A 1600 kg object is initially at rest 400 km above the earth’s surface.

[Scarlett]

Homework Statement

A 1600 kg object is initially at rest 400 km above the earth’s surface. The object falls straight
down and generates 8.3x10^8J of heat energy while descending to an altitude of 100 km.
What is the velocity of the object at this altitude?
(http://i1070.photobucket.com/albums/u488/ScatlettArmadillo/Question20.jpg)

Homework Equations

Ek = (mv^2)/2
Ep = -GMm/r
G=6.67^-11
Mass of Earth = 5.98x10^24 kg
Radius of Earth = 6380000 m
Force of Gravity = GMm/r^2

The Attempt at a Solution

http://i1070.photobucket.com/albums/u488/ScatlettArmadillo/Question20-1.jpg
Once I got to the final step I had to find the root of a negative, which is not possible, so I must have made an error somewhere else, but I can't seem to work out where.

 

[Xisune]

Your solution is correct, but the mistake lies in 1/r2 - 1/r1, this equals 6x10^-9, not 7.37 x 10^-12.

 

[Scarlett]

Your solution is correct, but the mistake lies in 1/r2 - 1/r1, this equals 6x10^-9, not 7.37 x 10^-12.

How?
(1/(6380000+100))-(1/(6380000+400))
=(1/6380100)-(1/6380400)
=1.57x10^-7-1.58x10-7
=7.37x10^-12

 

[Scarlett]

Oh, god, I knew I'd've made a stupid mistake, I forgot to convert km to m. Ugh, stupid, but at least I got it now, thanks for the help :)

 

[Nickie]

I would approach this problem by first checking my calculations and equations to make sure they are correct. It seems that you have made a mistake in your calculation of the force of gravity. The correct equation for force of gravity is F = GMm/r^2. You have used r instead of r^2 in your calculation.

Once you have corrected this mistake and recalculated the force of gravity, you can use the equation F = ma to find the acceleration of the object. From there, you can use the equation v^2 = u^2 + 2as to find the final velocity of the object at an altitude of 100 km. This should give you a positive value for the velocity, as it is impossible to have a negative velocity.

Additionally, as a scientist, I would also consider the assumptions and limitations of this problem. For example, the object is assumed to be falling in a vacuum, neglecting air resistance. This may affect the accuracy of the calculations. I would also consider the potential for energy loss due to other factors, such as friction or heat transfer to the surroundings.