What strategies can be used to solve complex scientific problems?

[mopar969]

I need help starting and solving this problem. See attachment for problem.

 

[ideasrule]

Can you list all relevant equations as well as your attempt at a solution?

 

[ashishsinghal]

you first need to show some genuine attempt yourself so that we can help you!

 

[AlexChandler]

Try to find the equation for the gravitational field at a point within the Earth using gauss' law for gravity which is:

$$\oint_S \vec g \cdot d \vec A = - 4 \pi G \oint_V \rho dV$$

If you haven't see the symbol $$\oint$$ it simply means that the integration is being taken over a closed surface or volume.

 

[ashishsinghal]

Homework Statement

Homework Equations

The Attempt at a Solution

Do not leave all these blank. Do some critical thinking yourself. Thats how PF works.

 

[mopar969]

Here is what I have done:
Mass Earth = volume time (row) which is density
so M = 4/3 pi r^3 times row

so F= -GMm all over R^2 sub Mass Earth for big m (Question why do I sub for big not little m)
and get
f= -(4/3piG(row))mR
this has the form f = -kx so k = 4/3 piG(row) m
and T = 2pi times square root of m over k sub for k and get 2 pi times square root of 3pi all over row times G.

My question is how did my friend get that answer for the period and what do I do next?

 

[mopar969]

Anybody know how this period equation was found?

 

[AlexChandler]

Anybody know how this period equation was found?

Yes for a differential equation of the form

$$\ddot x = - (\omega_0)^2 x$$

where the dots denote time derivatives

the general solution is

$$x = A cos( \omega_0 t - \delta )$$

and from here you can find the period as

$$T = \frac{2 \pi}{\omega_0}$$

If you are wondering how to solve differential equations like this for yourself, the best way is to simply guess. We want a function whose second derivative is equal to a negative multiple of itself. What can you think of? There are only a few things that can satisfy such an equation. Sine and cosine, and exponential functions of imaginary numbers, which actually turn out to be equivalent. For example:

$$cos(x) = \frac{e^{ix} + e^{-ix}}{2}$$

 

[mopar969]

Okay but know what should I do to find the answer to the problem?