There is a legend of a Dutch boy who bravely held back the whole Atlantic Ocean by plugging a hole in a dike with his finger. Is this possible and reasonable? Estimate the force if the hole were about 1.5 square centimeter in area and 1.8 meter below the water level.
Calculate the water pressure at that depth. It is only about 0.2 atmospheres above atmospheric pressure. The force that the finger would have apply is that times the hole area.
2*10^4 N/m^2 * 1.5*10^-4 m^2 = 3 newtons, which is less than one pound of force.
No, the legend of a Dutch boy holding back the whole Atlantic Ocean by plugging a hole in a dike with his finger is not possible or reasonable. This is simply a fictional story and not based on scientific principles. The force exerted by the Atlantic Ocean would be massive and far beyond the capability of any individual to counteract.
To estimate the force exerted by the water, we can use the formula F = P * A, where F is the force, P is the pressure, and A is the area.
First, we need to calculate the pressure exerted by the water at a depth of 1.8 meters. The pressure increases with depth due to the weight of the water above. The formula for pressure due to the weight of a fluid is P = ρ * g * h, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth. The density of water is approximately 1,000 kg/m^3 and the acceleration due to gravity is approximately 9.8 m/s^2.
Using these values, we can calculate the pressure:
P = (1,000 kg/m^3) * (9.8 m/s^2) * (1.8 m) = 17,640 Pa (Pascal)
Now, we can calculate the force exerted by the water on the 1.5 square centimeter hole:
A = (1.5 cm^2) * (1 m^2 / 10,000 cm^2) = 0.00015 m^2
F = (17,640 Pa) * (0.00015 m^2) = 2.646 N (Newton)
So, the estimated force exerted by the water on a 1.5 square centimeter hole at a depth of 1.8 meters is approximately 2.646 Newtons. Again, this is a significant force, and trying to hold it back with just a finger would not be possible.
To determine if it is possible for a Dutch boy to hold back the Atlantic Ocean by plugging a hole in a dike with his finger, we need to consider the forces involved.
First, let's calculate the force exerted by the water on the hole. The force exerted by a fluid (in this case, water) depends on the pressure and the area. The formula to calculate force is:
Force = Pressure x Area
In order to calculate the force, we need to know the pressure of the water at the hole. The pressure of a fluid at a given depth can be calculated using the formula:
Pressure = Density x Gravity x Depth
Where:
- Density is the density of water, which is approximately 1000 kg/m³
- Gravity is the acceleration due to gravity, which is approximately 9.8 m/s²
- Depth is the depth of the hole, given as 1.8 meters in this case
Let's calculate the pressure first:
Pressure = Density x Gravity x Depth
= 1000 kg/m³ x 9.8 m/s² x 1.8 m
= 17,640 Pascal
Now that we have calculated the pressure, we can determine the force exerted by the water on the hole using the given hole area of 1.5 square centimeters. However, we need to convert the area to square meters before calculating the force.
Area = 1.5 cm² = 0.0015 m²
Now let's calculate the force:
Force = Pressure x Area
= 17,640 Pa x 0.0015 m²
= 26.46 Newtons
Therefore, the force exerted by the water on the hole is estimated to be approximately 26.46 Newtons.
Now, let's consider whether it is reasonable for a Dutch boy to hold back the entire Atlantic Ocean with his finger. With a force of 26.46 Newtons, it is highly unlikely that a human finger or hand can withstand this force for an extended period of time.
Additionally, the Atlantic Ocean is an enormous body of water with a surface area of approximately 106,460,000 square kilometers. Even if we assume that the hole being plugged by the Dutch boy's finger is the only opening, the pressure exerted by the entire Atlantic Ocean would be much greater than the 26.46 Newtons initially estimated.
Therefore, while the legend may be a popular story, it is not physically possible or reasonable for a Dutch boy to hold back the entire Atlantic Ocean by plugging a hole with his finger.