Essential University Physics
4th Edition
ISBN: 9780134988559
Author: Wolfson, Richard
Publisher: Pearson Education,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 7, Problem 68P
Biomechanical engineers developing artificial limbs for prosthetic and robotic applications have developed a two-spring design for their replacement Achilles tendon. The first spring has constant k and the second ak, where a > 1. When the artificial tendon is stretched from x = 0 to x = x1, only the first spring is engaged. For x > x1 a mechanism engages the second spring, giving a configuration like that described in part (a) of Chapter 4’s Problem 62. Find an expression for the energy stored in the artificial tendon when it’s stretched a distance 2x1.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
I'm not sure how to work this problem. The solutions give the answer to be V1f=0.20 m/s, v2f=2.75 m/s for part A. For part B the solutions give the answer to be x=0.22 for maximum compression for the spring. I attached a picture of the problem.
A spring attached to a mass is displaced 30 cm from its equilibrium position, At this
point it has 2.0 J of potential energy. What is the spring constant, k, of the spring?
O 44 Nm
3600 Nm
0.004 Nm
0.36 Nm
A pen contains a spring with a spring
constant of 295 N/m. When the tip of the
pen is in its retracted position, the spring is
compressed 5.20 mm from its unstrained
length. In order to push the tip out and lock it
into its writing position, the spring must be
compressed an additional 6.90 mm. How
much work is done by the spring force to
ready the pen for writing? Be sure to include
the proper algebraic sign with your answer.
Number
i
Units
Chapter 7 Solutions
Essential University Physics
Ch. 7.1 - Suppose it takes the same amount of work to push a...Ch. 7.2 - Gravitational force actually decreases with...Ch. 7.3 - A bowling ball is tied to the end of a long rope...Ch. 7.4 - For which of the following systems is (1)...Ch. 7.5 - A bowling ball is tied to the end of a long rope...Ch. 7.6 - The figure shows the potential energy associated...Ch. 7 - Figure 7.14 shows force vectors at different...Ch. 7 - Is the conservation-of-mechanical-energy principle...Ch. 7 - Why cant we define a potential energy associated...Ch. 7 - Can potential energy be negative? Can kinetic...
Ch. 7 - If the potential energy is zero at a given point,...Ch. 7 - If the difference in potential energy between two...Ch. 7 - If the difference in potential energy between two...Ch. 7 - If conservation of energy is a law of nature, why...Ch. 7 - Determine the work you would have to do to move a...Ch. 7 - Now lake Fig. 7.15 lo lie in a vertical plane, and...Ch. 7 - Rework Example 7.1, now taking the zero of...Ch. 7 - Find the potential energy associated with a 70-kg...Ch. 7 - You fly from Bostons Logan Airport, at sea level,...Ch. 7 - How much energy can be stored in a spring with k =...Ch. 7 - How far would you have to stretch a spring with k...Ch. 7 - A biophysicist grabs the ends of a DNA strand with...Ch. 7 - A skier starts down a frictionless 32 slope. After...Ch. 7 - A 10,000-kg Navy jet lands on an aircraft carrier...Ch. 7 - A 120-g arrow is shot vertically from a bow whose...Ch. 7 - In a railroad yard, a 35,000-kg boxcar moving at...Ch. 7 - You work for a toy company, and youre designing a...Ch. 7 - A 54-kg ice skater pushes off the wall of the...Ch. 7 - Prob. 23ECh. 7 - A particle slides along the frictionless track...Ch. 7 - A particle slides back and forth on a frictionless...Ch. 7 - A particle is trapped in a potential well...Ch. 7 - Example 7.3: A climbing rope is designed to exert...Ch. 7 - Example 7.3: A climbing rope exerts a force given...Ch. 7 - Example 7.3: The force on an electron in an...Ch. 7 - Example 7.3: The potential energy of an electron...Ch. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Example 7.5: In a railroad switchyard, a rail car...Ch. 7 - Prob. 34ECh. 7 - The reservoir at Northfield Mountain Pumped...Ch. 7 - A carbon monoxide molecule can be modeled as a...Ch. 7 - A more accurate expression for the force law of...Ch. 7 - For small stretches, the Achilles tendon can be...Ch. 7 - A particle moves along the x-axis under the...Ch. 7 - As a highway engineer, youre asked to design a...Ch. 7 - A spring of constant k, compressed a distance x,...Ch. 7 - A child is on a swing whose 3.2-m-long chains make...Ch. 7 - With x x0 = h and a = g, Equation 2.11 gives the...Ch. 7 - The nuchal ligament is a cord-like structure that...Ch. 7 - A 200-g block slides back and forth on a...Ch. 7 - Automotive standards call for bumpers that sustain...Ch. 7 - A block slides on the frictionless loop-the-loop...Ch. 7 - The maximum speed of the pendulum bob in a...Ch. 7 - A mass m is dropped from height h above the top of...Ch. 7 - A particle with total energy 3.5 J is trapped in a...Ch. 7 - (a) Derive an expression for the potential energy...Ch. 7 - In ionic solids such as NaCl (salt), the potential...Ch. 7 - Repeat Exercise 19 for the case when the...Ch. 7 - As an energy-efficiency consultant, youre asked to...Ch. 7 - A spring of constant k = 340 N/m is used to launch...Ch. 7 - A bug slides back and forth in a bowl 15 cm deep,...Ch. 7 - A 190-g block is launched by compressing a spring...Ch. 7 - Prob. 58PCh. 7 - An 840-kg roller-coaster car is launched from a...Ch. 7 - Prob. 60PCh. 7 - A child sleds down a frictionless hill whose...Ch. 7 - A bug lands on top of the frictionless, spherical...Ch. 7 - A particle of mass m is subject to a force...Ch. 7 - A block of weight 4.5 N is launched up a 30...Ch. 7 - Your engineering department is asked to evaluate...Ch. 7 - Your roommate is writing a science fiction novel...Ch. 7 - You have a summer job at your universitys zoology...Ch. 7 - Biomechanical engineers developing artificial...Ch. 7 - Blocks with different masses are pushed against a...Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....
