Application to Physics

In summary, the problem involves a cylindrical barrel filled with muddy water and the task is to calculate the total work required to pump the water to the top of the barrel. The barrel has a diameter of 1 meter and a height of 1.8 meters, with the water level at 1.5 meters. The density of the water at a depth of h meters is given by the function \delta(h)=1+kh kg/m3, where k is a positive constant. Using the formula for the force of gravity on a slice of water, the volume of the slice, and the work done on the slice, the total work can be calculated by integrating from 0 to 1.5 meters. The resulting formula is \
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Homework Statement


A cylindrical barrel, standing upright on its circular end, contains muddy water. The top of barrel, which has diameter 1 meter, is open. Height of barrel is 1.8 meter and it is filled to a depth of 1.5 meter. Density of water at a depth of h meters below surface is given by [tex]\delta[/tex](h)=1+kh kg/m3, where k is a positive constant. Find total work done to pump muddy water to top rim of barrel. Answer is .366(k+1.077)g[tex]\pi[/tex] joules


Homework Equations


force of gravity on slice=density*g*volume


The Attempt at a Solution


volume of slice[tex]\approx[/tex][tex]\pi[/tex](1/2)2[tex]\Delta[/tex]h m3
1+kh(g)([tex]\pi[/tex]/4)[tex]\Delta[/tex]h nt
work done on slice[tex]\approx[/tex]force*distance=1+kh(g)([tex]\pi[/tex]/4)(1.8-h)[tex]\Delta[/tex]h joules
total work=[tex]\int[/tex]01.5[tex]\pi[/tex]/4g(1+kh)(1.8-h)dh joules=[tex]\pi[/tex]/4g(1.8h-h2/2+1.8kh2/2-kh3/3)
 
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Here are some tips on LaTeX.

Use one pair of tags for a whole line, rather than piecemeal.
Inside LaTeX tags, use _n for subscripts and ^n for exponents. If the subscript or exponent is more than a single character, surround them with braces - {}
Integrals look like this (without the leading spaces in the brackets):
[ tex]\int_{a}^{b} f(h) dh [ /tex]
 

1. What is an "application to physics"?

An application to physics refers to the practical use of physics concepts, theories, and principles in various real-world scenarios. It involves using physics to solve problems, design and improve technology, and further our understanding of the natural world.

2. What are some examples of applications to physics?

Examples of applications to physics include the development of new technologies such as computers, medical imaging devices, and renewable energy sources. Other examples include the study of motion and forces in sports, the use of optics in cameras and telescopes, and the application of thermodynamics in refrigeration and air conditioning systems.

3. How does an application to physics benefit society?

Applications to physics have numerous benefits for society. They allow us to develop new technologies that improve our quality of life, such as medical treatments and communication devices. They also help us understand and predict natural phenomena, leading to advancements in fields like weather forecasting and disaster prevention. Additionally, applications to physics contribute to economic growth by creating job opportunities and driving innovation.

4. What skills are needed for an application to physics?

To apply physics principles in real-world situations, one needs a strong foundation in mathematical and analytical skills. Critical thinking, problem-solving, and data analysis skills are also essential. Additionally, knowledge of computer programming and laboratory techniques may be necessary depending on the specific application.

5. How can I get involved in applications to physics?

There are various ways to get involved in applications to physics. One can pursue a degree in physics or a related field and work in research and development in industries such as engineering, healthcare, and technology. Another option is to join a physics-related organization or participate in hands-on projects and experiments. Additionally, staying informed about current advancements and engaging in discussions and collaborations with other scientists can also contribute to the application of physics in the real world.

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