A dike in Holland springs a leak through a hole of area 0.60cm2 at a depth of 1.4m 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.
Your teach is too easy.
What is the weight of a column of water of area .6cm^2 1.4 meters high?
Weight= volume*density*g
= .60cm(1m/100cm)^2* 1.4m*1E6kg/m^3*9.8N/kg=
=.6*EE-4*1.4*1EE6*9.8
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To determine the force that the boy must apply to stop the leak, we can use the concept of pressure. The force required can be calculated using the formula:
Force = Pressure × Area
First, let's calculate the pressure exerted by the water. Pressure is defined as force per unit area, and can be calculated using Pascal's law:
Pressure = Density × Gravitational acceleration × Depth
The density of water is approximately 1000 kg/m3, and the gravitational acceleration is 9.8 m/s2. The depth is given as 1.4 m.
Density = 1000 kg/m3
Gravitational acceleration = 9.8 m/s2
Depth = 1.4 m
Now, let's calculate the pressure:
Pressure = 1000 kg/m3 × 9.8 m/s2 × 1.4 m
= 13720 Pa (rounded to the nearest whole number)
Next, we'll convert the hole area from square centimeters to square meters:
Area = 0.60 cm2
= 0.0006 m2
Finally, we can calculate the force required:
Force = Pressure × Area
= 13720 Pa × 0.0006 m2
= 8.2 N
Rounding to two significant figures and including the appropriate unit, the force that the boy must apply to the hole with his thumb to stop the leak is approximately 8.2 newtons (N).