According tot he diagram, frame ##S## is moving to the right at speed ##V##, but according to what you wrote, you have it moving vertically at speed ##u##. You also use ##u## for the speed of one of the particles in the collision.
As you were told above, physics does not answer questions about how something happens.
When considering quantum phenomena, it is best to discard any and all expectations you have based on the macroscopic world you see around you. Trying to find everyday analogies for quantum phenomena will at...
Yes, ##F## is gravity. For ##a##, go back and look at uniform circular motion; there is an equation that relates the angular speed to the radius and mass.
Do what was suggested above: write down ##F = ma## for each star, and compare the equations. You will then see the answer to your question. Be careful with the radii.
I think you're over-thinking this. All they're asking for is the angle of the ramp that will make the car go 6 ft. You don't need to measure friction, forces, and so on, just the angle and the distance the car goes.
Just to be clear, the frictional force is not in the same direction as the net force. One thing you do know is that the tension must be greater in magnitude than the frictional force, or the block would not move. For the block on the table, you know that
F_{net} = T - F_{friction} since the...
What is ##F_r## supposed to be? At one point you set it equal to the frictional force, but you also say it is in the same direction as the net force. It can't be both. Perhaps if you figure that out, all will become clear to you. I presume that the pulley is supposed to be massless and...