tank of water with L=6m, W=3m, H=4m.
1) Find the force on the bottom of the tank from water. (ignore atmosphere pressure).
2) If the door to the tank is 1.5m by 1.5m and it is 2.25m (center bottom)from the edge of the tank, what is the force on the door and the position of force from bottom of tank.
Please help me solve these questions!
wouldn't the force on the bottom equal the weight of the water?
WEight=volume*density*g
Now figure the pressure at the bottom: Pressure= weight/areabottom
Force on door= pressure*areadoor
I though about the volume, this is what I have: F=72m^3x1000Km^3x9.8= 705600 KN/m^3
or 705.6 N/m^3. Is this right or no need to consider gravity?
weight is volume*density*g
g is 9.8N/kg density is kg/m^3
Sure, I can help you with that!
1) To find the force on the bottom of the tank from the water, you need to calculate the weight of the water. The weight of an object can be calculated using the formula:
Weight = mass × gravity
Where:
Mass = density × volume
Gravity = acceleration due to gravity (9.8 m/s²)
Given the dimensions of the tank (L = 6m, W = 3m, H = 4m), you can calculate the volume of water in the tank by multiplying its dimensions:
Volume = length × width × height
Volume = 6m × 3m × 4m = 72 cubic meters
Since the density of water is 1000 kg/m³, you can now calculate the mass of the water:
Mass = density × volume
Mass = 1000 kg/m³ × 72 m³ = 72000 kg
Now, we can calculate the force on the bottom of the tank:
Force = weight = mass × gravity
Force = 72000 kg × 9.8 m/s² = 705600 N
So, the force on the bottom of the tank from the water is 705600 Newtons.
2) To find the force on the door and the position of the force from the bottom of the tank, you'll need to consider the pressure exerted by the water on the door.
Pressure is defined as force per unit area:
Pressure = Force / Area
The area of the door is given as 1.5 m × 1.5 m = 2.25 square meters.
Using the formula for pressure, you can find the force on the door:
Force on the door = Pressure × Area
Now, to determine the position of the force from the bottom of the tank, you need to know the depth at which the center of the door is located. In this case, it is given as 2.25 meters from the bottom of the tank.
To calculate the position of the force from the bottom of the tank, you can use the concept of the center of pressure. The center of pressure can be calculated as:
Center of Pressure = Depth of center of object + (Area of object / Area of water) × (Height of water)
In this case, the depth of the center of the door is given as 2.25 meters, and the height of the water is 4 meters. You already know the area of the door (2.25 square meters), and since the area of the water is equal to the base area of the tank (6 m × 3 m = 18 square meters), you can use these values to calculate the center of pressure.
I hope this helps you solve the problem! Let me know if you have any further questions.