How Long Will It Take a Space Tug to Pull an Asteroid?

[Ztalin]

Physics assignment due tomorrow morning... a few questions.

1. At a time when mining asteroids has become feasible, astronauts have connected a line between their 3500kg space tug and a 6200kg asteroid. Using their ship's engine, they pull on the asteroid with a force of 490N. Initially the tug and the asteroid are at rest, 450 m apart. How much time does it take for the ship and the asteroid to meet?

This one I'm just having trouble picturing it. I don't even know what a space tug is. Are the "ship" and "space tug" synonymous? Hmmm...

2. Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.2m. Two of the spheres have a mass of 2.8kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces that the spheres exert on each other, what is the magnitude of the initial acceleration of the third sphere?

For this one... I don't see how you can get the acceleration of the 3rd sphere without its mass.

3. There is a pulley apparatus with a 412 N block on one end, and a 908 N block on one end. It asks for the acceleration and I find it. For part (b), there isn't a 908 N block, but instead, there is a hand pulling with a force of 908 N. It says "Find the acceleration of the remaining block. Explain why the answers in part a and b are different. Don't know why they'd be different if both forces are 908 N...

Any help is greatly appreciated. Thanks in advance.

 

[hotvette]

Re 1, yes, a tug is a ship in this case. It comes from tug boat that pulls other boats on a line. Tug means pull.

 

[Ztalin]

So if it's pulling it, wouldn't it be moving at the same speed as the asteroid? If so, how would the asteroid then ever catch up to it?

I'm assuming that it's pulling it with a string since it said line... but it's probably with some other mechanism. I'm probably making it harder than it is, and the tug probably doesn't move at all.

Still completely stuck with the other 2 though. And thank you.

 

[Ztalin]

Ok you guys:

I think for the tug that it's like a fishing reel. But if that's the case, wouldn't both masses undergo a force of 490 N? Then Newton's 3rd law would come into play, and they would both move at the same time. So I can probably get this one.

I know how to do the second one now... I forgot to split up the force equation so that it's independent of the second mass.

As for the pulley question, I still don't know why they'd be different either.

So is anyone can tell me why it would be different for pulling it with a hand (why is pulling at 908 N different than having a weight of 908 N doing it due to gravity?)