What is the objects velocity when it hits the earth

[martine80]

Hi, I am a student from norway, and I am strugeling with this problem, hope someone can help me og guide me in the direction:

A object is brought out in space in a distance of 3(6,37*10^6) from the senter of the earth. not any velocity when the object is released in space.
1) What is the objects velocity when it hits the Earth ( this I've solved)
2)
i)how long does the object use halfway towards the earth?
ii)how log does it take until the object hits the earth?

HELP PLEASE!

 

[George Jones]

Write down the equation for conservation of energy, with speed written as a derivative.

 

[martine80]

Write down the equation for conservation of energy, with speed written as a derivative.

how do i do that?
so far I've come up with this:

2*R(radius of the earth)=3R-integrate from 0 to t(1/2(integrate from 3R to 2R(-G*M(Earth)/r^2)) *t^2

 

[George Jones]

how do i do that?
so far I've come up with this:

2*R(radius of the earth)=3R-integrate from 0 to t(1/2(integrate from 3R to 2R(-G*M(Earth)/r^2)) *t^2

I'm not sure what you're doing here.

To make sure things are OK, just write down the conservation of energy equation, and leave the integrals until later.

 

[martine80]

I use : 1/2 mv^2
and Gravital Potential energy, and unerversial of gravity = Gm(1)m(2)/r^2

 

[George Jones]

I use : 1/2 mv^2
and Gravital Potential energy, and unerversial of gravity = Gm(1)m(2)/r^2

Let R be the radius of the Earth, and suppose that the object is a distance r from the centre of the Earth. If the object starts at rest from 3R, what is the *equation* for conservation of energy.

 

[martine80]

Let R be the radius of the Earth, and suppose that the object is a distance r from the centre of the Earth. If the object starts at rest from 3R, what is the *equation* for conservation of energy.

I don't know, I've sat down with a teacher and he didnt know eather , just the equation i told you about

 

[George Jones]

I don't know, I've sat down with a teacher and he didnt know eather

?

Let K be kinetic energy and V be gravitational potential energy.

K_initial + V_intitial = K_final + V_final

Can you substitute expressions for each of the terms in this equation?

 

[martine80]

?

Let K be kinetic energy and V be gravitational potential energy.

K_initial + V_intitial = K_final + V_final

Can you substitute expressions for each of the terms in this equation?

I know, but i toght i was suppose to use potentional energi in this ? I am not sure... I am about to give up now. As far as i know I am supose to end up with an integral I have to use Maple to solve ...

 

[George Jones]

I know, but i toght i was suppose to use potentional energi in this ?

Again, I'm confused. My equation involves potential energy.

As far as i know I am supose to end up with an integral I have to use Maple to solve ...

If you'll substitute expressions (that I think you know) into the equation that I wrote previously, I'll help you get the integral, but, since this is homework (and thus should be in the homework section), I'm, at this point, not going to write down the answer.

 

[martine80]

hehe, no its not homework, I don't have to do this ... Its voluntary

I come jp with this :

1/2mv(0)^2+ G M(earth) m(object) (1/r1-1/r2)=1/2mv^2+ G M(earth) m(object) (1/r1-1/r2)
Im sure its wrong :(

 

[George Jones]

hehe, no its not homework, I don't have to do this ... Its voluntary

I come jp with this :

1/2mv(0)^2+ G M(earth) m(object) (1/r1-1/r2)=1/2mv^2+ G M(earth) m(object) (1/r1-1/r2)
Im sure its wrong :(

Almost.

If the object starts from rest, then, initially, v = 0, so K_initial = 0. This gets rid of one of the terms in the equation.

Also, the gravitation potential energy (of the system) when the object is a distance r from Earth's centre is

V = - G M m/r^2.

Use r_initial and r_final to get V_initial and V_final.

Because of work and family commitments, I might not be able to get back to this thread until tomorrow.

 

[martine80]

Almost.

If the object starts from rest, then, initially, v = 0, so K_initial = 0. This gets rid of one of the terms in the equation.

Also, the gravitation potential energy (of the system) when the object is a distance r from Earth's centre is

V = - G M m/r^2.

Use r_initial and r_final to get V_initial and V_final.

Because of work and family commitments, I might not be able to get back to this thread until tomorrow.

V initial = 0 and Vfinal is 2GM(E)/3radius of the Earth ...
Thank u for yore time , Ill let you know by tomorrow if I've solved the problem!