Density of Asteroids, Escape Velcoity and Jumping

[TFM]

[SOLVED] Density of Asteroids, Escape Velcoity and Jumping

Homework Statement

The question wants to know the maximum radius of an asteroid that you can escape from by simply jumpibng off.

The Variables given:
densities = 2500 kg/m cubed
radii = 470km downwards
height of jump = 1m

Homework Equations

v(Escape) = sqrt(GM/r)
m = d/r cubed
V squared = U squared + 2as (for initial jump speed)

The Attempt at a Solution

using a = 9.8 and s = 1, I calculated the initial jump speed is 4.43
rearranging the equation for EScape Velocity:
v(escape) = sqrt[(G(d/r cubed))/r]
v sqyared = (G(d/r cubed))/r
v squared = GD/r squared
r squared = Gd/v sqyared
r = sqrt [GD/v squared]

but this isn't giving me the right answer?

 

[kamerling]

[
m = d/r cubed

This isn't right. mass is density * volume. and the volume of a sphere is?

 

[Shooting Star]

HI TFM,

It's given that you can jump 1 m on earth. Using that, find the speed you can generate at the start of the jump. Then apply that speed for v_escape to find r. All other data are given.

 

[TFM]

The question assumes the asteroids are speherically symmetrical - which is why I should use the volume of a sphere, 4/3 Pi r cubed.

i.e:

(escape) = sqrt[(G(d/(4/3) pi r cubed))/r]

TFM

 

[Shooting Star]

The question assumes the asteroids are speherically symmetrical - which is why I should use the volume of a sphere, 4/3 Pi r cubed.

i.e:

(escape) = sqrt[(G(d/(4/3) pi r cubed))/r]

TFM

Yes, spherically symmetrical and of uniform density. However, the following formula you've written is not correct.

>
2. Homework Equations

v(Escape) = sqrt(GM/r)
>

 

[TFM]

I've just checked -its sqrt[(2GM)/r]

this all gives:

R squared = (3*V escape squared)/(8*G*density*pi)

TFM

 

[TFM]

I have now got the (right) answer of 3.7km (using a 10^-3 conversion factor)

Thanks all,

TFM