Fixing an Incorrect Equation Answer

[highschoolphysics]

Homework Statement

How much gravitational potential energy is required to lift a 9270-kg Progress spacecraft to the altitude of the International Space Station, 424 km above the surface of the Earth?

Relevant Equations

gpe=mgh

I tried just using that equation but I apparently didn't get the correct answer.

 

[etotheipi]

The exact expression for GPE, with the zero reference set at infinity, is $U_{GPE} = -\frac{GMm}{r}$. If we are at the surface of the Earth and consider a small change in $r$, then $\delta U = gm \delta r$ is approximately correct and we say $U_{GPE} = mgh$, once we set our zero reference somewhere suitable near the surface of the Earth. This is just an approximation, however.

Since $424 \text{km}$ is quite a long way, you'll need to find $\Delta U_{GPE}$ with the exact expression to get a more reasonable answer!

 

[highschoolphysics]

The exact expression for GPE, with the zero reference set at infinity, is $U_{GPE} = -\frac{GMm}{r}$. If we are at the surface of the Earth and consider a small change in $r$, then $\delta U = gm \delta r$ is approximately correct and we say $U_{GPE} = mgh$, once we set our zero reference somewhere suitable near the surface of the Earth. This is just an approximation, however.

Since $424 \text{km}$ is quite a long way, you'll need to find $\Delta U_{GPE}$ with the exact expression to get a more reasonable answer!

So with that equation I got an answer of -8.71*10^15. Does that sound right to you? I'm supposed to answer with 3 sig figs and units.

 

[etotheipi]

Try and also show your work, otherwise it's not obvious what calculation you've performed

You're after a change in GPE from radius of $R_{E}$ to $R_{E} + 424 \text{km}$. So first of all, this is going to be a positive number.

The expression is $U_{grav} = -\frac{GM_{E}m}{r}$, so you should be able to substitute in the two values of $r$ and subtract to get your change. Or better yet, do it algebraically and substitute in at the end!

 

[Janus]

So with that equation I got an answer of -8.71*10^15. Does that sound right to you? I'm supposed to answer with 3 sig figs and units.

The GPE equation above give the value relative to a point an infinite distance from the source of gravity ( where GPE is considered zero). What you want is the difference in GPE between two points.

 

[hutchphd]

so what are the units??
Also just use mgh first as sanity check...it should be within 7%(424/6000) of exact answer (not quite 3 sig fig!). Then do the exact using 1/r