A dike in Holland springs a leak through a hole of area 0.80 cm2 at a depth of 1.2 m below the water surface.
How much force must a boy apply to the hole with his thumb to stop the leak?
3 horses
pressure = rho g h
= 1000 kg/m^3 * 9.81 * 1.2
Force = pressure * area
= 1000 * 9.81 cm^2/m^2 *1.2 * .8 /(10,000cm^2/m^2)
A dike in Holland springs a leak through a hole of area 0.80 cm2 at a depth of 1.2 m below the water surface.
How much force must a boy apply to the hole with his thumb to stop the leak?
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To calculate the force required to stop the leak, we need to consider the pressure exerted by the water at that depth.
The pressure at a given depth in a fluid is given by the equation:
P = ρgh
Where:
P represents pressure
ρ represents density of the fluid (in this case, water)
g represents acceleration due to gravity
h represents the depth of the fluid
First, let's convert the area of the hole from cm^2 to m^2. Since 1 m = 100 cm, to convert from cm^2 to m^2, we divide by 10,000:
0.80 cm^2 ÷ 10,000 = 0.000080 m^2
Next, let's calculate the pressure at that depth using the known values:
Density of water (ρ) = 1000 kg/m^3 (approximately)
Acceleration due to gravity (g) = 9.8 m/s^2
Depth (h) = 1.2 m
P = (1000 kg/m^3)(0.000080 m^2)(9.8 m/s^2)(1.2 m)
P = 0.09408 N
Therefore, the pressure exerted by the water at that depth is approximately 0.09408 Newtons.
Now, the force required to stop the leak is equal to the pressure multiplied by the area of the hole:
F = P × A
Where:
F represents force
P represents pressure
A represents the area of the hole
F = 0.09408 N × 0.000080 m^2
F = 0.0000075264 N
Therefore, the force required to stop the leak is approximately 0.0000075264 Newtons.