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i Chrome File Edit View History Bookmarks People Window Help 52 33% D Fri 10:01 AM us. WileyPLUS Ahmad > d Secure! https://edugen.wileyplus.com/edugen/student/mainfr.uni : Apps V WileyPLUSDifferential calculus Ish University of South D Apple iCloud Yahoo D Bing W Wikipedia Facebook y Twitter LinkedIn Other Bookmarks n Shot WileyPLUS Haliday, Fundamentals of Physics, 10e 9.28 PM Calculus-based Physics I ⅈ (PH 201-202) Home Read, Study& Practice Gradebook ORION Downloadable eTextbook Assianment > Open Assignment FULL SCREEN PRINTER VERSION BACK NEXT odf ASSIGNMENT RESOURCES Chapter 08, Problem 038 201-11 The figure shows a plot of potential energy U versus position x of a 0,240 kg partidle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9.00 J, UC = 20.0 J and UD = 24.0 J. The particle is released at the point where u rrms a "potential hill" or"height" UB = 12.0 J, with kinetic energy 8.00 . what is the speed of the particle at (a): 3.50 m and (b)x 6.50 m? What is the position of the turning point on (c) the right side and (d) the left side? n Shot 11.56 PM 054 n Shot 8.32 PM Obiective n Shot x (m) 8.36 PM (a) Number (b) Number (c) Number (d) Number Units Units n Shot 47.15 PM Units Units All Rights Reserved. A Division of John Wiley &Sons;, Ins. Version 4.24.1.23 6,409 29

Explanation / Answer

a)
The initial mechanical energy
Ei = Ki + Ui
= 8 + 12
= 20 J
E = K + U
K (x = 3.5) = E – UA = 20 – 9
= 11.00 J
The definition of kinetic energy yields
K = (1/2)mv2
v = (2K/m)
= v = sqrt(2*11/0.240)
= 9.6 m/s

b)
K (x = 6.5) = E – UA = 20 – 0
= 20.00 J
The definition of kinetic energy yields
K = (1/2)mv2
v = (2K/m)
= v = sqrt(2*20/0.240)
= 12.9 m/s

c)
U = [(UD - 0)/(7-6)]*(x-7) = 24(x-7)

=> 20 = 24(x-7)
=> x = 7.83 m

d)
U = [(UA - UC)/(3-1)]×(x-1) + UC
U = -5.5(x - 1) + 20
The function takes the value of E = 20 J at
20 = -5.5(x - 1) + 20
x = 1 m

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