A dike in Holland springs a leak through a hole of area 0.60cm 2 cm^2 at a depth of 1.4m m below the water surface.
How much force must a boy apply to the hole with his thumb to stop the leak?
Express your answer to two significant figures and include the appropriate units.
To determine the force required to stop the leak, we can use Pascal's principle, which states that the pressure applied to a fluid at rest is transmitted equally in all directions. We can use the formula:
Pressure = Force / Area
First, let's convert the hole's area to square meters (m^2):
Area = 0.60 cm^2 = 0.60 cm^2 * (1 m / 100 cm)^2 = 0.006 m^2
Next, let's calculate the pressure at the depth of the hole. The pressure in a fluid increases with depth due to the weight of the fluid above it. The pressure in liquids can be given by the formula:
Pressure = Density * g * Depth
Where:
- Density is the density of the fluid
- g is the acceleration due to gravity
- Depth is the depth of the hole below the water surface
In this case, we'll assume the fluid is water, so we'll use a density of 1000 kg/m^3 and the acceleration due to gravity is 9.8 m/s^2:
Pressure = 1000 kg/m^3 * 9.8 m/s^2 * 1.4 m = 13,720 Pa
Now, we can use Pascal's principle to find the force required to stop the leak:
Pressure = Force / Area
Rearranging the equation, we have:
Force = Pressure * Area
Substituting the values we calculated:
Force = 13,720 Pa * 0.006 m^2 = 82.32 N
Therefore, the boy must apply a force of 82.32 Newtons to stop the leak.