A dike in Holland springs a leak through a hole of area 0.80 cm2 at a depth of 1.4 m below the water surface.How much force must a boy apply to the hole with his thumb to stop the leak? Could he do it?
To calculate the force required to stop the leak, we can use Pascal's Law, which states that the pressure applied to a fluid in a confined space is transmitted uniformly in all directions.
Here's how you can calculate the force:
1. Determine the pressure at the depth of the hole:
Pressure = Density of fluid × Acceleration due to gravity × Depth
The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².
Pressure = 1000 kg/m³ × 9.8 m/s² × 1.4 m
2. Calculate the force on the hole:
Force = Pressure × Area of the hole
The area should be converted from cm² to m², so divide by 10,000.
Force = (Pressure × 0.80 cm²) ÷ 10,000 m²
By substituting the values into the formula, we can find the force required to stop the leak.
Now let's calculate the force:
Pressure = 1000 kg/m³ × 9.8 m/s² × 1.4 m = 13,720 N/m²
Force = (13,720 N/m² × 0.80 cm²) ÷ 10,000 m² = 109.76 N
Therefore, the force required to stop the leak is approximately 109.76 Newtons.
Whether a boy can apply this amount of force with his thumb depends on his strength. The average adult male can apply around 200-300 Newtons of force with their thumb, so it is possible for an average boy to exert this force and stop the leak. However, it's important to remember that individual strength may vary.