a dike in Holland springs a leak through a hole of area 1cm squared at a depth of 2m below the water surface. How much force must a boy apply to the hole with his thumb to stop the leak? can he do it?
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To determine the force required to stop the leak, we can use Pascal's law, which states that pressure is transmitted equally in all directions in a fluid.
First, let's calculate the pressure at the depth of the leak. The pressure at a given depth in a fluid is given by the formula:
P = ρ * g * h
Where:
P is the pressure,
ρ is the density of the fluid (in this case, water),
g is the acceleration due to gravity, and
h is the depth.
In this case, the depth of the leak is 2 meters. The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s².
So, plugging in the values:
P = 1000 kg/m³ * 9.8 m/s² * 2 m = 19600 Pa
Next, we need to calculate the force required to stop the leak. The force can be calculated using the formula:
F = P * A
Where:
F is the force,
P is the pressure,
A is the area of the hole.
In this case, the area of the hole is 1 cm², which is equivalent to 0.0001 m².
So, plugging in the values:
F = 19600 Pa * 0.0001 m² = 1.96 N
Therefore, the force required to stop the leak is 1.96 Newtons.
Now, can a boy apply this force with his thumb? The average thumb can exert a force of approximately 200 Newtons. Since the required force to stop the leak is only 1.96 Newtons, the boy can easily apply enough force with his thumb to stop the leak.