Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition
6
Work and Energy
Change chapter

6-1: Work, Constant Force
6-2: Work, Varying Force
6-3: Kinetic Energy; Work-Energy Principle
6-4 and 6-5: Potential Energy
6-6 and 6-7: Conservation of Mechanical Energy
6-8 and 6-9: Law of Conservation of Energy
6-10: Power

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 44
Q

A block of mass mm is attached to the end of a spring (spring stiffness constant kk), Fig. 6–43. The mass is given an initial displacement x0x_0 from equilibrium, and an initial speed v0v_0. Ignoring friction and the mass of the spring, use energy methods to find

  1. its maximum speed, and
  2. its maximum stretch from equilibrium, in terms of the given quantities.
Problem 44.
Figure 6-43.
A
  1. see video
  2. see video
  3. vmax=vo2+kxo2mv_{max} = \sqrt{v_o^2 + \dfrac{kx_o^2}{m}}
  4. xmax=xo2+mvo2kx_{max} = \sqrt{x_o^2 + \dfrac{mv_o^2}{k}}
Giancoli 7th Edition, Chapter 6, Problem 44 solution video poster
Padlock

In order to watch this solution you need to have a subscription.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. This spring is initially stretched some distance, x naught, and it's given some speed, v naught. So, it has some initial elastic potential energy and it has some kinetic energy. And the total of the elastic potential and the kinetic energy, that total amount of energy is gonna be the same throughout while it's going back and forth because there's no energy being lost to friction, we assume. Now in part (a), the maximum speed will occur when the block is at this spring's equilibrium position, when there's no potential energy and all of the energy is gonna be kinetic in this case. And so we'll do that for part (a). And then part (b) will have the maximum stretch happening when there's no speed; in other words, when the kinetic energy is zero. So for part (a), we have initial kinetic plus initial potential equals when we have maximum kinetic energy and no potential energy and because the spring isn't stretched at all, at this position. And that's one-half m v naught squared plus one-half k x naught squared equals one-half m v max squared. And then we can solve this for v max; the one-halves cancel everywhere divide each term by m, so this becomes just v naught squared and this becomes k x naught squared over m. And then take the square root of both sides, and we have this, v max is square root of v initial speed squared plus k times the initial stretch squared over mass. And then for the case, where we are finding the maximum stretch, we have the same initial kinetic and potential energies equals one-half k times the maximum stretch squared. And the one-halves cancel everywhere, divide each term by k and then take the square root of both sides and we have the maximum stretch is the square root of x naught squared plus m v naught squared over k.

Find us on:

Facebook iconTrustpilot icon
Giancoli Answers, including solutions and videos, is copyright © 2009-2024 Shaun Dychko, Vancouver, BC, Canada. Giancoli Answers is not affiliated with the textbook publisher. Book covers, titles, and author names appear for reference purposes only and are the property of their respective owners. Giancoli Answers is your best source for the 7th and 6th edition Giancoli physics solutions.