Gravitational Forces on Ship Stranded Near Black Hole

[rpcarroll]

Homework Statement

A ship in the shape of a cylinder has length 100m, and mass 1000kg with occupants. It has strayed too close to a black hole with mass 100 times greater than the sun (100*2.0*10^30). The nose of the ship is pointed towards the black hole and is 10km from the center of the black hole.
(a) What is the total force on the ship?
(b) What is the difference in the gravitational fields acting on the occupants in the front of the ship compared to those in the rear (furthest from the hole)?

Homework Equations

Gravitational Field= (F_g/m)
F_g=G * [(m₁*m₂)/r²]

The Attempt at a Solution

(a) F_g= [1000kg*(100*2.0*10³⁰]/10000²m=1.3*10¹⁷N

Not sure about b, do I need to calculate F_g at the two different distances (front and rear of the ship)?

 

[asleight]

Homework Statement

A ship in the shape of a cylinder has length 100m, and mass 1000kg with occupants. It has strayed too close to a black hole with mass 100 times greater than the sun (100*2.0*10^30). The nose of the ship is pointed towards the black hole and is 10km from the center of the black hole.
(a) What is the total force on the ship?
(b) What is the difference in the gravitational fields acting on the occupants in the front of the ship compared to those in the rear (furthest from the hole)?

Homework Equations

Gravitational Field= (F_g/m)
F_g=G * [(m₁*m₂)/r²]

The Attempt at a Solution

(a) F_g= [1000kg*(100*2.0*10³⁰]/10000²m=1.3*10¹⁷N

Not sure about b, do I need to calculate F_g at the two different distances (front and rear of the ship)?

I'm assuming that's what they want to know. :)

 

[LowlyPion]

Pretty much that's the way to do it looks like to me.

Those in front are at 10 km and those in the back are at 10.1 km.

 

[borgwal]

The idea of question b is for you to figure out how large the "spaghettification" effect is.
You'll know what it is once you've calculated it :-)

 

[rpcarroll]

So when they ask for the 'total force on the ship', is it just measured at 10km and not, say, 10.05 (I think that would be the center of mass of the cylinder shaped ship)?

 

[LowlyPion]

So when they ask for the 'total force on the ship', is it just measured at 10km and not, say, 10.05 (I think that would be the center of mass of the cylinder shaped ship)?

With part a) yes I think you can use the center of mass to calculate the total force. (10.05 km would be good, though at these numbers the precision within 1/2 % is not exactly that important.)

For part b) they are looking for the difference in the gravitational field.

That only involves the mass of the black hole, not the whole ship. That's given more simply by GM/r