Gravity and Angular acceleration

[sreya]

Homework Statement

There is strong evidence that Europa, a satellite of Jupiter, has a liquid ocean beneath its icy surface. Many scientists think we should land a vehicle there to search for life. Before launching it, we would want to test such a lander under the gravity conditions at the surface of Europa. One way to do this is to put the lander at the end of a rotating arm in an orbiting Earth satellite.

If the arm is 5.25m long and pivots about one end, at what angular speed (in rpm) should it spin so that the acceleration of the lander is the same as the acceleration due to gravity at the surface of Europa? The mass of Europa is 4.8E22kg and its diameter is 3138 km.

$\omega$ =_____rpm

Homework Equations

$v=\omega r$

$\frac{GMm}{R^2}=a$

$T = \frac{2\pi}{\omega}$

The Attempt at a Solution

$\frac{GMm}{R^2}=a$

$\frac{mv^2}{R}=ma$

$\frac{\omega^2R}{a}$

$\omega=\sqrt{\frac{a}{R}}$

$\omega=\sqrt{\frac{GM}{R_{europa}^2*R_{sat}}}$

$\frac{60\omega}{2\pi}$ = x rpm

Edit: Figured out the problem. The diameter of Europa is given in Km, you have to convert it to meters. Stupid Mastering Physics...

Apparently that's not right though??

 

[Simon Bridge]

$\frac{GMm}{R^2}=a$

... this is not correct: dimensions don't match.

Your reasoning is unclear - you seem to want to put the centripetal acceleration of the station centrifuge equal to the acceleration due to gravity at the surface of Europa.

Try writing centripetal acceleration in terms of angular velocity.

 

[sreya]

Sorry that should be
$\frac{GMm}{R^2}=g_{europa}$

Which "technically" is still acceleration but that wasn't clear

 

[Simon Bridge]

Still not correct.
Dimension still don't match.

Does the acceleration of gravity depend on the mass of the object falling?
Hint: leaning tower of Pisa.

What about writing centripetal acceleration in terms of angular velocity?