Integral Areas and Physics Application

In summary, the conversation is about a new member introducing themselves to a forum and asking for help with some math problems related to calculus and physics. The problems involve calculating the force on a dam, determining the size of a motor needed to empty a pool, finding the volume of soot deposited by a garbage incinerator, and calculating the length of a parabolic cable. The other members remind the new member to follow forum rules and post in the appropriate section with their attempts at solving the problems.
  • #1
rhymes116
4
0
Greetings everyone! I am new to this forum. I take a variety of
mathematic courses and needed some help so found this website. Its
great to see a variety of people interested in mathematics!

In my current calculus class, we are learning about Integral areas in
geometric shapes and application in physics. Here are a few problems
practice problems that I had trouble with. If anyone can solve them
(you can put the last definite integral formula to be solved) with an
explanation, I'd appreciate that!

1.) A dam is approximatly shaped like a trapezoid with height 726
feet, width at top of 1244 ft and width at base of 660 ft. Determine
total force on dam if the water is 700ft deep. (Water weighs about
62.4 lb/feet cubed.)



2.) A rectangular pool measures 10 feet deep, 15 feet wide, and 40
feet long. It is filled with pure water to 6 inches below the top. If
a one horsepower motor can perform 550 ft*lbs of work per second, then
what size motor is required to empty the pool in 1 hour? The weight
density of pure water is about 62.4 lbs per cubic feet.

3.) Soot produced by a garbage incinerator spread out in a circular
pattern. The depth, H(r) (in mm) of the soot deposited each month at a
distance r kilometers from the incinerator is gvien by H(r)=
0.23e^-2r. Determine the volume of soot in meters cubed, deposited
within a 5km radius of the incinerator.

4.) Cables connecting the towers of the George Washignton Bridge are
approximated by the parabola: y=0.00013x^2 ft, where x is the
horizontal distance from the vertex of the cable. If the distance
between the two towers is 3500 feet, then determine the exact length
of the cable that spans them. Also give the 4 sign. fig approximation.
 
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  • #2
This should go in homework, dude.
 
  • #3
rhymes116

you will have to be clear and show us what you are having problems in regards to those problems. merely posting them like that, it is not very helpful for anybody.
 
  • #4
Perhaps he purposely posted in this thread knowing that he would also post in the appropriate one in the homework section, just to add to his post count! Who would do such a thing...
 
  • #5
oops, sorry. I am new to this place. I figured it out anyways. Thanks for the heads up.
 
  • #6
You were expected to read the forum rules before you started posting!

Homework problems go in the homework section and you must show what you have already tried on the problem- just posting the problems themselves will get you a lot of "nasty" responses!
 

1. What is the significance of integral areas in physics?

Integral areas are used in physics to represent the total value of a physical quantity over a given interval. They are important because they allow us to calculate the exact amount or value of a quantity, rather than just an estimate.

2. How are integral areas used in physics applications?

Integral areas are used in a wide range of physics applications, such as calculating the work done by a force, finding the center of mass of an object, and determining the total energy of a system. They are also used in many equations and formulas, such as those for calculating momentum and torque.

3. Can you explain the concept of integration in relation to physics?

Integration is the mathematical process of finding the area under a curve. In physics, this is used to find the total value of a physical quantity over a given interval, as well as to solve various equations and problems.

4. How does the use of integral areas differ from other mathematical methods in physics?

The use of integral areas is unique in that it allows for precise calculations of physical quantities over a given interval, rather than just approximations. Other mathematical methods in physics, such as derivatives and differential equations, are often used to describe the behavior of physical systems rather than to calculate exact values.

5. Are there any limitations to using integral areas in physics?

While integral areas are a powerful tool in physics, they do have some limitations. They may not be applicable to all types of physical systems, and in some cases, other mathematical methods may provide more accurate results. Additionally, the process of integration can be complex and time-consuming, making it difficult to use in certain situations.

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