Physics Question with Friction and Newtons' Laws

Question

A child sits on a freshly oiled, straight stair rail that is effectively frictionless and slides down it. She has a mass of 25 kg, and the rail makes an angle of 40° above the ground. If she slides 4.0 m before reaching the bottom, what is her speed there?

Please show me the equations I need to use the answer the question, along with an explanation of how to do it/how it works. I care more for learning how to solve this problem than for the specific answer.

Answer 1

Hello, Paul!

I like that you want to learn rather than have a ready answer. However, I think the issue is not learning to solve this particular problem but learning the general method of Physics problem solving. I could teach you the method if you are interested.

As for this one, you need to think Physics first: the kid slides down the rail pulled by the component of gravity force along the rail (no friction here). This gives you your first equation - Newton's 2nd Law along the rail - as

mg sinα = ma. (1)

If the zero on the rail is where the child starts sliding and the x-axis points down along the rail, then the kid's position at the bottom is described by the position equation:

d = 0 + at²/2 (2).

The velocity at the bottom is then described by the velocity equation:

v_f = 0 + at (3)

Solving these three equations together will take you to the answer. Good luck!