1. The problem statement, all variables and given/known data We are dealing with a block of 20 kg mass on a ramp that is at an angle of 30 degrees. The spring constant given is 500 N/m. Picture- https://flic.kr/p/A3aCsM The only difference is that that we are supposed to be holding the spring stationary, it isn't attached to a wall. Assume frictionless for a and b.The questions wants to know a) how far the spring will stretch at rest b)You pull so the block is accelerating at 4m/s^2 up the ramp. How far does the spring stretch? c)Now you are to assume you are on a ramp with the following coefficients of friction us=0.3 and uk= 0.2. If you are initially holding the free end of the spring and you pull the spring so that the block is accelerating at 4m/s up the ramp, how far is the spring stretched? 2. Relevant equations Fspring=kx 3. The attempt at a solution a) I used F=mgsinΘ to find that the force is 98 N, then I used F=kx to get x=F/k= 98N/500N/m=0.196m I think this is how to do it, but I was wondering if someone could help me understand where F=mgsinΘ came from? Is the force of the spring equal to the x component of the weight because the block is attached at rest? b) I am at a full loss of how to start the second part. I think the question means that since we are holding the free end of the spring, we just pull it back. But i'm not sure how acceleration plays into any of the equations for the spring unless since.. Fspring=mgsinΘ=kx and ∑Fx=mgsinΘ=ma because we pull on it, we can set ma=kx, and solve for x? That's the only thing I can think to do.