P h3) A disk with radius r and uniformly distributed mass m is pulled to the right with force Fp by a massless cord at a height h above its base. In this problem we will consider what happens as we vary the height h. The disk rolls without slipping. (i) If h = 21" (the rope pulls from the top of the disk), then what is the force of friction (magnitude and direction) from the ground on the base of the disk? (ii) If h = r (the rope pulls from the middle of the disk), then what is the force of friction (magnitude and direction) from the ground on the base of the disk? You should nd that the force of friction from the ground has reversed compared to Part (i)! (iii) Find the height he at which the force of friction (magnitude and direction) from the ground on the wheel is zero. At this height the torque from the string is exactly what is needed to produce an angular acceleration satisfying the rolling condition a = (rem/r. Above or below this point friction does what it needs to do to ensure the total torque satises the rolling condition. (iv) Show that ho (from Part (iii)) for a hoop of mass m is 21': since the hoop has a larger moment of inertia, the force Fp needs to act at a larger radius to produce (1 = acm / R = F / mr