conservative or nonconservative? Explain. FIGURE P9.30 In each case, the work is found using the integral of Fdr along the path (Equation 9.21). W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz) (a) The work done along path 1, we first need to integrate along dr=dxi from (0,0) to (7,0) and then along dr=dyj from (7,0) to (7,4): W1=x=0;y=0x=7;y=0(3y2i+xj)(dxi)+x=7;y=0x=7;y=4(3y2i+xj)(dyj) Performing the dot products, we get W1=x=0;y=0x=7;y=03y2dx+x=7;y=0x=7;y=4xdy Along the first part of this path, y = 0 therefore the first integral equals zero. For the second integral, x is constant and can be pulled out of the integral, and we can evaluate dy. W1=0+x=7;y=0x=7;y=4xdy=xy|x=7;y=0x=7;y=4=28J (b) The work done along path 2 is along dr=dyj from (0,0) to (0,4) and then along dr=dxi from (0,4) to (7,4): W2=x=0;y=0x=0;y=4(3y2i+xj)(dyj)+x=0;y=4x=7;y=4(3y2i+xj)(dyi) Performing the dot product, we get: W2=x=0;y=0x=0;y=4xdy+x=0;y=4x=7;y=43y2dx Along the first part of this path, x = 0. Therefore, the first integral equals zero. For the second integral, y is constant and can be pulled out of the integral, and we can evaluate dx. W2=0+3y2x|x=0;y=4x=7;y=4=336J (c) To find the work along the third path, we first write the expression for the work integral. W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz)W=rtrf(3y2dx+xdy)(1) At first glance, this appears quite simple, but we cant integrate xdy=xy like we might have above because the value of x changes as we vary y (i.e., x is a function of y.) [In parts (a) and (b), on a straight horizontal or vertical line, only x or y changes]. One approach is to parameterize both x and y as a function of another variable, say t, and write each integral in terms of only x or y. Constraining dr to be along the desired line, we can relate dx and dy: tan=dydxdy=tandxanddx=dytan(2) Now, use equation (2) in (1) to express each integral in terms of only one variable. W=x=0;y=0x=7;y=43y2dx+x=0;y=0x=7;y=4xdyW=y=0y=43y2dytan+x=0x=7xtandx We can determine the tangent of the angle, which is constant (the angle is the angle of the line with respect to the horizontal). tan=4.007.00=0.570 Insert the value of the tangent and solve the integrals. W=30.570y33|y=0y=4+0.570x22|x=0x=7W=112+14=126J (d) Since the work done is not path-independent, this is non-conservative force. Figure P9.30ANSarrow_forwardA particle of mass m = 1.18 kg is attached between two identical springs on a frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in Figure P7.50. Show that the force exerted by the springs on the particle is F=2kx(1Lx2+L2)i (b) Show that the potential energy of the system is U(x)=kx2+2kL(Lx2+L2) (c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/m. (d) If the panicle is pulled 0.500 m to the right and then released, what is its speed when it reaches x = 0? Figure P7.50arrow_forwardA block is connected to a spring that is suspended from the ceiling. Assuming air resistance is ignored, describe the energy transformations that occur within die system consisting of the block, the Earth, and the spring when the block is set into vertical motion.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Kinetic Energy and Potential Energy; Author: Professor Dave explains;https://www.youtube.com/watch?v=g7u6pIfUVy4;License: Standard YouTube License, CC-BY