Gravitation and velocity problem

[canicon25]

Homework Statement

Homework Equations

2ΔEk=-ΔEp

The Attempt at a Solution

-Gm1m2(1/r1-1/r2)-Q=mv²

plug in given values solve for v.

my answer is 5.35x10⁶m/s
given answer is 2100m/s

 

[CompuChip]

Homework Equations

The Attempt at a Solution

Any ideas?

 

[D H]

my answer is 5.35x10⁶m/s
given answer is 2100m/s

Watch your units, be careful to distinguish between altitude and radial distance, and most important of all, show your work. There's no way to tell you where you went wrong if you don't show your work.

BTW, the given answer is correct.

 

[alemsalem]

its 400000m not 400m

 

[canicon25]

1600v²=-G(1600)(5.98E24)/(6.38E6+400000) - (-G)(1600)(5.98E24)/ (6.38E6+100000) - 8.3E8

v=1407 m/s

still not getting the correct solution.

 

[D H]

Showing your work does not mean spewing out an equation without units and without justification. What are the relevant equations?

 

[canicon25]

i am stumped. i tried using

ΔEk+Q=-(0.5)ΔEp

where Ek= 0.5mv²

and Ep= -GMm/r

Q is heat energy. Given in problem.

 

[alemsalem]

why do you have a 0.5 in the energy conservation equation?

 

[canicon25]

upon further reading i found that

ΔEk+Q=-0.5ΔEP for CIRCULAR ORBITS ONLY

am i correct in assuming that

ΔEk+Q=ΔEp would apply for a object falling to Earth

 

[canicon25]

so i tried it and did get correct answer

0.5mv²+Q=-GMm(1/r1-1/r2)

r1=radius Earth + 400000km
r2=radius Earth + 100000km

when i solve for v i get 2133 m/s

 

[cupid.callin]

so i tried it and did get correct answer

0.5mv²+Q=-GMm(1/r1-1/r2)

r1=radius Earth + 400000km
r2=radius Earth + 100000km

when i solve for v i get 2133 m/s

I got 2096 m/s ≈ 2100 m/s

 

[BruceW]

so i tried it and did get correct answer

0.5mv²+Q=-GMm(1/r1-1/r2)

r1=radius Earth + 400000km
r2=radius Earth + 100000km

when i solve for v i get 2133 m/s

I think you've done it right, but there might be some rounding error, which means your answer isn't exactly the same as the given answer. good job!