Theory questions about Newton's Laws and Gravitation

[ohsolost]

I'm trying to figure out these two problems and I'm so lost!

1. Two planets are circling a star. The second planet has an orbit 4 times the size of the first planet. By the time the first planet revolves once, how many times the second one will?

My solution: the formula is T=2PiR/v... so wouldn't the second planet take 4 times as long?

2. Two blocks, which both have the mass of 3kg, are lying on a frictionless surface and are connected by a massless cord. One block is being pulled to the left with a force of 2.5N, and the other block is being pulled to the right with a force of 11.5N. What is the tension of the cord?

My solution: Since there's no friction, don't I just subtract the two forces?

 

[RoyalCat]

What's the relationship between the tangential speed v, and the radius of the circular motion under the influence of the gravitational force? They depend on each-other, the answer to question #1 is not trivial.

 

[LowlyPion]

Welcome to PF.

For 2, you need to determine the acceleration that the system is subjected to. Then you can apply that to the tension between the blocks

 

[ohsolost]

Thanks.Doesn't something weird happen to acceleration when there's no friction?

 

[LowlyPion]

Thanks.Doesn't something weird happen to acceleration when there's no friction?

Weird. Like no resistance to motion weird?

Then yes. Frictionless only seems to happen in physics homework problems.

For 2) you could treat the smaller force as though it were out-sized friction on the second block only.