Calculating Work Done by a Steam Engine Using Integral Calculus

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In summary, calculus is an important branch of mathematics that allows us to describe and analyze continuously changing systems, which is crucial in understanding and predicting physical phenomena. To improve understanding of calculus and physics concepts, one can practice solving problems, seek additional resources, and seek help from a tutor or teacher. When solving problems, it is important to carefully read and interpret the problem, set up the correct equations, and double check for accuracy. Calculus can be used to find rates of change and determine areas under curves, which can be applied to optimize systems and make predictions about physical behavior. Real-world applications of calculus and physics include designing structures, predicting motion in space, and analyzing complex systems in various fields.
  • #1
johnnyboy2005
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this is a question about a steam engine with the equation (sorry for lack of proper math language)

PV^1.4 = k (constant)


using the idea of integral from V1 to V2

ie...


the amount of work done is W=(int.V1 to V2) PdV

Where P1=160lbs/in^2
and V1 = 100 in^3...V2=800 in^3

solving for P we can find P=kV^(-1.4)...where k is 100953.1751

now i solved for in the integral

160*(100953.1751) *[ .4 V^.4] from 100 to 800 (for V)

i found W=9.35 * 10^11


Did i do this properly?
thanks for the help.
 
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  • #2
anyone...?
 
  • #3
it's okay...i figured out where i went wrong
 

1. What is calculus and why is it important in physics?

Calculus is a branch of mathematics that deals with rates of change and accumulation. It is important in physics because it allows us to describe and analyze the behavior of continuously changing systems, such as motion and forces. Without calculus, many physical phenomena would be difficult to understand and predict.

2. How can I improve my understanding of calculus and physics concepts?

One way to improve your understanding is to practice solving problems and working through examples. You can also seek out additional resources such as textbooks, online tutorials, and study groups. Additionally, seeking help from a tutor or teacher can be beneficial.

3. What are some common mistakes to avoid in calculus and physics problems?

Some common mistakes include not fully understanding the problem, not setting up the correct equations, and making calculation errors. It is important to carefully read and interpret the problem, draw diagrams if necessary, and double check your work for accuracy.

4. How can I use calculus to solve physics problems?

Calculus can be used to find the rate of change of a physical quantity, such as velocity or acceleration, and to determine the area under a curve, which can represent quantities like displacement or work. It can also be used to optimize systems and make predictions about the behavior of physical systems.

5. What are some real-world applications of calculus and physics?

Calculus and physics have numerous real-world applications, such as designing structures and bridges, predicting the motion of objects in space, and understanding the behavior of fluids in engineering and environmental systems. They are also used in fields like economics, biology, and chemistry to model and analyze complex systems.

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