Need help tonight- Integration Buoyancy Problem

In summary, the conversation revolves around calculating the work required to push a 4 cm diameter cylinder 10 cm deeper into water. The attempt at a solution involves using the integral formula and evaluating it to get a value of .0615 J, which is later found to be correct after discovering a typo in the book with the suggested answer.
  • #1
bcjochim07
374
0
1. Homework Statement
A 4 cm diameter cylinder floats in the water. How much work must be done to push the cylinder 10 cm deeper into the water?


2. Homework Equations



3. The Attempt at a Solution

I did the integral from 0 to .1 m of (.02m)^2 * pi * (1000kg/m^3) * (9.80) * x dx

= (12.3 x^2)/2 evaluated from 0 to .1 = .0615 J. However, the back of my book says .615 J. Somehow I ended up a decimal place off. Could someone help me?
 
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  • #2
Ok, so I found out the book had a typo in it, and my answer was correct.
 
  • #3
I'd say that you are right and the book is wrong.

(Oops... too late! You must have posted while I was distracted in mid post.)
 
Last edited:

Related to Need help tonight- Integration Buoyancy Problem

1. What is the problem of "Integration Buoyancy"?

The problem of "Integration Buoyancy" refers to the calculation of the force exerted by a fluid on an object that is fully or partially submerged in the fluid. This force, known as buoyancy, is essential in understanding the behavior of objects in fluids and is used in various engineering and scientific applications.

2. How is buoyancy calculated?

Buoyancy is calculated by multiplying the density of the fluid by the volume of the displaced fluid and the acceleration due to gravity. This can be represented by the equation Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

3. What factors affect buoyancy?

The buoyant force is affected by the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity. Additionally, the shape and size of the object and the depth at which it is submerged also play a role in determining the buoyant force.

4. How does buoyancy affect the behavior of objects in fluids?

Buoyancy affects the behavior of objects in fluids by determining whether they sink or float. If the buoyant force is greater than the object's weight, it will float, and if the weight is greater, the object will sink. This principle is essential in designing boats, ships, and other watercraft, as well as understanding the behavior of objects in ocean and atmospheric conditions.

5. How is buoyancy used in real-world applications?

Buoyancy is used in various real-world applications, including ship design, submarine operation, underwater exploration, and even in the design of hot air balloons and blimps. It is also crucial in understanding the circulation of ocean currents and the behavior of marine life. Additionally, buoyancy is used in the development of various devices, such as life jackets and flotation devices, to keep humans safe in water.

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