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A horizontal board of negligible thickness and area 2.0 m2 hangs from a spring scale that reads 80 N when a 4.0 m/s wind moves beneath the board. The air above the board is stationary. What does the scale read when the wind stops? The density of air is 1.25 kg/m3 .

User Venatu
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2 Answers

8 votes

Final answer:

When the wind stops, the pressures above and below the board equalize since there is no longer any wind to create a pressure difference. Hence, the reading on the spring scale, which reads 80 N with the wind, would be approximately 0 N when the wind stops, given the board's weight is negligible.

Step-by-step explanation:

The student's question pertains to the application of Bernoulli's principle to a scenario involving air flow, pressure differences, and force exerted on a horizontal board. When the wind moves beneath the board and the air above is stationary, the pressure beneath the board decreases, resulting in a net upward force due to the higher pressure above the board. This is why the spring scale reads 80 N when there is wind. Once the wind stops, the pressures above and below the board equalize, and the board only exerts its weight due to gravity on the spring scale. The scale reads the weight of the board in Newtons, which will be less than 80 N assuming the board has negligible weight.

Since the weight of the board is negligible and the wind is what caused the 80 N reading on the scale, the reading on the scale when the wind stops would be approximately 0 N, as the scale is only measuring the weight of the board, which is negligible.

User Croyd
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3.3k points
9 votes

Answer:

Scale reading for no wind
W'=60N

Step-by-step explanation:

From the question we are told that

Area
A= 2.0 m^2

Weight of board
W=80

Velocity
V=4.0m/s

Density of air
\delta= 1.25 kg/m3 .

Generally the equation for pressure difference by Bernoulli equation is mathematically given by


dP=(1)/(2)pv^2


dP=10Pa

Generally force acting on the board by air is mathematically given by


F=\triangle PA


F=(10)2=>20N

Therefore

Scale reading for no wind W'


W'=W-F\\W'=80-20


W'=60N

Scale reading for no wind W'=60N

User Jeroen Vuurens
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3.5k points