# Hydrostatic Force and Center of a Mass - Calc 2

• Keldroc
In summary, the first problem is asking to find the coordinates of the centroid of the region bounded by the curves y=2x^3, x+y=3, and y=0. The equations used are M=int f(x)-g(x)dx from a to b, x bar= 1/M * int x[f(x)-g(x)]dx from a to b, and y bar= 1/M * int (1/2)[f(x)^2-g(x)^2]dx from a to b. The incorrect answer was found when using y=3-x for f(x) and y=2x^3 for g(x). The correct region has a triangular shape bounded by y=2x^2 and
Keldroc
Hey guys, I have a couple of problems about hydrostatic force and center of a mass that I was hoping someone could help me out with.

Center of mass

## Homework Statement

Sketch the region bounded by the curves y=2x^3, x+y=3 and y=0. Find the coordinates of the centroid.

## Homework Equations

Sorry I don't know how to make equations appear on here so I'll just type them out:
M=int f(x)-g(x)dx from a to b
x bar= 1/M * int x[f(x)-g(x)]dx from a to b
y bar= 1/M * int (1/2)[f(x)^2-g(x)^2]dx from a to b

## The Attempt at a Solution

I used y=3-x for f(x) and y=2x^3 for g(x) and plugged them into the equations, used a=0 and b=3 and I got the wrong answer so I'm not sure what to do now.
Hydrostatic Force

## Homework Statement

Find the following questions at the depth of 25m. The gravitational acceleration is g=9.8m/s^2 and the density of water is =1000kg/m^3:

Find the hydrostatic force on a square steel plate with sides 3m placed vertically.

## Homework Equations

Pressure=$$\rho$$gd
F=Pressure * Area

## The Attempt at a Solution

For pressure I did P=(1000kg/m^3)(9.8m/s^2)(25m)= 245000

Then, did Force=(245000 Pa)(3m * 3m)=2205000 N and it was the wrong answer.

Last edited:
Keldroc said:
Hey guys, I have a couple of problems about hydrostatic force and center of a mass that I was hoping someone could help me out with.

Center of mass

## Homework Statement

Sketch the region bounded by the curves y=2x3 x+y=3 and y=0. Find the coordinates of the centroid.

## Homework Equations

Sorry I don't know how to make equations appear on here so I'll just type them out:
M=int f(x)-g(x)dx from a to b
x bar= 1/M * int x[f(x)-g(x)]dx from a to b
y bar= 1/M * int (1/2)[f(x)^2-g(x)^2]dx from a to b

## The Attempt at a Solution

I used y=3-x for f(x) and y=2x^3 for g(x) and plugged them into the equations, used a=0 and b=3 and I got the wrong answer so I'm not sure what to do now.
I believe you are working with the wrong region. Did you sketch a graph of it? If you use vertical strips to calculate the area/mass, you will need two integrals, because the upper boundary changes at (1, 2). The region you should be working with has a sort of triangular shape (but with one curved side) and is bounded on its left side by y = 2x2 and on its right side by y = -x + 3.
Keldroc said:
Hydrostatic Force

## Homework Statement

Find the following questions at the depth of 25m. The gravitational acceleration is g=9.8m/s^2 and the density of water is =1000kg/m^3:

Find the hydrostatic force on a square steel plate with sides 3m placed vertically.

## Homework Equations

Pressure=$$\rho$$gd
F=Pressure * Area

## The Attempt at a Solution

For pressure I did P=(1000kg/m^3)(9.8m/s^2)(25m)= 245000

Then, did Force=(245000 Pa)(3m * 3m)=2205000 N and it was the wrong answer.

Mark44 said:
I believe you are working with the wrong region. Did you sketch a graph of it? If you use vertical strips to calculate the area/mass, you will need two integrals, because the upper boundary changes at (1, 2). The region you should be working with has a sort of triangular shape (but with one curved side) and is bounded on its left side by y = 2x2 and on its right side by y = -x + 3.

Thanks for the response but I don't quite understand what you mean by setting up two integrals? Could you explain it to me?

Also I could still use help for the second problem. Thanks alot!

## 1. What is hydrostatic force?

Hydrostatic force refers to the force exerted by a fluid at rest on an object immersed in it. This force is caused by the weight of the fluid above the object and is dependent on the density of the fluid, the depth of the object, and the acceleration due to gravity.

## 2. How is hydrostatic force calculated?

Hydrostatic force can be calculated using the formula F = ρghA, where ρ is the density of the fluid, g is the acceleration due to gravity, h is the depth of the object, and A is the area of the object in contact with the fluid. Alternatively, it can also be calculated by integrating the pressure over the surface of the object.

## 3. What is the center of mass?

The center of mass is the point at which the mass of an object is evenly distributed in all directions. It is also known as the center of gravity and is the point where the object is perfectly balanced.

## 4. How is the center of mass calculated?

The center of mass can be calculated by finding the average position of all the particles that make up the object. This can be done by dividing the sum of the mass of each particle multiplied by its position by the total mass of the object.

## 5. Why is it important to calculate the center of mass and hydrostatic force?

Calculating the center of mass and hydrostatic force is important in many fields, such as engineering and physics. It allows us to understand the stability and balance of objects, as well as the forces acting on them. This information is crucial in designing and building structures and predicting their behavior in different environments.

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