Velocity of an apple before strikes the surface of a white dwarf.

[ScienceGeek24]

Homework Statement

An apple is dropped from a height of 12.8*10^6 m above the surface of the white dwarf. With what speed does the apple strike the surface of the white dwarf?

M of white dwarf= 1.99*10^30
gravity of white dwarf= 3.29*10^6

Homework Equations

Vf^2=Vi^2+2a(deltaX)

The Attempt at a Solution

I tried doing this v=srqt( 2(3.29*10^6)(12.8*10^6 ) and my result was far of the real answer i got 9.17*10^6 m/s and the answer sheet showed 5.28 *10^6 m/s.

What did I do wrong?

 

[tiny-tim]

Hi ScienceGeek24

(try using the X² button just above the Reply box )

I tried doing this v=srqt( 2(3.29*10^6)(12.8*10^6)

that's only for constant acceleration

a white dwarf is only about the size of the Earth, so 10⁷ m is a long way up

you'll need the radius …

isn't there a relation between the radius and mass of a white dwarf? ​

 

[ScienceGeek24]

<sup>yes a=Gm/r^2 that's how i got the acceleration of the white dwarf

The radius is equal of the Earth's radius which is 6.37*10^2 and the mass was the same the sun which was 1.99*10^30. However, I still don't understand your question.</sup>

 

[tiny-tim]

You'll need to find the gravitational acceleration as a function of distance, and integrate (or use potential energy).

 

[SammyS]

Hi ScienceGeek24

(try using the X² button just above the Reply box )
…

<sup>yes a=Gm/r^2 that's how i got the acceleration of the white dwarf

The radius is equal of the Earth's radius which is 6.37*10^2 and the mass was the same the sun which was 1.99*10^30. However, I still don't understand your question.</sup>

tim's suggestion referred to super-scripts, not the whole post, so your post would look like:

yes a=Gm/r² that's how i got the acceleration of the white dwarf

The radius is equal of the Earth's radius which is 6.37*10² and the mass was the same the sun which was 1.99*10³⁰. However, I still don't understand your question.

BTW: Earth's radius is significantly greater than 6.37*10²m !

 

[ScienceGeek24]

The thing is that i don't think this problem should be base with integrals, it has to be an easier way, sqrt(3.27*10⁶)(12.8*10⁶+6.37*10⁶) and still i don't get the right answer.

I mean there has to be another factor that I am not taking into account. I know this problem does not need integrals.