Solving a Physics Problem Involving Hyperbolic Sines

In summary, the conversation discusses the difficulty of solving a physics problem involving a hyperbolic sine term and the suggestion of using a math table or computer software to obtain a solution. The likelihood of a human launching from Earth and reaching Jupiter is also mentioned, with the conclusion that the probability is extremely low due to the large energy barrier. The concept of quantum tunneling and the possibility of multiple universes is also brought up.
  • #1
Xkaliber
59
0
Hi everyone,

I was in the middle of solving a physics problem and came across a math term I am having trouble solving. It is the hyperbolic sine term in this equation:

[tex]T=\frac{2.0x10^{-8}}{sinh^{2}[\frac{\sqrt{130(2.6x10^{10}-130)}}{1.05x10^{-34}}6x10^{11}]+2.0x10^{-8}}[/tex]

When plugging the sinh term into the calculator, I receive an error due to the massive size of the solution. Is there an equivalent method of taking a hyperbolic sine that can be done by hand since the calulator cannot handle the large exponent?
 
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  • #2
You have the high road or the low road.

For the low road, get yourself a copy of the CRC Standard Math Tables. It has tables for Hyperbolic Functions.

For the high road there is Mathematica (my favorite) or MatLab.

For myself, even though I have copies of Mathematica and Matlab (both) at my easy disposal, I still like my book of standard math tables at times.
 
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  • #3
Why bother?

HypSine(Humungous) equals 1/2*e^Humungous.

And 1/Superbig is just about zero.
 
  • #4
Thanks for the replies. I suppose I will just use Mathematica this evening to obtain some number besides zero since it's a probability. Basically, it is the likelihood of a human launching from the Earth's surface at 4 m/s and reaching Jupiter.
 
  • #5
Tell use what the odds are. OK?
 
  • #6
Xkaliber said:
Thanks for the replies. I suppose I will just use Mathematica this evening to obtain some number besides zero since it's a probability. Basically, it is the likelihood of a human launching from the Earth's surface at 4 m/s and reaching Jupiter.
Why would you want an answer "besides zero"? Since 4 m/s is well below escape speed from earth, the "probabilty" of reaching Jupiter (or any thing except Earth itself) is zero.
 
  • #7
Well, quantum mechanically the probability is not exacly zero. Through the process known as "tunneling", a particle or object can travel through a potential energy barrier, in this case gravity, with its total energy less than the potential energy. I did actually put zero as my final answer in the end since I included my steps for solving the problem. The final probability ended up being something along the lines of [tex]e^{10^{44}}[/tex]
 
  • #8
I think you forgot a minus sign somewhere in your exponent. :smile:
 
  • #9
Actually, thanks to the many worlds variety of quantum mechanics there are [tex]e^{10^{5000}}[/tex] ways of a person launching from Earth at 4 m/s. So [tex]e^{10^{44}}[/tex] people actually escape Earth for each person that attempts to launch.

*nod*
 
  • #10
Office_Shredder said:
Actually, thanks to the many worlds variety of quantum mechanics there are [tex]e^{10^{5000}}[/tex] ways of a person launching from Earth at 4 m/s. So [tex]e^{10^{44}}[/tex] people actually escape Earth for each person that attempts to launch.

*nod*
Are you sure there shouldn't be a negative sign in the exponent? If not, I jump up and down a few times and Jupiter is overrun with people!
 
  • #11
Jupiters are overrun with people. But imagine how many Jupiters there are at that point
 

1. What is a hyperbolic sine function?

A hyperbolic sine function, also known as sinh(x), is a mathematical function that is used to describe the relationship between the sides of a right triangle in hyperbolic geometry. It is defined as the ratio of the length of the opposite side to the hypotenuse in a right triangle, where the hypotenuse is equal to the radius of the hyperbola.

2. How do I solve a physics problem involving hyperbolic sines?

To solve a physics problem involving hyperbolic sines, you will need to use the appropriate formulas and equations that relate to the specific problem you are trying to solve. This may involve using trigonometric identities, integrating or differentiating functions, and applying other mathematical concepts.

3. What are some real-world applications of hyperbolic sines?

Hyperbolic sines have many practical applications in fields such as physics, engineering, and economics. They are commonly used to model physical systems that exhibit exponential growth or decay, such as radioactive decay, population growth, and electrical circuits. They are also used in signal processing, control systems, and statistical analysis.

4. What are some key properties of hyperbolic sines that I should know?

Some important properties of hyperbolic sines include the fact that they are odd functions, meaning that sinh(-x) = -sinh(x). They also have a range of (-∞, ∞) and are continuous and differentiable for all real numbers. Additionally, they have a variety of trigonometric identities that can be used to simplify expressions.

5. Can I use a calculator to solve problems involving hyperbolic sines?

Yes, most scientific and graphing calculators have built-in functions for hyperbolic sines. However, it is important to understand the concepts behind the calculations in order to use a calculator effectively and verify the results. Additionally, some advanced problems may require using more complex techniques that cannot be solved with a calculator alone.

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