An Unfair Race This applet shows the results of releasing a frictionless block and a rolling disk with equal masses from the top of identical inclined planes. Part A Which of the following is the best explanation of the results shown in the applet? Which of the following is the best explanation of the results shown in the applet? The disk loses energy to friction as it rolls, but the box is frictionless and so it speeds up more quickly and gets to the bottom first. The potential energy of the disk is converted into translational and rotational kinetic energy, so the translational speed grows more slowly than that of the box, which has no rotational energy. The net forces on the two objects are equal, but the force on the disk gets partially used up in creating the torque necessary to make it roll. The net forces on the two objects are equal, but the force on the disk is not directed parallel to the ramp, and so does not create as great an acceleration down the ramp.
Part B This applet shows the same situation, but it also shows, through bar graphs that change with time, the way that the energy is transformed as the box and the disk go down the inclined plane. Assume that the box and disk each have mass , the top of the incline is at height , and the angle between the incline and the ground is (i. e., the incline is at an angle above the horizontal). Also, let the radius of the disk be . Part B How much sooner does the box reach the bottom of the incline than the disk? Express your answer in terms of some or all of the variables , , , and , as well as the acceleration due to gravity .