A submarine is trapped at the bottom of the ocean with its hatch at a depth of 20 m below the surface. The hatch is circular and 0.40 m. Calculate the force that would have to be exerted against it to open it. The air inside the submarine has a pressure of 1 Atm.
-I used P=f/a. Area being Pi*Radius^2. The pressure I converted to 1.013*10^5 N/m^2 and solved for F. However, I am not getting the textbook answer of 2.52*10^4 n/m^2.
20 meters down
pressure = rho g h
= 1000kg/m^3*9.81*20
= 196,200
= 1.96 *10^5 Pascals
I guess the radius is .4 m???
A = pi(.4)^2
F = P*A = 98,621 Newtons
Actually the radius is 0.2m since the diameter is 0.2. Therefore 196200*0,1256=24642N or 2.5*10^4 N
Sorry Diameter is 0.4m*
To calculate the force required to open the hatch of a submarine, you need to consider the pressure difference between the inside and outside of the submarine. Here's how you can approach the problem:
1. Determine the pressure difference: The pressure difference between the inside and outside of the submarine is equal to the difference in pressure at the depth of the hatch.
Since the hatch is 20 m below the surface, we need to consider the pressure due to the water column above it. The pressure of water increases by approximately 1 atmosphere (1 atm) for every 10 meters of depth.
So, at a depth of 20 m, the pressure due to the water column is 2 atmospheres (2 atm).
Therefore, the pressure difference is:
Pressure difference = Pressure inside submarine - Pressure due to water column
= 1 atm - 2 atm
= -1 atm
Note: The negative sign indicates that the pressure outside the submarine is greater than the pressure inside.
2. Calculate the force: Now, you can use the pressure difference and the area of the hatch to calculate the force required to open it.
Given:
Hatch radius (r) = 0.40 m
Pressure difference (ΔP) = -1 atm = -1.013 × 10^5 Newtons per square meter (N/m^2)
The force (F) can be calculated using the formula:
F = ΔP × A
where A is the area of the circular hatch.
Area (A) = π × r^2
= π × (0.40 m)^2
Now, substitute the values into the formula:
F = (-1.013 × 10^5 N/m^2) × (π × (0.40 m)^2)
Solve this equation to get the force required to open the hatch.
Make sure you have used the correct values and units in your calculation. If you still aren't getting the textbook answer, recheck your calculations or consult with your instructor or peers to identify any mistakes.