A smooth aluminum sphere hangs in air on a 0.5 m-long cable. Thesphere has a diameter of 10 cm and weighs 1.5 N (it is hollow). It isobserved that a steady wind causes the sphere and cable to be displacedso that = 20°. Assume that the weight of the cable and the drag forceon the cable are negligible.(a) What is the magnitude of the (horizontal) drag force on the sphere?(b) What is the wind speed U?Answer: (a) D≈ 0.55 N, (b) U≈ 15 m/sU

(a) To find: The magnitude of drag force. Given: The weight of the sphere is W=1.5 N. The radius of the sphere is r=5 cm1 m100 cm=0.05 m. The density of the air is ρ=1.29 kg/m3. The drag coefficient for sphere is Cd=0.47. FBD: The free body diagram of the sphere is shown below.Calculation: Balancing the vertical forces F cos20=W⇒F=1.5cos20=1.596 N The horizontal drag force can be obtained as D=F sin20=1.596×sin20=0.5459≈0.55 N Thus, the horizontal drag force on the sphere is 0.55 N.(b) To find: The wind speed. Calculation: The wind speed can be obtained as D=Cd·12ρAU20.55=0.47×12×1.29×πr2×U2⇒U=0.55×20.47×1.29×π×0.052=15.198 ≈15 m/s Thus, the wind speed is 15 m/s.

Engineering

Mechanical Engineering

A smooth aluminum sphere hangs in air on a 0.5 m-long cable. The sphere has a diameter of 10 cm and weighs 1.5 N (it is hollow). It is observed that a steady wind causes the sphere and cable to be displaced so that 0= 20°. Assume that the weight of the cable and the drag force on the cable are negligible. (a) What is the magnitude of the (horizontal) drag force on the sphere? (b) What is the wind speed U? Answer: (a) D≈ 0.55 N, (b) U≈ 15 m/s U

A smooth aluminum sphere hangs in air on a 0.5 m-long cable. The sphere has a diameter of 10 cm and weighs 1.5 N (it is hollow). It is observed that a steady wind causes the sphere and cable to be displaced so that 0= 20°. Assume that the weight of the cable and the drag force on the cable are negligible. (a) What is the magnitude of the (horizontal) drag force on the sphere? (b) What is the wind speed U? Answer: (a) D≈ 0.55 N, (b) U≈ 15 m/s U

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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