Mechanics, First year university Physics

[Isaac Pepper]

Homework Statement

A space traveller lands on a small planet whose circumference is 12,500 km. He releases a hammer and a table tennis ball simultaneously from rest and from a height of 1.6 m, timing their fall to take 0.66 s. Determine the density of the planet. What can you conclude about its atmosphere?

Homework Equations

$x = \frac{1}{2} \gamma t^2$
$V_sphere =\frac{4}{3} \π r³$
Circumference = $2 \pi r$

The Attempt at a Solution

$r = \frac{12,500}{2 \pi } = 1989 km$
$V_sphere = \frac{4}{3} \pi r³ = 3.30*10¹⁰ km³$
$\gamma = \frac{2x}{t^2} = \frac{3.2}{0.66^2} = 7.35 m.s^-2$

Since the density $ρ=m/V$, is there a way to determine the mass of the planet with the acceleration due to gravity, to then figure out the density with the formula?
Thanks for the help !
Also...a bit of help with LaTeX please !

 

[gneill]

Think about Newton's law of gravitation and how one can determine "g" from it.

For LaTeX, I'd suggest using the more convenient "##" tags to surround the expressions rather than the "itex" ones. And don't embed other bb code tags inside LaTeX expressions (i.e., don't use the x² or x₂ icons to form super- or subscripts. Instead use the LaTeX syntax).

 

[Isaac Pepper]

thanks ! I think I have worked it out.
Will use Newton's law of gravitation to work out M and then work out the density from that.

 

[haruspex]

don't embed other bb code tags inside LaTeX expressions (i.e., don't use the x² or x₂ icons to form super- or subscripts. Instead use the LaTeX syntax).

Also, make sure there are no bold or italics inside. This can be tricky because you don't necessarily see it. What looks like regular text can include (in the html, I guess) start and end controls for italics ("em") with no text between them. If that ends up inside the LaTeX delimiters, the LaTeX processor gives up. This problem arises when text is pasted in from somewhere else.

 

[gneill]

Also, make sure there are no bold or italics inside. This can be tricky because you don't necessarily see it. What looks like regular text can include (in the html, I guess) start and end controls for italics ("em") with no text between them. If that ends up inside the LaTeX delimiters, the LaTeX processor gives up. This problem arises when text is pasted in from somewhere else.

Yes, those are very good hints! Thanks for that, I hadn't considered the surprises hiding in cut&paste objects.

 

[Isaac Pepper]

Thanks guys I'll keep this advice in mind and try to make a more legible post next time because I am aware of how tiresome it is trying to read the equations otherwise!