1. The problem statement, all variables and given/known data In each of the diagrams (please see attached file (I am sorry for the rotated, the original was in normal form but when uploading it, it was somehow rotated)) and the description of each case below, a particle is moving on a smooth surface, so that the reaction force R acting on the particle from the surface is perpendicular to the surface. In each case give the horizontal (i) and vertical (k) components of the reaction force in terms of its unknown magnitude R (a) Particle on a horizontal table (b) Particle on a slope inclined at an angle theta to the horizontal (c) Particle on a slope inclined at an angle theta to the vertical (d) Particle on the outside of a sphere with latitude described by theta (e) Particle on the inside of a cylinder, with height above the bottom described by $theta$ (f) Particle on the inside of a paraboloid bowl (bowl surface is given by z = x2 +y2), instantaneously at a position where y=0. 2. Relevant equations 3. The attempt at a solution (a) R = Rk (b) R = Rcos(theta)k - Rsin(theta)i (c) R = Rsin(theta)k - Rcos(theta)i (d) Here I am not sure how to express R in terms of components since I am not sure how to find the angle formed by the vertical component and R or the angle formed by the horizontal component and R (e) R = Rcos(theta)k - Rsin(theta)i In this case I feel that I am oversimplifying the situation as the answer looks exactly as in (b) (f) Here I am not given any angles and so I am not sure how to use the given equation of the surface except for the fact that y=0 yields in z=x2. I would appreciate any help! Thank you in advance!