Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 7, Problem 54AP
The potential energy function for a system of particles is given by U(x) = −x3 + 2x2 + 3x, where x is the position of one particle in the system. (a) Determine the force Fx on the particle as a function of x. (b) For what values of x is the force equal to zero? (c) Plot U(x) versus x and Fx versus x and indicate points of stable and unstable equilibrium.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A two-dimensional, conservative force is zero on the x- and y-axes, andsatisfies the condition ⎛⎝dFx /dy⎞⎠ =⎛⎝dFy /dx⎞⎠ =⎛⎝4 N/m3⎞⎠xy . What is the magnitude of the force at the pointx = y = 1 m?
The potential energy of a system is given by:
U(x,y,z)=5(J/m^2) x^2 + 7(J/m^3) xy^2 + 8(J/m^2) zy
Find:
The force acting on the system. Write the forces as the sum of its components.
The magnitude of the force when x=1, y=0, z=2
A block with mass m = 2.20 kg is placed against a spring on a frictionless incline with angle e = 30.0°. (The block is not attached to the spring.) The spring, with spring constant k = 21.0 N/cm, is compressed 17.0 cm and then released.
(a) What is the elastic potential energy of the compressed spring?
(b) What is the change in the gravitational potential energy of the block-Earth system as the block moves from the release point to its highest point on the incline?
(c) How far along the incline is the highest point from the release point?
Chapter 7 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 7.2 - Prob. 7.1QQCh. 7.2 - shows four situations in which a force is applied...Ch. 7.3 - Which of the following statements is true about...Ch. 7.4 - A dart is inserted into a spring-loaded dart gun...Ch. 7.5 - A dart is inserted into a spring-loaded dart gun...Ch. 7.6 - Choose the correct answer. The gravitational...Ch. 7.6 - A ball is connected to a light spring suspended...Ch. 7.8 - What does the slope of a graph of U(x) versus x...Ch. 7 - Prob. 1OQCh. 7 - If the net work done by external forces on a...
Ch. 7 - Prob. 3OQCh. 7 - A cart is set rolling across a level table, at the...Ch. 7 - Let N represent the direction horizontally north,...Ch. 7 - Prob. 6OQCh. 7 - Prob. 7OQCh. 7 - As a simple pendulum swings back and forth, the...Ch. 7 - Bullet 2 has twice the mass of bullet 1. Both are...Ch. 7 - Prob. 10OQCh. 7 - If the speed of a particle is doubled, what...Ch. 7 - Prob. 12OQCh. 7 - Prob. 13OQCh. 7 - A certain spring that obeys Hookes law is...Ch. 7 - A cart is set rolling across a level table, at the...Ch. 7 - Prob. 16OQCh. 7 - Can a normal force do work? If not, why not? If...Ch. 7 - Object 1 pushes on object 2 as the objects move...Ch. 7 - Prob. 3CQCh. 7 - (a) For what values of the angle u between two...Ch. 7 - Prob. 5CQCh. 7 - Discuss the work done by a pitcher throwing a...Ch. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - Prob. 10CQCh. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Cite two examples in which a force is exerted on...Ch. 7 - A shopper in a supermarket pushes a cart with a...Ch. 7 - Prob. 2PCh. 7 - In 1990, Walter Arfeuille of Belgium lifted a...Ch. 7 - The record number of boat lifts, including the...Ch. 7 - A block of mass m = 2.50 kg is pushed a distance d...Ch. 7 - Spiderman, whose mass is 80.0 kg, is dangling on...Ch. 7 - Prob. 7PCh. 7 - Vector A has a magnitude of 5.00 units, and vector...Ch. 7 - Prob. 9PCh. 7 - Find the scalar product of the vectors in Figure...Ch. 7 - Prob. 11PCh. 7 - Using the definition of the scalar product, find...Ch. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - A particle is subject to a force Fx that varies...Ch. 7 - In a control system, an accelerometer consists of...Ch. 7 - When a 4.00-kg object is hung vertically on a...Ch. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - A small particle of mass m is pulled to the top of...Ch. 7 - The force acting on a particle is Fx = (8x 16),...Ch. 7 - When different loads hang on a spring, the spring...Ch. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Review. The graph in Figure P7.20 specifies a...Ch. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - A 0.600-kg particle has a speed of 2.00 m/s at...Ch. 7 - A 4.00-kg particle is subject to a net force that...Ch. 7 - A 2 100-kg pile driver is used to drive a steel...Ch. 7 - Review. In an electron microscope, there is an...Ch. 7 - Review. You can think of the workkinetic energy...Ch. 7 - Prob. 38PCh. 7 - Review. A 5.75-kg object passes through the origin...Ch. 7 - A 1 000-kg roller coaster car is initially at the...Ch. 7 - A 0.20-kg stone is held 1.3 m above the top edge...Ch. 7 - Prob. 42PCh. 7 - A 4.00-kg particle moves from the origin to...Ch. 7 - Prob. 44PCh. 7 - A force acting on a particle moving in the xy...Ch. 7 - Prob. 46PCh. