PROBLEM 2 A cube of mass m is placed in a rotating funnel. (The funnel is rotating around the vertical axis shown in the diagram.) There is no friction between the cube and the funnel but the funnel is rotating at just the right speed needed to keep the cube rotating with the funnel. The cube travels in a circular path of radius r, and the angle between the vertical and the wall of the funnel is 0. Express your answers to parts (b) and (c) in terms of m, r, g, and/or 0. (a) Sketch a free-body diagram for the cube. Show all the forces acting on it, and show the appropriate coordinate system to use for this problem. (b) What is the normal force acting on the cube? FN=mg58 (c) What is the speed v of the cube? (d) If the speed of the cube is different from what you determined in part (c), a force of friction is necessary to keep the cube from slipping in the funnel. If the funnel is rotating slower than it was above, draw a new free-body diagram for the cube to show which way friction…

Circular turns of radius r in a race track are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present.   Write an expression for the tan(θ) of a car going around the banked turn in terms of the car's speed v, the radius of the turn r, and g so that the car will not move up or down the incline of the turn.  tan(θ) =

The character Min Min from Arms was a DLC character added to Super Smash Bros.  Min Min’s arms are large springs, with a spring constant of 8.53 ⋅ 10^3 N/m, which she uses to punch and fling away her opponents.  Min Min pushes her spring arm against Steve, who is not moving, compressing it 1.20 m as shown in figure A.  Steve has a mass of 81.6 kg.  Assuming she uses only the spring to launch Steve, how fast is Steve moving when the spring is no longer compressed? As Steve goes flying away he goes over the edge of the level, as shown in figure C.  What is the magnitude of Steve’s velocity when he is 2.00 m below where he started?