One of the popular demonstrations in science museums involves the suspension of
ID: 1815345 • Letter: O
Question
One of the popular demonstrations in science museums involves the suspension of a ping-pong ball (m = 2.6 g and d = 3.8 cm) by an upward air jet (see. Figure). Air values: p = 1.184 kg/m3 and eta = 18.5 times 10-6 Pa s Volume of the sphere: V = 4/3 pi r3 Calculate the weight W and the buoyant force F0 of the ball in the air. Draw a free body diagram of the ball and use Newton's second law to derive an equation for the air velocity v as a function of the drag coefficient CD. As can be seen in the Figure above, the drag coefficient cD depends on the Reynolds number. In order to determine a unique value for the air velocity v you need to use an iterative approach. Choose an arbitrary starting value for the air velocity between 1 and 6 m/s. Calculate the Reynolds number. Go the chart above and determine the corresponding Co value. Take your answer from b) and calculate a new velocity value. Then repeat the procedure until v converges. Explain why the ball always coming back to the center when it is pushed by a finger to the side of the jet.Explanation / Answer
Ball data
m=2.6*10^-3 Kg
d=3.8*10^-2m
Air data
= 1.184 kg/m^3
Buoyancy force
Fb =*V
Fb=1.184*9.81*(4/3)(3.8/2*10^-2)3
F3 = 3.337*10^-4 N
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