Einstein's theory of relativity predicts that a body of mass m0 at rest has mass: m = m0/√(1-(v^2/c^2)) , where c is the velocity of light and v is the velocity of the body.
Use a series to obtain the approximation: mc^2 ≈ m0c^2 + 1/2m0v^2
Other Info that may be needed:
1. Mass energy formula: E = mc^2
2. Kinetic energy of a body at rest: v = 1/2m0v^2 (where mass is m0 and velocity is v)
I am so sorry about this. your probably getting frustrated at me. To show work in my problem, I am not sure how to go from the McLaurin series to being able to show that the series is the approximation. How did you arrive at the fact that the McLaurin series is the approximation? Sorry again but I need to show tons of work for these problems.
You see. I dont know physics well to see if their is another way of doing this problem, but if CaptainBlack is right about this then you need to do what I said. The only problem is, if you dont know what a power series(do you?) is then you can hardly put it down as your work. It will be suspicious. The whole premise of the Maclaurin series is that if a function is equal to a polynomial at a point and increases at the same rate as the polynomial then the function is equal to that polynomial. That is the basic premise of Maclaurin series. It is a lot more math than I can show in this thread. It requires a lot of prerequisite math knowledge. What math class are you currently enrolled in?
Im in Calc II. I know about power series but I am just not getting the jist of this problem. I understand about the series that I have to use. I am just confused on what to plug into it. Do I do a ratio or root test to it? I am just confused on how I can use that series to approximate Einstein's theory.
Hey jules027,
Captain has correctly specified what you have to do, and Mathstud28 continued with the definition of McLaurin series to help you.
Clearly f(0) = 1,
Then do a little computation to obtain f''(0) = 1.
Now from Mathstud28's formula
So
Now
But from the previous approximation if we let , we get:
Substituting this in we get,
Done