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - For the potential energy curve shown in Figure...Ch. 7 - A right circular cone can theoretically be...Ch. 7 - The potential energy function for a system of...Ch. 7 - Prob. 55APCh. 7 - A particle moves along the xaxis from x = 12.8 m...Ch. 7 - Prob. 57APCh. 7 - Prob. 58APCh. 7 - Prob. 59APCh. 7 - Why is the following situation impossible? In a...Ch. 7 - Prob. 61APCh. 7 - Prob. 62APCh. 7 - An inclined plane of angle = 20.0 has a spring of...Ch. 7 - Prob. 64APCh. 7 - Prob. 65APCh. 7 - A particle of mass m = 1.18 kg is attached between...Ch. 7 - Prob. 67CP
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 block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle = 25.0 below the horizontal as shown in Figure P6.3. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block. Figure P6.3arrow_forwardConsider a particle on which a force acts that depends on the position of the particle. This force is given by . Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x-axis.arrow_forwardAssume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50 cm and holds it in position with a force of 150 N. If the mass of the arrow is 50 g and the “spring” is massless, what is the speed of the arrow immediately after it leaves the bow?arrow_forward
- A 4.00-kg particle moves along the x axis. Its position O varies with time according to x = t + 2.0t3, where x is in meters and t is in seconds. Find (a) the kinetic energy of the particle at any time t (b) the acceleration of the particle and the force acting on it at time t, (c) the power being delivered to the particle at time t and (d) the work done on the particle in the interval t = 0 to t = 2.00 s.arrow_forwardA 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 block is placed on top of a vertical spring, and the spring compresses. Figure P8.24 depicts a moment in time when the spring is compressed by an amount h. a. To calculate the change in the gravitational and elastic potential energies, what must be included in the system? b. Find an expression for the change in the systems potential energy in terms of the parameters shown in Figure P8.24. c. If m = 0.865 kg and k = 125 N/m, find the change in the systems potential energy when the blocks displacement is h = 0.0650 m, relative to its initial position. FIGURE P8.24arrow_forward
- 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 block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P7.79). The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point , the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The blocks speed at the bottom of the track is = 12.0 m/s, and the block experiences an average friction force of 7.00 N while sliding up the track. (a) What is x? (b) If the block were to reach the top of the track, what would be its speed at that point? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top?arrow_forwardAn object of mass m = 5.8 kg moves under the influence of one force. That force causes the object to move along a path given by x = 6.0 + 5.0t + 2.0t2, where x is in meters and t is in seconds. Calculate the work done by the force on the object from t = 2.0 s to t = 7.0 s.arrow_forward
- A 4.00-kg particle moves from the origin to position ©, having coordinates x = 5.00 m and y = 5.00 m (Fig. P6.42). One force on the particle is the gravitational force acting in the negative y direction. Using Equation 6.3, calculate the work done by the gravitational force on the particle as it goes from O to © along (a) the purple path, (b) the red path, and (c) the blue path. (d) Your results should all be identical. Why? Figure P6.42 Problems 42 through 45.arrow_forwardA 4.00-kg particle moves from the origin to position , having coordinates x = 5.00 m and y = 5.00 m (Fig. P7.31). One force on the particle is the gravitational force acting in the negative y direction. Using Equation 7.3, calculate the work done by the gravitational force on the particle as it goes from O to along (a) the purple path, (b) the red path, and (c) the blue path, (d) Your results should all be identical. Why? Figure P7.31arrow_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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher: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
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Mechanical work done (GCSE Physics); Author: Dr de Bruin's Classroom;https://www.youtube.com/watch?v=OapgRhYDMvw;License: Standard YouTube License, CC-BY