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.

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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.

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Concept explainers

Metrology of surface finish

In general terms, the application of scientific principles in the study of measurements is known as metrology. When speaking about measurement, it could be of time, length, microstructures, grain structures, internal crystal discontinuities, surface roughness, measurements of angles, height, width, and so on. While coming to the domain of mechanical engineering, metrology is considered the science of measurements of surface finish, length, surface texture, and angles.

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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 = 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

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