Additional Science Textbook Solutions
Find more solutions based on key concepts
The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see...
College Physics
Using the definitions in Eqs. 1.1 and 1.4, and appropriate diagrams, show that the dot product and cross produc...
Introduction to Electrodynamics
5.33 You are lowering two boxes, one on top of the other, down a ramp by pulling on a rope parallel to the surf...
University Physics with Modern Physics (14th Edition)
59. Consider the circuit in Figure 21.64 (a) Just after the switch is closed, what is the current through each ...
College Physics (10th Edition)
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective
Which is hotter, the piece of mantle material at Position A or the piece of mantle material at Position D? Expl...
Lecture- Tutorials for Introductory Astronomy
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 small particle of mass m is pulled to the top of a friction less half-cylinder (of radius R) by a light cord that passes over the top of the cylinder as illustrated in Figure P7.15. (a) Assuming the particle moves at a constant speed, show that F = mg cos . Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times. (b) By directly integrating W=Fdr, find the work done in moving the particle at constant speed from the bottom to the top of the hall-cylinder. Figure P7.15arrow_forwardA small object is attached to two springs of the same length l, but with different spring constants k1 and k2 as shown in Figure P9.31. Initially, both springs are relaxed. The object is then displaced straight along the x axis from xi to xf. Find an expression for the work done by the springs on the object.arrow_forwardConsider the data for a block of mass m = 0.250 kg given in Table P16.59. Friction is negligible. a. What is the mechanical energy of the blockspring system? b. Write expressions for the kinetic and potential energies as functions of time. c. Plot the kinetic energy, potential energy, and mechanical energy as functions of time on the same set of axes. Problems 5965 are grouped. 59. G Table P16.59 gives the position of a block connected to a horizontal spring at several times. Sketch a motion diagram for the block. Table P16.59arrow_forward
- The two springs are identical, with unstretched length 0.4 m. When the 50-kg mass is suspended at B, the length of each spring increases to 0.6 m. What is the spring constant k?arrow_forwardA certain spring has a length of 47.6 cm when a 4.49 kg mass is hung from it and a length of 58.6 cm when a 8.23 kg mass is hung from it. What is the spring constant for this spring in N/m?arrow_forwardThe block of 4.5 kg is attached to a spring with spring constant k = -1.6 and extended to an initial displacement of 9 cm. It takes 20 s to make a full cycle. What is the displacement after 7s?arrow_forward
- How far must you stretch a spring with k = 2000_N/m to store 300 J of energy? Express your answer using two significant figures. 195 Π ΑΣΦ As = 199 ? | m Εarrow_forward07 Prove that the force F = x²yi + y²xj follows from a function potential energy and to determine it.arrow_forwardThe drawing shows three situations in which a block is attached to a spring. The position labeled "O m" represents the unstrained position of the spring. The block is moved from an initial position xo to a final position Xf, the magnitude of the displacement being denoted by the symbol s. Suppose the spring has a spring constant of k = 74.0 N/m. Using the data provided in the drawing, determine the total work done by the restoring force of the spring for each situation. In the case of zero put your result as "+0". (a) Position of box when spring is unstrained (b) -3.00 m mini -3.00 m (a)W= (b)W= (c)W= < < < Om +1.00 m Mi Om +1.00 m N Om +3.00 m +3.00 m < < <arrow_forward
- Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in the figure below. When the main leaf spring is compressed by distance yo, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 4.90 x 105 N/m, the helper spring constant is 3.60 x 105 N/m, and yo = 0.500 m. Truck body Axle (a) What is the compression of the leaf spring for a load of 4.70 x 105 N? 0.87 Your response differs from the correct answer by more than 10%. Double check your calculations. m (b) How much work is done in compressing the springs? 0.855 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. Jarrow_forwardThe drawing shows three situations in which a block is attached to a spring. The position labeled "O m" represents the unstrained position of the spring. The block is moved from an initial position xo to a final position Xf, the magnitude of the displacement being denoted by the symbol s. Suppose the spring has a spring constant of k = 74.0 N/m. Using the data provided in the drawing, determine the total work done by the restoring force of the spring for each situation. In the case of zero put your result as "+0". Position of box when spring is unstrained (a) (b) -3.00 m (c) min -3.00 m (a)W= (b)W= (c)W= < < < 0m i +1.00 m Om +1.00 m Om +3.00 m +3.00 m < <arrow_forwardA student releases the 3.6kg bob of a 2.01m long pendulum from the position shown. Neglect loss. What is the pendulum's height (h) above its lowest point? unit v What is the pendulum's maximum speed during the swing? 21° unit v What is the tension in the string at the lowest point? unit harrow_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 Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
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
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Work and Energy - Physics 101 / AP Physics 1 Review with Dianna Cowern; Author: Physics Girl;https://www.youtube.com/watch?v=rKwK06stPS8;License: Standard YouTube License, CC-BY