# Understanding Potential Energy and Speed**Problem Statement:**The figure shows a 0.536-kg frictionless particle's potential energy as a function of position along the x-axis. Find the particle's speed at \( x = 6 \, \text{m} \) if its speed at the origin is \( 5.1 \, \text{m/s} \).**Diagram Analysis:**- **Graph Description:** - The graph displays potential energy \( U(x) \) on the y-axis (measured in joules, J) and position \( x \) on the x-axis (measured in meters, m). - The curve traces the potential energy of the particle across various positions. - Notable points on the graph include several local minima and maxima, indicating varying levels of potential energy as the particle moves along the x-axis.- **Key Points on the Graph:** - At \( x = 0 \, \text{m} \), the particle's speed is given as \( 5.1 \, \text{m/s} \). - At \( x = 6 \, \text{m} \), the task is to determine the particle's speed.**Equation to Find Speed:**\[ v = \, _____ \, \text{m/s} \]**Instructions:**Record your numerical answer below, assuming three significant figures. Remember to include a "-" if/when necessary.---This exercise allows students to explore concepts of potential and kinetic energy conservation in a frictionless environment. Understanding the relationship between potential energy changes and speed is key to mastering these physics principles.

Name: # Understanding Potential Energy and Speed**Problem Statement:**The f
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Description: # Understanding Potential Energy and Speed**Problem Statement:**The figure shows a 0.536-kg frictionless particle's potential energy as a function of position along the x-axis. Find the particle's speed at \( x = 6 \, \text{m} \) if its speed at the

Given Data mass of the particle m = 0.536 kgsince friction is not present in the systen which implies Mechanical energy is conservedtaking the initial position at origin and final position of the system at x = 6mInitial Potential energy of the system from graph is Ui = 10 JInitial speed of particle at origin vi = 5.1 m/sInitial kinetic energy of the system Ti = 12mvi2 Ti = 12(0.536 kg)×5.1 m/s2 = 6.97 JTotal mechancial energy of the system is Hi =Ti + Ui Hi =(6.97+ 10) J Hi =16.97 Jlet vf denotes the speed of particle at x =6 mfinal Potential energy of particle as seen from graph Uf = 4 Jfinal Kinetic energy of particle Tf =12mvf2Total mechanical energy of the system Hf=Tf+UfHi=Hf16.97 = 4+TfTf = 12.9712mvf2 = 12.97vf2 = 2×12.970.536⇒vf = 6.95 m/s Answer : Speed of the particle at x = 6 m is 6.95 m/s

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Physics

The figure shows a 0.536-kg frictionless particle's potential energy as a function of position along the x-axis. Find the particle's speed at x = 6 m if its speed at the origin is 5.1 m/s. U (J) 10.0 8.0 6.0 4.0 2.0 M 12 3 4 V= 5 6 789 m/s x (m) Record your numerical answer below, assuming three significant figures. Remember to include a "-" if/when necessary.

The figure shows a 0.536-kg frictionless particle's potential energy as a function of position along the x-axis. Find the particle's speed at x = 6 m if its speed at the origin is 5.1 m/s. U (J) 10.0 8.0 6.0 4.0 2.0 M 12 3 4 V= 5 6 789 m/s x (m) Record your numerical answer below, assuming three significant figures. Remember to include a "-" if/when necessary.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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