Problem #2. A brass cylinder with uniform density, b = 8505 kg/m3, is hung from
ID: 1482604 • Letter: P
Question
Problem #2. A brass cylinder with uniform density, b = 8505 kg/m3, is hung from a spring scale by a lightweight string as shown in the figure. When the cylinder was suspended in air (A), the tension in the string was TA = 653.0 N. When completely submerged in an unknown fluid (B), the tension was TB = 574.9 N. You can neglect the weight of the string. SYMBOLIC VARIABLES b, TA, TB, and g. Object and Spring Scale Your answers need to have 4 significant figures. (a) What are the actual and apparent weights of the cylinder? mg = 9 N Wapp = 10 N (b) What is the magnitude of the buoyant force on the cylinder when it's suspended in the fluid? FB = 11 N (c) Write a symbolic expression for the volume of the cylinder then calculate its numeric value. Vcyl = = 13 m3 (d) Write a symbolic expression for the density of the fluid then calculate its numeric value. f = = 15 kg/m3 (e) Suppose that a floor scale was used to measure the weight of the fluid-filled beaker with and without the cylinder. How much would the reading on the floor scale change when the cylinder was suspended in the beaker of fluid? Floor Scale with Cylinder: 16 N
Explanation / Answer
part a:
actual weight=tension in the string when cylinder is in air=653 N
apparent weight=when cylinder is submerged in water=574.9 N
part b:
buoyant force=actual weight-apparent weight=78.1 N
part c:
weight of the cylinder=mass*g
=volume*density*g
==>volume=actual weight/(density*g)
=Ta/(pho_b*g)
using the values for different symbols,
volume=653/(8505*9.8)=7.8345*10^(-3) m^3
part d:
as the entire cylinder is submerged, water removed by cylinder=volume of cylinder
buyoant force=volume of cylinder*density of fluid*g
density of fluid=buoyant force/(volume of cylinder*g)
=78.1/(7.8345*10^(-3)*9.8)=1017.217 kg/m^3
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