Now we’re going to roll that wheel down a hill. Suppose it has a mass of 1 kg and a radius 0.5 m, and it rolls without slipping down a ramp of angle θ = 30°. Find the size and direction of the frictional force by the ramp on the wheel. Here’s some help doing that. a) Suppose the wheel starts from rest and rolls a distance l down the ramp. What is the change in its gravitational potential energy? b) Assume all of that energy goes into kinetic energy. Use what you know from the last problem, and find the speed of the wheel as a function of l, the distance it has rolled along the ramp. c) Knowing the speed v of the wheel after it has moved a you can find the linear acceleration of the center of mass. d) Knowing the acceleration, you can now find the size and direction of the friction force by the ramp on the wheel. Does the result make sense?