Pad 6:45 PM a session-masteringphysics.com c Home wichita.edu Pearson\'s MyLab &

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Pad 6:45 PM a session-masteringphysics.com c Home wichita.edu Pearson's MyLab & Mastering Physics HW14 Wichita State Un PHYSICS-I-B 14.24 nhanced with Video Solution Problem 14.24 Enhanced with Video Solution Styrofoam has a density of 300 kg/m3.What is the maximum mass that can hang without snkingfrom a60.0 cm dameter styrosoam sphere in water? You may want to review (DRages 370372) For help with math skills, you may want to review: For general problem-solving tips and strategies for this topic, you may want to view a video Tutor Solution ofEloring howling bal Part A Assume the volume of the mass is negligible compared to that of the sphere. Express your answer with the appropriate units. 0.15 kg Submit M Answers Give Up Incorrect: Try Again: 3 attempts remaining Con Provide Feedback

Explanation / Answer

Problem 14.24

Given

   diameter of the styrofoam is d = 60 cm = 0.6 m

   radius is r = 0.3 m

volume of the sphere is V = (4/3) pir^3
           V = (4/3)pi*0.3^3 m^3
           V = 0.1131 m^3

from this the total mass of the sphere is 113.1 kg

now from the information mass of the sphere is m = density *volume

                       m = 300*0.1131 kg

                       m = 33.93 kg

so the additional mass required for the sphere to sink is = 113.1- 33.93 kg = 79.17 kg
  

Problem 14.20

  
mass of rock m = 3.6 kg,
density of the rock rho =4700 kg/m^3

half of the rock's volume is under water

now volume of the rock is V = m/rho = 3.6/4700 m^3 = 0.76596*10^-3 m^3

as half of the rock's volume is under water , then volume of the displaced water is V_w = V/2 = 0.38298*10^-3 m^3

the forces acting on the rock ar e

weight w = m*g = 3.6*9.8 N = 35.28 N downward and

   tension in the string upward T

and the Buoyance force upward = rho*v*g= 1000*0.38298*10^-3*9.8 N = 3.753204 N

writing the forces so that the rock is in equilibrium , equating all the force to zero then

   T+fb-W = 0

   T = W -fb

   T = 35.28-3.753204 N

   T = 31.526796 N

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